Hidden physics models: Machine learning of nonlinear partial differential equations
While there is currently a lot of enthusiasm about “big data”, useful data is usually “small” and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-e...
Uložené v:
| Vydané v: | Journal of computational physics Ročník 357; s. 125 - 141 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Cambridge
Elsevier Inc
15.03.2018
Elsevier Science Ltd |
| Predmet: | |
| ISSN: | 0021-9991, 1090-2716 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | While there is currently a lot of enthusiasm about “big data”, useful data is usually “small” and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier–Stokes, Schrödinger, Kuramoto–Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data. |
|---|---|
| AbstractList | While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data. |
| Author | Karniadakis, George Em Raissi, Maziar |
| Author_xml | – sequence: 1 givenname: Maziar surname: Raissi fullname: Raissi, Maziar email: maziar_raissi@brown.edu – sequence: 2 givenname: George Em surname: Karniadakis fullname: Karniadakis, George Em email: gk@dam.brown.edu |
| BookMark | eNp9kE1PwzAMhiMEEuPjB3CrxLnFbrakhRNCwJCGOADnKE0dlqqkXdIh7d_TbZw47GTZeh9bfs7Yse88MXaFkCGguGmyxvRZDigzxAx4ecQmCCWkuURxzCYAOaZlWeIpO4uxAYBiNi0m7H3u6pp80i830ZmYfHc1tfE2edVm6TwlLengnf9KOpuMJ9txpkPS6zA43Sa1s5YC-V1Dq7UeXOfjBTuxuo10-VfP2efT48fDPF28Pb883C9Sw0UxpMLAbKoNCqiELWTBK03F1FQ5cg2VLi0Bt7K0wIXNheW8qmdyRpwKLlGKnJ-z6_3ePnSrNcVBNd06-PGkyoFDDhJ5OaZwnzKhizGQVX1w3zpsFILaulONGt2prTuFqGDHyH-MccPuuSFo1x4k7_bkaJF-HAUVjSNvqHaBzKDqzh2gfwFuNotn |
| CitedBy_id | crossref_primary_10_1177_14759217251361808 crossref_primary_10_1109_JOE_2023_3292417 crossref_primary_10_3390_fluids8070212 crossref_primary_10_1109_TAC_2022_3232058 crossref_primary_10_1016_j_enganabound_2023_11_024 crossref_primary_10_1016_j_jcp_2019_109136 crossref_primary_10_1007_s40436_025_00545_0 crossref_primary_10_1007_s11095_022_03330_x crossref_primary_10_1016_j_engappai_2025_111283 crossref_primary_10_1007_s11804_025_00683_8 crossref_primary_10_1016_j_rinam_2025_100539 crossref_primary_10_1016_j_enganabound_2023_03_021 crossref_primary_10_1029_2018SW002061 crossref_primary_10_1007_s00466_023_02365_0 crossref_primary_10_1007_s11071_025_11697_w crossref_primary_10_1017_dce_2022_2 crossref_primary_10_1016_j_jtbi_2022_111342 crossref_primary_10_1098_rsta_2021_0201 crossref_primary_10_1088_1742_6596_3117_1_012002 crossref_primary_10_1017_jfm_2018_872 crossref_primary_10_1177_8755293020919419 crossref_primary_10_2514_1_J058462 crossref_primary_10_1016_j_cma_2021_114083 crossref_primary_10_1016_j_engstruct_2024_118077 crossref_primary_10_1186_s40323_025_00283_9 crossref_primary_10_1016_j_cma_2023_115971 crossref_primary_10_1155_2021_5569645 crossref_primary_10_1016_j_jcp_2019_06_042 crossref_primary_10_1155_2022_5926663 crossref_primary_10_1016_j_petrol_2022_110460 crossref_primary_10_1016_j_wear_2020_203549 crossref_primary_10_1016_j_neunet_2021_08_015 crossref_primary_10_1016_j_compfluid_2020_104759 crossref_primary_10_1016_j_jweia_2023_105534 crossref_primary_10_1002_wics_1534 crossref_primary_10_1080_17455030_2022_2128464 crossref_primary_10_1002_fld_5250 crossref_primary_10_1016_j_enganabound_2025_106178 crossref_primary_10_1016_j_jcp_2019_05_008 crossref_primary_10_1016_j_jocs_2022_101906 crossref_primary_10_1061__ASCE_EM_1943_7889_0002038 crossref_primary_10_1080_00401706_2023_2203175 crossref_primary_10_1137_18M1189828 crossref_primary_10_1016_j_jcp_2022_111010 crossref_primary_10_3390_fractalfract6100606 crossref_primary_10_1007_s11538_020_00794_z crossref_primary_10_1016_j_ces_2022_118195 crossref_primary_10_3390_computation8010015 crossref_primary_10_1016_j_finel_2023_104047 crossref_primary_10_1016_j_physleta_2021_127408 crossref_primary_10_1088_1361_648X_abb996 crossref_primary_10_1038_s41598_025_85605_y crossref_primary_10_3390_e24081134 crossref_primary_10_1126_scirobotics_aay5063 crossref_primary_10_1007_s40304_022_00329_z crossref_primary_10_1016_j_chaos_2024_115215 crossref_primary_10_1016_j_jcp_2019_07_050 crossref_primary_10_1016_j_neucom_2024_129134 crossref_primary_10_3390_jrfm15120616 crossref_primary_10_1016_j_strusafe_2019_101918 crossref_primary_10_1016_j_cam_2024_115989 crossref_primary_10_1007_s43681_021_00132_6 crossref_primary_10_1021_acs_iecr_5c00708 crossref_primary_10_1155_2022_2729408 crossref_primary_10_1186_s40323_025_00304_7 crossref_primary_10_1142_S0218126624502232 crossref_primary_10_1016_j_ocemod_2024_102453 crossref_primary_10_1063_5_0020376 crossref_primary_10_1016_j_cma_2021_114181 crossref_primary_10_1007_s11071_021_06996_x crossref_primary_10_1177_09544062231164575 crossref_primary_10_1016_j_engstruct_2020_111582 crossref_primary_10_1017_jfm_2020_453 crossref_primary_10_1007_s10915_020_01324_8 crossref_primary_10_1016_j_jcp_2023_112624 crossref_primary_10_1155_2022_3684176 crossref_primary_10_1016_j_matcom_2024_10_001 crossref_primary_10_1007_s42979_024_03566_x crossref_primary_10_1007_s10462_024_10784_5 crossref_primary_10_1016_j_cma_2024_117149 crossref_primary_10_1038_s41598_023_36799_6 crossref_primary_10_1016_j_cpc_2025_109582 crossref_primary_10_3390_a15120447 crossref_primary_10_1016_j_epsl_2024_118923 crossref_primary_10_1017_S0962492919000059 crossref_primary_10_1007_s11071_025_11292_z crossref_primary_10_1155_2022_9871800 crossref_primary_10_1016_j_cma_2024_117144 crossref_primary_10_1016_j_cnsns_2022_106664 crossref_primary_10_1007_s10915_020_01282_1 crossref_primary_10_3390_a16060305 crossref_primary_10_1017_eds_2024_19 crossref_primary_10_1016_j_camwa_2023_11_015 crossref_primary_10_3390_en15217864 crossref_primary_10_1017_jfm_2017_637 crossref_primary_10_1103_PhysRevResearch_6_033276 crossref_primary_10_3390_app122110962 crossref_primary_10_1109_ACCESS_2019_2963390 crossref_primary_10_1016_j_cma_2024_117379 crossref_primary_10_1016_j_chaos_2022_112712 crossref_primary_10_1016_j_cma_2025_117798 crossref_primary_10_1038_s41586_023_06393_x crossref_primary_10_1016_j_jappgeo_2024_105479 crossref_primary_10_1073_pnas_2311808121 crossref_primary_10_1007_s10915_022_01899_4 crossref_primary_10_1016_j_pecs_2022_101010 crossref_primary_10_1088_2632_2153_ad513a crossref_primary_10_1016_j_jcp_2019_07_048 crossref_primary_10_1016_j_jcp_2022_111261 crossref_primary_10_1007_s42452_020_2814_0 crossref_primary_10_1016_j_ijmultiphaseflow_2021_103704 crossref_primary_10_1038_s41598_024_51897_9 crossref_primary_10_3390_su13073797 crossref_primary_10_1016_j_jcp_2021_110900 crossref_primary_10_1137_21M1433514 crossref_primary_10_3390_lubricants12110365 crossref_primary_10_1016_j_neunet_2022_09_023 crossref_primary_10_1038_s41598_023_47988_8 crossref_primary_10_1016_j_engappai_2025_112218 crossref_primary_10_1016_j_jcp_2019_07_043 crossref_primary_10_1016_j_cma_2021_114096 crossref_primary_10_3389_frai_2021_780271 crossref_primary_10_1016_j_jcp_2022_111053 crossref_primary_10_32604_cmes_2023_030278 crossref_primary_10_1063_5_0217742 crossref_primary_10_1016_j_petrol_2022_110175 crossref_primary_10_1016_j_jocs_2023_102001 crossref_primary_10_1080_21693277_2024_2305358 crossref_primary_10_1145_3611383 crossref_primary_10_1016_j_ces_2024_120950 crossref_primary_10_1103_PhysRevX_15_011005 crossref_primary_10_3390_math12233873 crossref_primary_10_3390_lubricants11110463 crossref_primary_10_1016_j_compchemeng_2022_108111 crossref_primary_10_1016_j_zemedi_2018_11_002 crossref_primary_10_1016_j_compchemeng_2025_109201 crossref_primary_10_3788_CJL241440 crossref_primary_10_1017_jfm_2018_770 crossref_primary_10_1137_20M134513X crossref_primary_10_1155_2022_8553330 crossref_primary_10_1016_j_mfglet_2022_08_013 crossref_primary_10_1016_j_neunet_2021_08_033 crossref_primary_10_1109_ACCESS_2020_2987324 crossref_primary_10_1016_j_compbiomed_2024_108133 crossref_primary_10_1016_j_jcp_2020_109719 crossref_primary_10_1016_j_brainresbull_2025_111318 crossref_primary_10_1016_j_oceaneng_2022_112360 crossref_primary_10_1016_j_ijmultiphaseflow_2023_104603 crossref_primary_10_1016_j_neucom_2025_129917 crossref_primary_10_1016_j_ymssp_2022_109984 crossref_primary_10_1088_2632_2153_ac567a crossref_primary_10_1016_j_tre_2024_103799 crossref_primary_10_1051_0004_6361_202040152 crossref_primary_10_1140_epjp_s13360_024_05111_4 crossref_primary_10_1007_s10915_021_01532_w crossref_primary_10_1088_1572_9494_ac2055 crossref_primary_10_1109_TNNLS_2022_3157963 crossref_primary_10_1061__ASCE_CP_1943_5487_0000965 crossref_primary_10_1016_j_mattod_2024_09_005 crossref_primary_10_1016_j_procs_2023_10_113 crossref_primary_10_1109_ACCESS_2019_2963375 crossref_primary_10_1103_PhysRevResearch_6_043062 crossref_primary_10_3390_math13111882 crossref_primary_10_1007_s00366_023_01883_y crossref_primary_10_1063_5_0128661 crossref_primary_10_1016_j_eswa_2025_127655 crossref_primary_10_1016_j_chaos_2023_113611 crossref_primary_10_1016_j_ijnonlinmec_2023_104633 crossref_primary_10_1016_j_jmbbm_2025_106961 crossref_primary_10_1016_j_cja_2021_08_009 crossref_primary_10_1016_j_cma_2021_114474 crossref_primary_10_1137_22M1522504 crossref_primary_10_1093_imanum_drab032 crossref_primary_10_1002_prep_202200265 crossref_primary_10_1007_s10444_022_09985_9 crossref_primary_10_32604_cmc_2020_012911 crossref_primary_10_1088_1572_9494_abb7c8 crossref_primary_10_1007_s10694_020_01069_8 crossref_primary_10_1016_j_chaos_2024_115197 crossref_primary_10_1137_18M1203602 crossref_primary_10_1080_10556788_2020_1775828 crossref_primary_10_1016_j_jcp_2019_109099 crossref_primary_10_1016_j_probengmech_2023_103534 crossref_primary_10_1080_00423114_2024_2393340 crossref_primary_10_1002_gamm_201900008 crossref_primary_10_1016_j_compfluid_2020_104474 crossref_primary_10_1016_j_physd_2021_132911 crossref_primary_10_1063_5_0264041 crossref_primary_10_1109_TAI_2025_3544591 crossref_primary_10_1007_s11009_021_09871_9 crossref_primary_10_1016_j_jcp_2021_110152 crossref_primary_10_1016_j_compfluid_2023_106114 crossref_primary_10_1016_j_cma_2025_118045 crossref_primary_10_1109_TAI_2022_3179681 crossref_primary_10_1038_s41467_025_61575_7 crossref_primary_10_1088_2632_2153_ada221 crossref_primary_10_3389_fmars_2024_1309775 crossref_primary_10_1038_s41598_023_28328_2 crossref_primary_10_1061_JENMDT_EMENG_7558 crossref_primary_10_1093_jge_gxad085 crossref_primary_10_1016_j_compchemeng_2023_108320 crossref_primary_10_1016_j_jqsrt_2021_107705 crossref_primary_10_1007_s11440_021_01431_2 crossref_primary_10_1007_s11071_024_09605_9 crossref_primary_10_1007_s13131_024_2329_4 crossref_primary_10_1002_cnm_3471 crossref_primary_10_1016_j_jcp_2019_05_053 crossref_primary_10_1016_j_cma_2021_114117 crossref_primary_10_1007_s40687_021_00265_4 crossref_primary_10_1016_j_jcmds_2021_100008 crossref_primary_10_1016_j_engappai_2023_106867 crossref_primary_10_5781_JWJ_2025_43_4_7 crossref_primary_10_1016_j_eswa_2021_115409 crossref_primary_10_1016_j_resconrec_2024_107796 crossref_primary_10_1016_j_enganabound_2025_106214 crossref_primary_10_1016_j_photonics_2022_101076 crossref_primary_10_2118_218258_PA crossref_primary_10_1007_s00162_019_00512_z crossref_primary_10_1016_j_cnsns_2024_108103 crossref_primary_10_1016_j_advwatres_2024_104870 crossref_primary_10_1145_3485128 crossref_primary_10_1007_s40997_025_00850_w crossref_primary_10_1016_j_tws_2024_111693 crossref_primary_10_1016_j_jcp_2019_04_049 crossref_primary_10_1137_21M140691X crossref_primary_10_1007_s11036_019_01319_2 crossref_primary_10_1016_j_jhydrol_2022_128828 crossref_primary_10_1038_s41566_020_0685_y crossref_primary_10_1002_bit_28851 crossref_primary_10_1016_j_mfglet_2023_08_074 crossref_primary_10_1017_jfm_2023_372 crossref_primary_10_1515_jiip_2022_0005 crossref_primary_10_1016_j_eml_2020_100659 crossref_primary_10_1016_j_enganabound_2025_106448 crossref_primary_10_1016_j_ijnonlinmec_2025_105158 crossref_primary_10_1016_j_knosys_2023_110744 crossref_primary_10_1016_j_actaastro_2020_05_021 crossref_primary_10_1016_j_euromechsol_2025_105798 crossref_primary_10_3390_lubricants12040122 crossref_primary_10_59277_RomRepPhys_2025_77_102 crossref_primary_10_1007_s00466_020_01859_5 crossref_primary_10_1016_j_plrev_2018_06_012 crossref_primary_10_3390_math11132791 crossref_primary_10_1515_jnet_2021_0008 crossref_primary_10_1016_j_advwatres_2023_104564 crossref_primary_10_1016_j_ymssp_2022_109426 crossref_primary_10_1109_LSP_2020_3040941 crossref_primary_10_3390_risks7010016 crossref_primary_10_1007_s44198_024_00240_x crossref_primary_10_1080_00401706_2020_1817790 crossref_primary_10_3390_fluids9070153 crossref_primary_10_1137_19M1305136 crossref_primary_10_1016_j_jcp_2021_110362 crossref_primary_10_1016_j_jcp_2021_110364 crossref_primary_10_1007_s10462_022_10329_8 crossref_primary_10_1016_j_neunet_2024_106369 crossref_primary_10_1038_s43588_025_00804_x crossref_primary_10_1007_s10994_023_06315_y crossref_primary_10_1016_j_jcp_2019_05_027 crossref_primary_10_1121_10_0022460 crossref_primary_10_1007_s13253_022_00514_1 crossref_primary_10_1016_j_cpc_2025_109867 crossref_primary_10_7498_aps_74_20250147 crossref_primary_10_2118_217972_PA crossref_primary_10_1016_j_istruc_2023_105712 crossref_primary_10_1016_j_jcp_2019_108925 crossref_primary_10_1109_TCAD_2022_3166103 crossref_primary_10_1038_s41524_024_01365_9 crossref_primary_10_3390_en15249609 crossref_primary_10_1007_s10915_021_01462_7 crossref_primary_10_1016_j_commatsci_2022_111812 crossref_primary_10_1016_j_compfluid_2019_104258 crossref_primary_10_1109_TIM_2025_3575975 crossref_primary_10_3390_math10050786 crossref_primary_10_1016_j_engappai_2025_111879 crossref_primary_10_1016_j_physleta_2024_130008 crossref_primary_10_1016_j_ymssp_2025_113238 crossref_primary_10_1007_s00285_023_01946_0 crossref_primary_10_1016_j_etran_2025_100420 crossref_primary_10_1016_j_jcp_2022_111541 crossref_primary_10_1007_s12652_019_01185_6 crossref_primary_10_1007_s42985_023_00254_y crossref_primary_10_1016_j_cma_2023_115912 crossref_primary_10_1016_j_amc_2023_128498 crossref_primary_10_1002_mma_10181 crossref_primary_10_1016_j_jcp_2021_110193 crossref_primary_10_1016_j_energy_2025_137215 crossref_primary_10_1016_j_physleta_2021_127456 crossref_primary_10_1007_s44379_024_00009_5 crossref_primary_10_1007_s10489_025_06552_9 crossref_primary_10_1016_j_commatsci_2020_109687 crossref_primary_10_1007_s00466_019_01704_4 crossref_primary_10_1016_j_eswa_2023_122219 crossref_primary_10_1002_aisy_202100067 crossref_primary_10_1007_s11128_023_03871_z crossref_primary_10_1016_j_jcp_2022_111531 crossref_primary_10_1016_j_jcp_2023_111953 crossref_primary_10_1148_ryai_240167 crossref_primary_10_1016_j_energy_2022_125907 crossref_primary_10_1088_2632_2153_ab7d30 crossref_primary_10_1615_InterJFluidMechRes_2025057347 crossref_primary_10_1088_1742_6596_1672_1_012003 crossref_primary_10_1109_JMMCT_2021_3057793 crossref_primary_10_1146_annurev_fluid_010719_060214 crossref_primary_10_1007_s42979_025_03752_5 crossref_primary_10_1061__ASCE_EM_1943_7889_0002121 crossref_primary_10_3390_s21113708 crossref_primary_10_3390_s21051654 crossref_primary_10_3390_app15189895 crossref_primary_10_3390_axioms11060294 crossref_primary_10_1093_imanum_drab093 crossref_primary_10_3390_fluids8070195 crossref_primary_10_1007_s40430_024_04755_8 crossref_primary_10_1016_j_jhydrol_2024_131556 crossref_primary_10_1371_journal_pcbi_1010599 crossref_primary_10_1007_s10958_025_07597_4 crossref_primary_10_1155_2022_5010251 crossref_primary_10_1016_j_nic_2025_05_002 crossref_primary_10_1007_s10208_022_09565_9 crossref_primary_10_1016_j_enganabound_2023_08_025 crossref_primary_10_1016_j_jcp_2022_111202 crossref_primary_10_1146_annurev_physchem_082423_031037 crossref_primary_10_1109_TPS_2023_3268170 crossref_primary_10_1016_j_physd_2022_133489 crossref_primary_10_1016_j_jcp_2021_110279 crossref_primary_10_1016_j_jcp_2021_110295 crossref_primary_10_1155_2021_3200865 crossref_primary_10_1609_aaai_12021 crossref_primary_10_1016_j_ijnonlinmec_2022_104202 crossref_primary_10_1146_annurev_bioeng_092419_061429 crossref_primary_10_1007_s10483_023_2941_6 crossref_primary_10_1016_j_compfluid_2024_106239 crossref_primary_10_1007_s44379_025_00016_0 crossref_primary_10_1016_j_jocs_2025_102575 crossref_primary_10_1139_er_2020_0019 crossref_primary_10_1002_vzj2_20136 crossref_primary_10_1016_j_oceaneng_2025_122652 crossref_primary_10_1016_j_jcp_2025_114002 crossref_primary_10_3233_JCM_237131 crossref_primary_10_1016_j_petrol_2021_109046 crossref_primary_10_1002_nme_7296 crossref_primary_10_1007_s11063_021_10693_6 crossref_primary_10_1016_j_jcp_2025_114127 crossref_primary_10_1007_s44270_024_00005_3 crossref_primary_10_1016_j_neunet_2022_06_019 crossref_primary_10_1016_j_taml_2024_100511 crossref_primary_10_1007_s00466_023_02295_x crossref_primary_10_1137_22M1526708 crossref_primary_10_18466_cbayarfbe_1145651 crossref_primary_10_1063_5_0200684 crossref_primary_10_1016_j_cma_2019_07_007 crossref_primary_10_1093_imanum_drac085 crossref_primary_10_1016_j_optlastec_2023_109590 crossref_primary_10_1016_j_ymssp_2020_107552 crossref_primary_10_1016_j_ces_2025_121624 crossref_primary_10_1016_j_jcp_2021_110657 crossref_primary_10_1002_gamm_202100006 crossref_primary_10_1016_j_cma_2021_114507 crossref_primary_10_1016_j_jcp_2021_110414 crossref_primary_10_1016_j_cma_2021_113777 crossref_primary_10_1007_s10915_022_01980_y crossref_primary_10_1016_j_jcp_2020_109278 crossref_primary_10_1016_j_jcp_2020_109275 crossref_primary_10_1007_s10921_020_00705_1 crossref_primary_10_1007_s11042_020_09142_8 crossref_primary_10_1051_0004_6361_202039956 crossref_primary_10_1002_gamm_202100002 crossref_primary_10_1016_j_actbio_2023_07_040 crossref_primary_10_1016_j_compstruc_2021_106557 crossref_primary_10_1038_s41746_019_0193_y crossref_primary_10_1061_JHEND8_HYENG_13190 crossref_primary_10_1016_j_jcp_2021_110412 crossref_primary_10_1016_j_jcp_2021_110896 crossref_primary_10_1007_s10444_022_09970_2 crossref_primary_10_1007_s10915_022_01939_z crossref_primary_10_1016_j_cma_2019_112603 crossref_primary_10_1007_s11071_023_08712_3 crossref_primary_10_1007_s12043_024_02861_9 crossref_primary_10_1016_j_jcp_2021_110549 crossref_primary_10_1016_j_cja_2021_07_027 crossref_primary_10_1007_s11837_020_04399_8 crossref_primary_10_1016_j_pocean_2023_103050 crossref_primary_10_1016_j_ifacol_2023_10_1214 crossref_primary_10_1007_s12273_025_1304_0 crossref_primary_10_1016_j_enganabound_2024_01_004 crossref_primary_10_1007_s40042_025_01456_w crossref_primary_10_1016_j_jcp_2021_110781 crossref_primary_10_1016_j_cma_2023_116019 crossref_primary_10_1016_j_ijnonlinmec_2024_104988 crossref_primary_10_1016_j_jhydrol_2022_128779 crossref_primary_10_1016_j_cossms_2019_100797 crossref_primary_10_3390_math7080757 crossref_primary_10_1007_s10013_023_00674_8 crossref_primary_10_1007_s10915_022_01883_y crossref_primary_10_3390_fractalfract6080433 crossref_primary_10_1016_j_earscirev_2025_105232 crossref_primary_10_3390_fractalfract8100592 crossref_primary_10_1016_j_jmps_2022_104856 crossref_primary_10_1016_j_engappai_2023_106907 crossref_primary_10_1088_2632_2153_ad0286 crossref_primary_10_1098_rspa_2025_0383 crossref_primary_10_1137_18M1204991 crossref_primary_10_1088_1572_9494_aba243 crossref_primary_10_1016_j_oceaneng_2025_122223 crossref_primary_10_1016_j_neunet_2024_106750 crossref_primary_10_1007_s40820_025_01781_6 crossref_primary_10_1146_annurev_fluid_121021_025220 crossref_primary_10_1016_j_addma_2024_104574 crossref_primary_10_1016_j_physd_2022_133562 crossref_primary_10_1109_ACCESS_2020_2976199 crossref_primary_10_3390_fluids6090332 crossref_primary_10_1088_2632_2153_abb6d3 crossref_primary_10_1080_00268976_2025_2501775 crossref_primary_10_1109_TAP_2022_3186710 crossref_primary_10_1155_2021_2388697 crossref_primary_10_1016_j_jsv_2021_116196 crossref_primary_10_3390_mi12101220 crossref_primary_10_1016_j_chaos_2023_113488 crossref_primary_10_1098_rsos_221475 crossref_primary_10_1063_5_0065874 crossref_primary_10_1007_s00158_022_03369_9 crossref_primary_10_1007_s40819_021_01076_5 crossref_primary_10_1016_j_nucengdes_2019_110197 crossref_primary_10_1016_j_engappai_2025_110772 crossref_primary_10_1016_j_ifacol_2025_07_164 crossref_primary_10_3390_rs17071211 crossref_primary_10_1007_s10208_022_09556_w crossref_primary_10_1016_j_camwa_2025_02_004 crossref_primary_10_1016_j_newton_2025_100138 crossref_primary_10_1016_j_physd_2021_133037 crossref_primary_10_1103_PhysRevFluids_6_050501 crossref_primary_10_1016_j_jcp_2023_112069 crossref_primary_10_1103_PhysRevFluids_6_094401 crossref_primary_10_1177_0954410021999864 crossref_primary_10_1007_s10092_023_00507_7 crossref_primary_10_1016_j_cma_2023_116299 crossref_primary_10_1016_j_jobe_2023_107286 crossref_primary_10_1631_jzus_A2000397 crossref_primary_10_1088_1361_6439_adf5cb crossref_primary_10_1088_1402_4896_accbb6 crossref_primary_10_3390_s22010183 crossref_primary_10_1016_j_jmps_2024_105570 crossref_primary_10_1016_j_compstruc_2023_107163 crossref_primary_10_1007_s40687_019_0183_3 crossref_primary_10_1155_2022_1405139 crossref_primary_10_1140_epjp_s13360_025_06220_4 crossref_primary_10_1007_s10553_024_01782_y crossref_primary_10_1007_s11831_020_09405_5 crossref_primary_10_1016_j_compfluid_2022_105759 crossref_primary_10_3390_bdcc6040140 crossref_primary_10_1016_j_cam_2024_116226 crossref_primary_10_7566_JPSJ_93_064002 crossref_primary_10_1109_ACCESS_2021_3132942 crossref_primary_10_1016_j_jcp_2021_110218 crossref_primary_10_1109_TNNLS_2023_3310585 crossref_primary_10_1007_s00521_020_05340_5 crossref_primary_10_1016_j_jcp_2022_110970 crossref_primary_10_1007_s00158_022_03456_x crossref_primary_10_1007_s12551_020_00776_4 crossref_primary_10_1016_j_cma_2019_112628 crossref_primary_10_1016_j_jcp_2021_110592 crossref_primary_10_1371_journal_pone_0262244 crossref_primary_10_3390_s22062331 crossref_primary_10_1016_j_neucom_2025_131222 crossref_primary_10_1016_j_compgeo_2024_106162 crossref_primary_10_1007_s00466_023_02434_4 crossref_primary_10_1016_j_cej_2021_131220 crossref_primary_10_1038_s43588_022_00217_0 crossref_primary_10_1140_epjp_s13360_022_03078_8 crossref_primary_10_1063_5_0060489 crossref_primary_10_1016_j_camwa_2023_05_014 crossref_primary_10_1007_s00366_021_01586_2 crossref_primary_10_1137_20M1344883 crossref_primary_10_1007_s10483_022_2926_9 crossref_primary_10_1002_ppap_202100155 crossref_primary_10_1016_j_eswa_2025_128279 crossref_primary_10_1016_j_geoen_2023_212474 crossref_primary_10_1016_j_ijmecsci_2022_107236 crossref_primary_10_1137_18M1194730 crossref_primary_10_1016_j_egyai_2025_100554 crossref_primary_10_1073_pnas_1917285117 crossref_primary_10_1016_j_compfluid_2023_105811 crossref_primary_10_1007_s43670_023_00067_5 crossref_primary_10_1016_j_engappai_2020_103996 crossref_primary_10_1137_18M1225409 crossref_primary_10_1007_s11207_019_1412_z crossref_primary_10_1002_cmm4_1164 crossref_primary_10_1007_s11207_019_1434_6 crossref_primary_10_1016_j_camwa_2020_08_012 crossref_primary_10_1007_s11071_023_08396_9 crossref_primary_10_1016_j_jcp_2021_110318 crossref_primary_10_3390_app13126892 crossref_primary_10_3390_math12172784 crossref_primary_10_1007_s10915_023_02260_z crossref_primary_10_1109_MCSE_2024_3352451 crossref_primary_10_1016_j_physd_2021_133003 crossref_primary_10_1016_j_ultras_2023_107041 crossref_primary_10_1016_j_physd_2024_134097 crossref_primary_10_1109_TNNLS_2022_3140726 crossref_primary_10_1016_j_fuel_2022_125908 crossref_primary_10_1016_j_jcp_2019_02_002 crossref_primary_10_4271_2022_01_0948 crossref_primary_10_1016_j_cma_2019_112789 crossref_primary_10_1088_1873_7005_ad917c crossref_primary_10_1007_s42114_021_00229_w crossref_primary_10_1016_j_ymssp_2020_107528 crossref_primary_10_1007_s00466_023_02287_x crossref_primary_10_1007_s11071_021_06550_9 crossref_primary_10_1016_j_mineng_2025_109297 crossref_primary_10_1007_s40314_022_02180_y crossref_primary_10_1016_j_apm_2024_115807 crossref_primary_10_1029_2020WR027642 crossref_primary_10_1007_s13160_023_00577_8 crossref_primary_10_1007_s43670_023_00055_9 crossref_primary_10_1088_1361_6420_ad065f crossref_primary_10_3390_batteries9100511 crossref_primary_10_1016_j_cma_2025_118180 crossref_primary_10_1016_j_petrol_2021_109205 crossref_primary_10_1007_s10915_021_01539_3 crossref_primary_10_1016_j_jmps_2021_104474 crossref_primary_10_1016_j_cma_2020_113028 crossref_primary_10_1016_j_cma_2024_116819 crossref_primary_10_1080_00295450_2022_2102848 crossref_primary_10_1186_s12859_024_05929_w crossref_primary_10_1016_j_mechrescom_2019_103443 crossref_primary_10_1109_ACCESS_2020_2993562 crossref_primary_10_1016_j_jcp_2021_110325 crossref_primary_10_1016_j_compstruc_2025_107899 crossref_primary_10_1016_j_jcp_2022_110983 crossref_primary_10_3390_s23052792 crossref_primary_10_1016_j_cma_2024_117226 crossref_primary_10_1016_j_ultrasmedbio_2024_08_004 crossref_primary_10_1007_s10915_020_01404_9 crossref_primary_10_1016_j_cma_2024_117342 crossref_primary_10_1515_phys_2023_0121 crossref_primary_10_1088_0256_307X_41_3_030201 crossref_primary_10_1016_j_cma_2019_112791 crossref_primary_10_1016_j_physd_2020_132409 crossref_primary_10_1080_10618562_2022_2146677 crossref_primary_10_1016_j_jcp_2020_109307 crossref_primary_10_3390_pr9050737 crossref_primary_10_1016_j_ijforecast_2022_03_007 crossref_primary_10_1002_gamm_202470014 crossref_primary_10_1088_2632_2153_ac5f60 crossref_primary_10_1016_j_apnum_2021_05_011 crossref_primary_10_1002_htj_23268 crossref_primary_10_1016_j_jcp_2020_109672 crossref_primary_10_1145_3514228 crossref_primary_10_1109_TITS_2021_3106259 crossref_primary_10_1098_rsos_211823 crossref_primary_10_1016_j_cma_2021_113814 crossref_primary_10_1016_j_engappai_2023_107183 crossref_primary_10_1007_s00211_022_01294_z crossref_primary_10_1016_j_cma_2024_117458 crossref_primary_10_1007_s10208_023_09620_z crossref_primary_10_1016_j_trc_2021_103008 crossref_primary_10_1080_00036811_2024_2302405 crossref_primary_10_3390_ai5030074 crossref_primary_10_1016_j_aml_2024_109440 crossref_primary_10_1016_j_cma_2022_115399 crossref_primary_10_1137_19M1260141 crossref_primary_10_1002_cnm_3905 crossref_primary_10_1002_elsa_202100185 crossref_primary_10_1063_1_5139992 crossref_primary_10_1016_j_jcp_2019_01_036 crossref_primary_10_1038_s43247_023_01144_2 crossref_primary_10_1080_24725579_2024_2398592 crossref_primary_10_1007_s00466_019_01740_0 crossref_primary_10_1016_j_neunet_2025_107179 crossref_primary_10_1016_j_chphma_2022_03_004 crossref_primary_10_1063_5_0168104 crossref_primary_10_1016_j_trc_2021_103240 crossref_primary_10_1007_s10596_022_10145_7 crossref_primary_10_1016_j_jcp_2023_112100 crossref_primary_10_1073_pnas_1909854116 crossref_primary_10_1007_s10915_023_02352_w crossref_primary_10_1016_j_paerosci_2025_101130 crossref_primary_10_1088_1402_4896_ad55be crossref_primary_10_1016_j_advwatres_2021_103941 crossref_primary_10_1016_j_taml_2022_100334 crossref_primary_10_1088_1361_651X_acfe28 crossref_primary_10_1016_j_physd_2025_134652 crossref_primary_10_1007_s11071_025_11403_w crossref_primary_10_32604_cmes_2023_022699 crossref_primary_10_1007_s40314_021_01531_5 crossref_primary_10_1029_2019WR026731 crossref_primary_10_1016_j_fbp_2023_11_004 crossref_primary_10_2514_1_J059250 crossref_primary_10_1061__ASCE_HY_1943_7900_0002019 crossref_primary_10_3390_app142311140 crossref_primary_10_1016_j_neunet_2023_03_014 crossref_primary_10_1103_PhysRevResearch_3_L042010 crossref_primary_10_1038_s41467_024_52501_4 crossref_primary_10_1007_s12289_018_1448_x crossref_primary_10_2514_1_J060131 crossref_primary_10_1155_2021_1272502 crossref_primary_10_1016_j_petrol_2022_111056 crossref_primary_10_1186_s40323_021_00213_5 crossref_primary_10_1063_1_5138681 crossref_primary_10_1007_s11071_021_07146_z crossref_primary_10_3390_sym16070824 crossref_primary_10_1016_j_jcp_2020_109760 crossref_primary_10_1016_j_tws_2023_111423 crossref_primary_10_1016_j_jhydrol_2023_129707 crossref_primary_10_1016_j_jcp_2023_112102 crossref_primary_10_1063_5_0270295 crossref_primary_10_1016_j_ijheatmasstransfer_2023_124336 crossref_primary_10_1016_j_jhydrol_2022_128321 crossref_primary_10_1016_j_mtcomm_2021_102719 crossref_primary_10_1016_j_engappai_2023_106049 crossref_primary_10_1016_j_eswa_2024_124108 crossref_primary_10_1108_HFF_07_2023_0358 crossref_primary_10_1016_j_neucom_2019_12_099 crossref_primary_10_1007_s11071_022_08182_z crossref_primary_10_1103_PhysRevE_101_010203 crossref_primary_10_1016_j_ress_2023_109849 crossref_primary_10_1088_1402_4896_ac883f crossref_primary_10_1186_s13662_018_1886_2 crossref_primary_10_3390_biomedicines10092157 crossref_primary_10_1109_TIM_2022_3152321 crossref_primary_10_1007_s11071_024_10093_0 crossref_primary_10_3390_jmse12081292 crossref_primary_10_1016_j_cma_2020_113575 crossref_primary_10_1007_s11431_023_2520_6 crossref_primary_10_1017_dce_2024_2 crossref_primary_10_1063_5_0087344 crossref_primary_10_1029_2023JB028037 crossref_primary_10_1016_j_pmatsci_2021_100810 crossref_primary_10_1016_j_strusafe_2025_102604 crossref_primary_10_1016_j_heliyon_2023_e19525 crossref_primary_10_1007_s11071_021_07043_5 crossref_primary_10_3390_fluids8020046 crossref_primary_10_1007_s13160_023_00617_3 crossref_primary_10_1016_j_cma_2022_115078 crossref_primary_10_1016_j_camwa_2024_10_036 crossref_primary_10_1016_j_sysconle_2025_106191 crossref_primary_10_1016_j_ymssp_2022_108833 crossref_primary_10_1016_j_cpc_2022_108538 crossref_primary_10_1109_TCSI_2024_3515146 crossref_primary_10_1016_j_jcp_2020_109339 crossref_primary_10_3390_s23115313 crossref_primary_10_3934_era_2025110 crossref_primary_10_1007_s42967_023_00334_1 crossref_primary_10_1016_j_jcp_2020_109341 crossref_primary_10_1088_1572_9494_ac7202 crossref_primary_10_1109_ACCESS_2023_3265722 crossref_primary_10_1016_j_camwa_2023_03_021 crossref_primary_10_1016_j_physd_2019_132261 crossref_primary_10_1016_j_chaos_2024_115669 crossref_primary_10_1016_j_jcp_2023_112369 crossref_primary_10_1088_1572_9494_ac1cd9 crossref_primary_10_1007_s42967_023_00357_8 crossref_primary_10_1016_j_jcp_2023_112263 crossref_primary_10_1016_j_marstruc_2022_103305 crossref_primary_10_3390_mca28050102 crossref_primary_10_1016_j_jcp_2019_109119 crossref_primary_10_1016_j_cma_2023_116358 crossref_primary_10_1103_PhysRevResearch_3_043101 crossref_primary_10_1007_s10409_021_01119_6 crossref_primary_10_1016_j_cma_2020_113560 crossref_primary_10_1017_S0956792520000224 crossref_primary_10_1007_s00466_021_02069_3 crossref_primary_10_1137_23M1583302 crossref_primary_10_1007_s11071_021_06819_z crossref_primary_10_1016_j_compstruc_2024_107626 crossref_primary_10_1007_s11831_021_09539_0 crossref_primary_10_1016_j_cma_2021_113831 crossref_primary_10_1109_TNNLS_2025_3545967 crossref_primary_10_1016_j_cma_2025_117912 crossref_primary_10_1016_j_physleta_2022_128373 crossref_primary_10_1080_17455030_2023_2192818 crossref_primary_10_1137_22M154209X crossref_primary_10_1007_s00376_023_3119_1 crossref_primary_10_1016_j_actamat_2022_118051 crossref_primary_10_1016_j_ijheatmasstransfer_2023_124788 crossref_primary_10_1016_j_oceaneng_2022_111791 crossref_primary_10_1371_journal_pone_0261571 crossref_primary_10_1007_s40314_024_03067_w crossref_primary_10_1016_j_jcp_2019_109125 crossref_primary_10_1007_s00366_024_01955_7 crossref_primary_10_1016_j_engstruct_2025_121084 crossref_primary_10_1016_j_cnsns_2024_107869 crossref_primary_10_1155_2022_6082280 crossref_primary_10_1016_j_euromechsol_2019_103874 crossref_primary_10_1109_TGRS_2020_2964850 crossref_primary_10_1016_j_actaastro_2023_07_039 crossref_primary_10_1137_18M1229845 crossref_primary_10_1088_1402_4896_ad5053 crossref_primary_10_1088_1402_4896_ad7353 crossref_primary_10_1016_j_cma_2020_113547 crossref_primary_10_1016_j_cma_2021_113722 crossref_primary_10_1088_1361_6420_ac5ac7 crossref_primary_10_1063_5_0251475 crossref_primary_10_1093_imatrm_tnac001 crossref_primary_10_3390_buildings14113515 crossref_primary_10_1016_j_jat_2020_105472 crossref_primary_10_1103_PhysRevResearch_7_013332 crossref_primary_10_1038_s41598_021_99609_x |
| Cites_doi | 10.1080/01621459.1976.10480344 10.1016/0167-2789(85)90056-9 10.1073/pnas.0609476104 10.1103/PhysRevLett.83.3422 10.1111/j.2517-6161.1996.tb02080.x 10.1103/PhysRevLett.57.325 10.1140/epjst/e2014-02285-8 10.1073/pnas.1118984109 10.1137/140965909 10.1016/S0098-1354(98)00191-4 10.1016/j.jcp.2017.07.050 10.1126/science.1165893 10.1063/1.4772195 10.1088/1478-3975/8/5/055011 10.1126/science.1227079 10.1090/S0002-9947-1950-0051437-7 10.1007/BF01589116 10.1109/MLSP.2010.5589113 10.1109/TMBMC.2016.2633265 10.1016/0167-2789(86)90166-1 10.1073/pnas.0900173106 10.1007/s11071-005-2824-x 10.1038/ncomms9133 10.1137/130949282 10.1038/s41467-017-00030-8 10.1016/j.jcp.2007.03.005 10.1109/IJCNN.2016.7727626 10.1017/S0962492910000061 10.1126/sciadv.1602614 10.1103/PhysRevLett.106.154101 10.1073/pnas.1517384113 10.2514/1.J053287 10.1371/journal.pone.0119821 10.4310/CMS.2003.v1.n4.a5 10.1073/pnas.1302752110 10.1073/pnas.1318679110 10.1016/j.cma.2007.08.014 10.1109/5.58326 10.1146/annurev-fluid-011212-140652 10.1016/j.jcp.2017.01.060 10.1016/0045-7930(86)90036-8 10.1073/pnas.1417063112 |
| ContentType | Journal Article |
| Copyright | 2017 Elsevier Inc. Copyright Elsevier Science Ltd. Mar 15, 2018 |
| Copyright_xml | – notice: 2017 Elsevier Inc. – notice: Copyright Elsevier Science Ltd. Mar 15, 2018 |
| DBID | AAYXX CITATION 7SC 7SP 7U5 8FD JQ2 L7M L~C L~D |
| DOI | 10.1016/j.jcp.2017.11.039 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Solid State and Superconductivity Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Solid State and Superconductivity Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Physics |
| EISSN | 1090-2716 |
| EndPage | 141 |
| ExternalDocumentID | 10_1016_j_jcp_2017_11_039 S0021999117309014 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 5VS 6OB 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAXUO AAYFN ABBOA ABFRF ABJNI ABMAC ABNEU ABYKQ ACBEA ACDAQ ACFVG ACGFO ACGFS ACNCT ACRLP ACZNC ADBBV ADEZE AEBSH AEFWE AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AIVDX AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD AXJTR BKOJK BLXMC CS3 DM4 DU5 EBS EFBJH EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HLZ HVGLF IHE J1W K-O KOM LG5 LX9 LZ4 M37 M41 MO0 N9A O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q38 RIG RNS ROL RPZ SDF SDG SDP SES SPC SPCBC SPD SSQ SSV SSZ T5K TN5 UPT YQT ZMT ZU3 ~02 ~G- 29K 6TJ 8WZ 9DU A6W AAQXK AATTM AAXKI AAYWO AAYXX ABFNM ABWVN ABXDB ACLOT ACNNM ACRPL ACVFH ADCNI ADFGL ADIYS ADJOM ADMUD ADNMO AEIPS AEUPX AFFNX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN BBWZM CAG CITATION COF D-I EFKBS FGOYB G-2 HME HMV HZ~ NDZJH R2- SBC SEW SHN SPG T9H UQL WUQ ZY4 ~HD 7SC 7SP 7U5 8FD AFXIZ AGCQF AGRNS JQ2 L7M L~C L~D SSH |
| ID | FETCH-LOGICAL-c368t-6c054ac160b6f8783bae84cb213a0ba9fe03f79f036f26f33bd575e3e83717623 |
| ISICitedReferencesCount | 1119 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000427393800006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0021-9991 |
| IngestDate | Sun Jul 13 05:14:45 EDT 2025 Sat Nov 29 03:10:19 EST 2025 Tue Nov 18 22:41:04 EST 2025 Fri Feb 23 02:17:18 EST 2024 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Small data Uncertainty quantification Fractional equations System identification Bayesian modeling Probabilistic machine learning |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c368t-6c054ac160b6f8783bae84cb213a0ba9fe03f79f036f26f33bd575e3e83717623 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://doi.org/10.1016/j.jcp.2017.11.039 |
| PQID | 2030207139 |
| PQPubID | 2047462 |
| PageCount | 17 |
| ParticipantIDs | proquest_journals_2030207139 crossref_primary_10_1016_j_jcp_2017_11_039 crossref_citationtrail_10_1016_j_jcp_2017_11_039 elsevier_sciencedirect_doi_10_1016_j_jcp_2017_11_039 |
| PublicationCentury | 2000 |
| PublicationDate | 2018-03-15 |
| PublicationDateYYYYMMDD | 2018-03-15 |
| PublicationDate_xml | – month: 03 year: 2018 text: 2018-03-15 day: 15 |
| PublicationDecade | 2010 |
| PublicationPlace | Cambridge |
| PublicationPlace_xml | – name: Cambridge |
| PublicationTitle | Journal of computational physics |
| PublicationYear | 2018 |
| Publisher | Elsevier Inc Elsevier Science Ltd |
| Publisher_xml | – name: Elsevier Inc – name: Elsevier Science Ltd |
| References | Tibshirani (br0210) 1996 Vapnik (br0370) 2013 Tipping (br0390) 2001; 1 Schölkopf, Smola (br0380) 2002 Colonius, Taira (br0640) 2008; 197 E. Snelson, Z. Ghahramani, Sparse Gaussian processes using pseudo-inputs, in: Advances in Neural Information Processing Systems, pp. 1257–1264. Mangan, Brunton, Proctor, Kutz (br0230) 2016; 2 Raissi, Karniadakis (br0500) 2016 Chambers, Mallows, Stuck (br0670) 1976; 71 Grosse, Salakhutdinov, Freeman, Tenenbaum (br0470) 2012 Raissi, Perdikaris, Karniadakis (br0320) 2017; 335 Mackey, Schaeffer, Osher (br0270) 2014; 12 Schmidt, Lipson (br0200) 2009; 324 Nolan (br0660) 2003 Shraiman (br0600) 1986; 57 Hensman, Fusi, Lawrence (br0550) 2013 Mezić (br0150) 2005; 41 Aronszajn (br0430) 1950; 68 Liu, Nocedal (br0510) 1989; 45 Crutchfield, McNamara (br0030) 1987; 1 Gonzalez-Garcia, Rico-Martinez, Kevrekidis (br0050) 1998; 22 Budišić, Mohr, Mezić (br0160) 2012; 22 Raissi (br0560) 2017 Tikhonov, Arsenin (br0410) 1977 Poggio, Girosi (br0420) 1990; 78 Rasmussen, Williams (br0340) 2006 Brunton, Brunton, Proctor, Kaiser, Kutz (br0180) 2017; 8 Tran, Ward (br0310) 2016 Dauxois (br0580) 2008 Nicolaenko, Scheurer, Temam (br0610) 1985; 16 Proctor, Brunton, Brunton, Kutz (br0290) 2014; 223 Berlinet, Thomas-Agnan (br0450) 2011 Ye, Beamish, Glaser, Grant, Hsieh, Richards, Schnute, Sugihara (br0080) 2015; 112 G. Malkomes, C. Schaff, R. Garnett, Bayesian optimization for automated model selection, in: Advances in Neural Information Processing Systems, pp. 2900–2908. Sugihara, May, Ye, Hsieh, Deyle, Fogarty, Munch (br0070) 2012; 338 Daniels, Nemenman (br0110) 2015; 6 Voss, Kolodner, Abel, Kurths (br0060) 1999; 83 Daniels, Nemenman (br0120) 2015; 10 Kevrekidis, Gear, Hyman, Kevrekidid, Runborg, Theodoropoulos (br0040) 2003; 1 Rasmussen, Ghahramani (br0520) 2001 Wang, Yang, Lai, Kovanis, Grebogi (br0240) 2011; 106 Schmidt, Vallabhajosyula, Jenkins, Hood, Soni, Wikswo, Lipson (br0100) 2011; 8 Duvenaud, Lloyd, Grosse, Tenenbaum, Ghahramani (br0460) 2013 Majda, Franzke, Crommelin (br0130) 2009; 106 Murphy (br0350) 2012 Hyman, Nicolaenko (br0590) 1986; 18 Brunton, Proctor, Kutz (br0220) 2016; 113 Stuart (br0530) 2010; 19 Giannakis, Majda (br0140) 2012; 109 R. Calandra, J. Peters, C.E. Rasmussen, M.P. Deisenroth, Manifold Gaussian processes for regression, in: 2016 International Joint Conference on Neural Networks (IJCNN), IEEE, pp. 3338–3345. Tikhonov (br0400) 1963; 4 Saitoh (br0440) 1988 Ozoliņš, Lai, Caflisch, Osher (br0260) 2013; 110 Raissi, Perdikaris, Karniadakis (br0330) 2017; 348 Schaeffer, Caflisch, Hauck, Osher (br0250) 2013; 110 Mezić (br0170) 2013; 45 Weron, Weron (br0680) 1995 Kutz, Brunton, Brunton, Proctor (br0620) 2016 J. Hartikainen, S. Särkkä, Kalman filtering and smoothing solutions to temporal Gaussian process regression models, in: 2010 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), IEEE, pp. 379–384. Podlubny (br0650) 1998 Bai, Wimalajeewa, Berger, Wang, Glauser, Varshney (br0300) 2015; 53 Neal (br0360) 2012 Basdevant, Deville, Haldenwang, Lacroix, Ouazzani, Peyret, Orlandi, Patera (br0570) 1986; 14 Bongard, Lipson (br0190) 2007; 104 Rudy, Brunton, Proctor, Kutz (br0020) 2017; 3 Roberts (br0090) 2014 Taira, Colonius (br0630) 2007; 225 Raissi, Perdikaris, Karniadakis (br0010) 2017 Brunton, Tu, Bright, Kutz (br0280) 2014; 13 Liu (10.1016/j.jcp.2017.11.039_br0510) 1989; 45 Mezić (10.1016/j.jcp.2017.11.039_br0150) 2005; 41 Budišić (10.1016/j.jcp.2017.11.039_br0160) 2012; 22 Crutchfield (10.1016/j.jcp.2017.11.039_br0030) 1987; 1 Tipping (10.1016/j.jcp.2017.11.039_br0390) 2001; 1 Aronszajn (10.1016/j.jcp.2017.11.039_br0430) 1950; 68 Daniels (10.1016/j.jcp.2017.11.039_br0120) 2015; 10 Majda (10.1016/j.jcp.2017.11.039_br0130) 2009; 106 Ozoliņš (10.1016/j.jcp.2017.11.039_br0260) 2013; 110 Mangan (10.1016/j.jcp.2017.11.039_br0230) 2016; 2 Ye (10.1016/j.jcp.2017.11.039_br0080) 2015; 112 Proctor (10.1016/j.jcp.2017.11.039_br0290) 2014; 223 Gonzalez-Garcia (10.1016/j.jcp.2017.11.039_br0050) 1998; 22 Tran (10.1016/j.jcp.2017.11.039_br0310) Vapnik (10.1016/j.jcp.2017.11.039_br0370) 2013 Tibshirani (10.1016/j.jcp.2017.11.039_br0210) 1996 Schölkopf (10.1016/j.jcp.2017.11.039_br0380) 2002 Mezić (10.1016/j.jcp.2017.11.039_br0170) 2013; 45 Kevrekidis (10.1016/j.jcp.2017.11.039_br0040) 2003; 1 Chambers (10.1016/j.jcp.2017.11.039_br0670) 1976; 71 Rasmussen (10.1016/j.jcp.2017.11.039_br0520) 2001 Hensman (10.1016/j.jcp.2017.11.039_br0550) 2013 Raissi (10.1016/j.jcp.2017.11.039_br0010) Berlinet (10.1016/j.jcp.2017.11.039_br0450) 2011 Rasmussen (10.1016/j.jcp.2017.11.039_br0340) 2006 Nicolaenko (10.1016/j.jcp.2017.11.039_br0610) 1985; 16 Sugihara (10.1016/j.jcp.2017.11.039_br0070) 2012; 338 Colonius (10.1016/j.jcp.2017.11.039_br0640) 2008; 197 10.1016/j.jcp.2017.11.039_br0480 Nolan (10.1016/j.jcp.2017.11.039_br0660) 2003 Grosse (10.1016/j.jcp.2017.11.039_br0470) Schmidt (10.1016/j.jcp.2017.11.039_br0100) 2011; 8 Giannakis (10.1016/j.jcp.2017.11.039_br0140) 2012; 109 Tikhonov (10.1016/j.jcp.2017.11.039_br0410) 1977 Brunton (10.1016/j.jcp.2017.11.039_br0220) 2016; 113 Tikhonov (10.1016/j.jcp.2017.11.039_br0400) 1963; 4 Weron (10.1016/j.jcp.2017.11.039_br0680) 1995 Wang (10.1016/j.jcp.2017.11.039_br0240) 2011; 106 Raissi (10.1016/j.jcp.2017.11.039_br0500) Mackey (10.1016/j.jcp.2017.11.039_br0270) 2014; 12 Raissi (10.1016/j.jcp.2017.11.039_br0330) 2017; 348 Raissi (10.1016/j.jcp.2017.11.039_br0560) Schmidt (10.1016/j.jcp.2017.11.039_br0200) 2009; 324 Neal (10.1016/j.jcp.2017.11.039_br0360) 2012 Poggio (10.1016/j.jcp.2017.11.039_br0420) 1990; 78 Podlubny (10.1016/j.jcp.2017.11.039_br0650) 1998 Duvenaud (10.1016/j.jcp.2017.11.039_br0460) 10.1016/j.jcp.2017.11.039_br0690 10.1016/j.jcp.2017.11.039_br0490 Basdevant (10.1016/j.jcp.2017.11.039_br0570) 1986; 14 Saitoh (10.1016/j.jcp.2017.11.039_br0440) 1988 Hyman (10.1016/j.jcp.2017.11.039_br0590) 1986; 18 Kutz (10.1016/j.jcp.2017.11.039_br0620) 2016 Roberts (10.1016/j.jcp.2017.11.039_br0090) 2014 Murphy (10.1016/j.jcp.2017.11.039_br0350) 2012 Brunton (10.1016/j.jcp.2017.11.039_br0280) 2014; 13 Voss (10.1016/j.jcp.2017.11.039_br0060) 1999; 83 Stuart (10.1016/j.jcp.2017.11.039_br0530) 2010; 19 10.1016/j.jcp.2017.11.039_br0540 Taira (10.1016/j.jcp.2017.11.039_br0630) 2007; 225 Raissi (10.1016/j.jcp.2017.11.039_br0320) 2017; 335 Rudy (10.1016/j.jcp.2017.11.039_br0020) 2017; 3 Shraiman (10.1016/j.jcp.2017.11.039_br0600) 1986; 57 Dauxois (10.1016/j.jcp.2017.11.039_br0580) Daniels (10.1016/j.jcp.2017.11.039_br0110) 2015; 6 Schaeffer (10.1016/j.jcp.2017.11.039_br0250) 2013; 110 Brunton (10.1016/j.jcp.2017.11.039_br0180) 2017; 8 Bongard (10.1016/j.jcp.2017.11.039_br0190) 2007; 104 Bai (10.1016/j.jcp.2017.11.039_br0300) 2015; 53 |
| References_xml | – volume: 57 start-page: 325 year: 1986 ident: br0600 article-title: Order, disorder, and phase turbulence publication-title: Phys. Rev. Lett. – volume: 22 start-page: S965 year: 1998 end-page: S968 ident: br0050 article-title: Identification of distributed parameter systems: a neural net based approach publication-title: Comput. Chem. Eng. – volume: 113 start-page: 3932 year: 2016 end-page: 3937 ident: br0220 article-title: Discovering governing equations from data by sparse identification of nonlinear dynamical systems publication-title: Proc. Natl. Acad. Sci. – volume: 197 start-page: 2131 year: 2008 end-page: 2146 ident: br0640 article-title: A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions publication-title: Comput. Methods Appl. Mech. Eng. – volume: 110 start-page: 6634 year: 2013 end-page: 6639 ident: br0250 article-title: Sparse dynamics for partial differential equations publication-title: Proc. Natl. Acad. Sci. – volume: 45 start-page: 357 year: 2013 end-page: 378 ident: br0170 article-title: Analysis of fluid flows via spectral properties of the Koopman operator publication-title: Annu. Rev. Fluid Mech. – year: 2013 ident: br0460 article-title: Structure discovery in nonparametric regression through compositional kernel search – volume: 22 year: 2012 ident: br0160 article-title: Applied koopmanism a publication-title: Chaos – year: 2016 ident: br0500 article-title: Deep multi-fidelity Gaussian processes – volume: 1 start-page: 715 year: 2003 end-page: 762 ident: br0040 article-title: Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis publication-title: Commun. Math. Sci. – year: 2012 ident: br0350 article-title: Machine Learning: A Probabilistic Perspective – volume: 106 year: 2011 ident: br0240 article-title: Predicting catastrophes in nonlinear dynamical systems by compressive sensing publication-title: Phys. Rev. Lett. – volume: 13 start-page: 1716 year: 2014 end-page: 1732 ident: br0280 article-title: Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems publication-title: SIAM J. Appl. Dyn. Syst. – volume: 18 start-page: 113 year: 1986 end-page: 126 ident: br0590 article-title: The Kuramoto–Sivashinsky equation: a bridge between pde's and dynamical systems publication-title: Physica D – volume: 104 start-page: 9943 year: 2007 end-page: 9948 ident: br0190 article-title: Automated reverse engineering of nonlinear dynamical systems publication-title: Proc. Natl. Acad. Sci. – volume: 14 start-page: 23 year: 1986 end-page: 41 ident: br0570 article-title: Spectral and finite difference solutions of the Burgers equation publication-title: Comput. Fluids – year: 2006 ident: br0340 article-title: Gaussian Processes for Machine Learning, vol. 1 – year: 2002 ident: br0380 article-title: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond – year: 1977 ident: br0410 article-title: Solutions of Ill-Posed Problems – start-page: 379 year: 1995 end-page: 392 ident: br0680 article-title: Computer simulation of Lévy publication-title: Chaos—The Interplay Between Stochastic and Deterministic Behaviour – volume: 8 year: 2011 ident: br0100 article-title: Automated refinement and inference of analytical models for metabolic networks publication-title: Phys. Biol. – volume: 223 start-page: 2665 year: 2014 end-page: 2684 ident: br0290 article-title: Exploiting sparsity and equation-free architectures in complex systems publication-title: Eur. Phys. J. Spec. Top. – year: 1988 ident: br0440 article-title: Theory of Reproducing Kernels and Its Applications, vol. 189 – volume: 78 start-page: 1481 year: 1990 end-page: 1497 ident: br0420 article-title: Networks for approximation and learning publication-title: Proc. IEEE – reference: R. Calandra, J. Peters, C.E. Rasmussen, M.P. Deisenroth, Manifold Gaussian processes for regression, in: 2016 International Joint Conference on Neural Networks (IJCNN), IEEE, pp. 3338–3345. – volume: 16 start-page: 155 year: 1985 end-page: 183 ident: br0610 article-title: Some global dynamical properties of the Kuramoto–Sivashinsky equations: nonlinear stability and attractors publication-title: Physica D – year: 2014 ident: br0090 article-title: Model Emergent Dynamics in Complex Systems – year: 2012 ident: br0470 article-title: Exploiting compositionality to explore a large space of model structures – volume: 225 start-page: 2118 year: 2007 end-page: 2137 ident: br0630 article-title: The immersed boundary method: a projection approach publication-title: J. Comput. Phys. – volume: 324 start-page: 81 year: 2009 end-page: 85 ident: br0200 article-title: Distilling free-form natural laws from experimental data publication-title: Science – volume: 1 start-page: 121 year: 1987 ident: br0030 article-title: Equations of motion from a data series publication-title: Complex Syst. – reference: E. Snelson, Z. Ghahramani, Sparse Gaussian processes using pseudo-inputs, in: Advances in Neural Information Processing Systems, pp. 1257–1264. – volume: 83 start-page: 3422 year: 1999 ident: br0060 article-title: Amplitude equations from spatiotemporal binary-fluid convection data publication-title: Phys. Rev. Lett. – volume: 4 start-page: 1035 year: 1963 end-page: 1038 ident: br0400 article-title: Solution of incorrectly formulated problems and the regularization method publication-title: Soviet Math. Dokl. – volume: 68 start-page: 337 year: 1950 end-page: 404 ident: br0430 article-title: Theory of reproducing kernels publication-title: Trans. Am. Math. Soc. – year: 1998 ident: br0650 article-title: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, vol. 198 – start-page: 267 year: 1996 end-page: 288 ident: br0210 article-title: Regression shrinkage and selection via the lasso publication-title: J. R. Stat. Soc. B – year: 2017 ident: br0560 article-title: Parametric gaussian process regression for big data – volume: 10 year: 2015 ident: br0120 article-title: Efficient inference of parsimonious phenomenological models of cellular dynamics using s-systems and alternating regression publication-title: PLoS ONE – volume: 19 start-page: 451 year: 2010 end-page: 559 ident: br0530 article-title: Inverse problems: a Bayesian perspective publication-title: Acta Numer. – volume: 110 start-page: 18368 year: 2013 end-page: 18373 ident: br0260 article-title: Compressed modes for variational problems in mathematics and physics publication-title: Proc. Natl. Acad. Sci. – volume: 12 start-page: 1800 year: 2014 end-page: 1827 ident: br0270 article-title: On the compressive spectral method publication-title: Multiscale Model. Simul. – volume: 53 start-page: 920 year: 2015 end-page: 933 ident: br0300 article-title: Low-dimensional approach for reconstruction of airfoil data via compressive sensing publication-title: AIAA J. – year: 2012 ident: br0360 article-title: Bayesian Learning for Neural Networks, vol. 118 – volume: 338 start-page: 496 year: 2012 end-page: 500 ident: br0070 article-title: Detecting causality in complex ecosystems publication-title: Science – year: 2003 ident: br0660 article-title: Stable Distributions: Models for Heavy-Tailed Data – year: 2016 ident: br0310 article-title: Exact recovery of chaotic systems from highly corrupted data – year: 2013 ident: br0370 article-title: The Nature of Statistical Learning Theory – year: 2013 ident: br0550 article-title: Gaussian processes for big data publication-title: Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence – volume: 109 start-page: 2222 year: 2012 end-page: 2227 ident: br0140 article-title: Nonlinear laplacian spectral analysis for time series with intermittency and low-frequency variability publication-title: Proc. Natl. Acad. Sci. – year: 2017 ident: br0010 article-title: Numerical gaussian processes for time-dependent and non-linear partial differential equations – volume: 348 start-page: 683 year: 2017 end-page: 693 ident: br0330 article-title: Machine learning of linear differential equations using gaussian processes publication-title: J. Comput. Phys. – start-page: 294 year: 2001 end-page: 300 ident: br0520 article-title: Occam's razor publication-title: Adv. Neural Inf. Process. Syst. – volume: 335 start-page: 736 year: 2017 end-page: 746 ident: br0320 article-title: Inferring solutions of differential equations using noisy multi-fidelity data publication-title: J. Comput. Phys. – volume: 2 start-page: 52 year: 2016 end-page: 63 ident: br0230 article-title: Inferring biological networks by sparse identification of nonlinear dynamics publication-title: IEEE Trans. Mol. Biol. Multi-Scale Commun. – volume: 41 start-page: 309 year: 2005 end-page: 325 ident: br0150 article-title: Spectral properties of dynamical systems, model reduction and decompositions publication-title: Nonlinear Dyn. – volume: 1 start-page: 211 year: 2001 end-page: 244 ident: br0390 article-title: Sparse Bayesian learning and the relevance vector machine publication-title: J. Mach. Learn. Res. – volume: 71 start-page: 340 year: 1976 end-page: 344 ident: br0670 article-title: A method for simulating stable random variables publication-title: J. Am. Stat. Assoc. – volume: 45 start-page: 503 year: 1989 end-page: 528 ident: br0510 article-title: On the limited memory BFGS method for large scale optimization publication-title: Math. Program. – year: 2011 ident: br0450 article-title: Reproducing Kernel Hilbert Spaces in Probability and Statistics – year: 2016 ident: br0620 article-title: Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, vol. 149 – reference: J. Hartikainen, S. Särkkä, Kalman filtering and smoothing solutions to temporal Gaussian process regression models, in: 2010 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), IEEE, pp. 379–384. – year: 2008 ident: br0580 article-title: Fermi, Pasta, Ulam and a mysterious lady – volume: 3 year: 2017 ident: br0020 article-title: Data-driven discovery of partial differential equations publication-title: Sci. Adv. – volume: 106 start-page: 3649 year: 2009 end-page: 3653 ident: br0130 article-title: Normal forms for reduced stochastic climate models publication-title: Proc. Natl. Acad. Sci. – volume: 8 year: 2017 ident: br0180 article-title: Chaos as an intermittently forced linear system publication-title: Nat. Commun. – volume: 6 year: 2015 ident: br0110 article-title: Automated adaptive inference of phenomenological dynamical models publication-title: Nat. Commun. – reference: G. Malkomes, C. Schaff, R. Garnett, Bayesian optimization for automated model selection, in: Advances in Neural Information Processing Systems, pp. 2900–2908. – volume: 112 start-page: E1569 year: 2015 end-page: E1576 ident: br0080 article-title: Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling publication-title: Proc. Natl. Acad. Sci. – ident: 10.1016/j.jcp.2017.11.039_br0470 – volume: 71 start-page: 340 year: 1976 ident: 10.1016/j.jcp.2017.11.039_br0670 article-title: A method for simulating stable random variables publication-title: J. Am. Stat. Assoc. doi: 10.1080/01621459.1976.10480344 – year: 1977 ident: 10.1016/j.jcp.2017.11.039_br0410 – ident: 10.1016/j.jcp.2017.11.039_br0480 – volume: 16 start-page: 155 year: 1985 ident: 10.1016/j.jcp.2017.11.039_br0610 article-title: Some global dynamical properties of the Kuramoto–Sivashinsky equations: nonlinear stability and attractors publication-title: Physica D doi: 10.1016/0167-2789(85)90056-9 – year: 2013 ident: 10.1016/j.jcp.2017.11.039_br0550 article-title: Gaussian processes for big data – volume: 104 start-page: 9943 year: 2007 ident: 10.1016/j.jcp.2017.11.039_br0190 article-title: Automated reverse engineering of nonlinear dynamical systems publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.0609476104 – volume: 83 start-page: 3422 year: 1999 ident: 10.1016/j.jcp.2017.11.039_br0060 article-title: Amplitude equations from spatiotemporal binary-fluid convection data publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.83.3422 – start-page: 267 year: 1996 ident: 10.1016/j.jcp.2017.11.039_br0210 article-title: Regression shrinkage and selection via the lasso publication-title: J. R. Stat. Soc. B doi: 10.1111/j.2517-6161.1996.tb02080.x – volume: 57 start-page: 325 year: 1986 ident: 10.1016/j.jcp.2017.11.039_br0600 article-title: Order, disorder, and phase turbulence publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.57.325 – volume: 223 start-page: 2665 year: 2014 ident: 10.1016/j.jcp.2017.11.039_br0290 article-title: Exploiting sparsity and equation-free architectures in complex systems publication-title: Eur. Phys. J. Spec. Top. doi: 10.1140/epjst/e2014-02285-8 – ident: 10.1016/j.jcp.2017.11.039_br0010 – volume: 109 start-page: 2222 year: 2012 ident: 10.1016/j.jcp.2017.11.039_br0140 article-title: Nonlinear laplacian spectral analysis for time series with intermittency and low-frequency variability publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.1118984109 – volume: 12 start-page: 1800 year: 2014 ident: 10.1016/j.jcp.2017.11.039_br0270 article-title: On the compressive spectral method publication-title: Multiscale Model. Simul. doi: 10.1137/140965909 – year: 2016 ident: 10.1016/j.jcp.2017.11.039_br0620 – year: 2012 ident: 10.1016/j.jcp.2017.11.039_br0360 – volume: 22 start-page: S965 year: 1998 ident: 10.1016/j.jcp.2017.11.039_br0050 article-title: Identification of distributed parameter systems: a neural net based approach publication-title: Comput. Chem. Eng. doi: 10.1016/S0098-1354(98)00191-4 – volume: 348 start-page: 683 year: 2017 ident: 10.1016/j.jcp.2017.11.039_br0330 article-title: Machine learning of linear differential equations using gaussian processes publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2017.07.050 – ident: 10.1016/j.jcp.2017.11.039_br0560 – volume: 324 start-page: 81 year: 2009 ident: 10.1016/j.jcp.2017.11.039_br0200 article-title: Distilling free-form natural laws from experimental data publication-title: Science doi: 10.1126/science.1165893 – volume: 22 year: 2012 ident: 10.1016/j.jcp.2017.11.039_br0160 article-title: Applied koopmanism a publication-title: Chaos doi: 10.1063/1.4772195 – volume: 8 year: 2011 ident: 10.1016/j.jcp.2017.11.039_br0100 article-title: Automated refinement and inference of analytical models for metabolic networks publication-title: Phys. Biol. doi: 10.1088/1478-3975/8/5/055011 – volume: 4 start-page: 1035 year: 1963 ident: 10.1016/j.jcp.2017.11.039_br0400 article-title: Solution of incorrectly formulated problems and the regularization method publication-title: Soviet Math. Dokl. – volume: 1 start-page: 121 year: 1987 ident: 10.1016/j.jcp.2017.11.039_br0030 article-title: Equations of motion from a data series publication-title: Complex Syst. – volume: 338 start-page: 496 year: 2012 ident: 10.1016/j.jcp.2017.11.039_br0070 article-title: Detecting causality in complex ecosystems publication-title: Science doi: 10.1126/science.1227079 – ident: 10.1016/j.jcp.2017.11.039_br0500 – volume: 68 start-page: 337 year: 1950 ident: 10.1016/j.jcp.2017.11.039_br0430 article-title: Theory of reproducing kernels publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1950-0051437-7 – volume: 45 start-page: 503 year: 1989 ident: 10.1016/j.jcp.2017.11.039_br0510 article-title: On the limited memory BFGS method for large scale optimization publication-title: Math. Program. doi: 10.1007/BF01589116 – ident: 10.1016/j.jcp.2017.11.039_br0690 doi: 10.1109/MLSP.2010.5589113 – year: 2014 ident: 10.1016/j.jcp.2017.11.039_br0090 – year: 2003 ident: 10.1016/j.jcp.2017.11.039_br0660 – volume: 2 start-page: 52 year: 2016 ident: 10.1016/j.jcp.2017.11.039_br0230 article-title: Inferring biological networks by sparse identification of nonlinear dynamics publication-title: IEEE Trans. Mol. Biol. Multi-Scale Commun. doi: 10.1109/TMBMC.2016.2633265 – ident: 10.1016/j.jcp.2017.11.039_br0310 – volume: 18 start-page: 113 year: 1986 ident: 10.1016/j.jcp.2017.11.039_br0590 article-title: The Kuramoto–Sivashinsky equation: a bridge between pde's and dynamical systems publication-title: Physica D doi: 10.1016/0167-2789(86)90166-1 – volume: 106 start-page: 3649 year: 2009 ident: 10.1016/j.jcp.2017.11.039_br0130 article-title: Normal forms for reduced stochastic climate models publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.0900173106 – year: 2011 ident: 10.1016/j.jcp.2017.11.039_br0450 – volume: 41 start-page: 309 year: 2005 ident: 10.1016/j.jcp.2017.11.039_br0150 article-title: Spectral properties of dynamical systems, model reduction and decompositions publication-title: Nonlinear Dyn. doi: 10.1007/s11071-005-2824-x – year: 1988 ident: 10.1016/j.jcp.2017.11.039_br0440 – volume: 6 year: 2015 ident: 10.1016/j.jcp.2017.11.039_br0110 article-title: Automated adaptive inference of phenomenological dynamical models publication-title: Nat. Commun. doi: 10.1038/ncomms9133 – volume: 13 start-page: 1716 year: 2014 ident: 10.1016/j.jcp.2017.11.039_br0280 article-title: Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems publication-title: SIAM J. Appl. Dyn. Syst. doi: 10.1137/130949282 – volume: 8 year: 2017 ident: 10.1016/j.jcp.2017.11.039_br0180 article-title: Chaos as an intermittently forced linear system publication-title: Nat. Commun. doi: 10.1038/s41467-017-00030-8 – volume: 225 start-page: 2118 year: 2007 ident: 10.1016/j.jcp.2017.11.039_br0630 article-title: The immersed boundary method: a projection approach publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2007.03.005 – ident: 10.1016/j.jcp.2017.11.039_br0490 doi: 10.1109/IJCNN.2016.7727626 – start-page: 294 year: 2001 ident: 10.1016/j.jcp.2017.11.039_br0520 article-title: Occam's razor publication-title: Adv. Neural Inf. Process. Syst. – volume: 19 start-page: 451 year: 2010 ident: 10.1016/j.jcp.2017.11.039_br0530 article-title: Inverse problems: a Bayesian perspective publication-title: Acta Numer. doi: 10.1017/S0962492910000061 – volume: 3 year: 2017 ident: 10.1016/j.jcp.2017.11.039_br0020 article-title: Data-driven discovery of partial differential equations publication-title: Sci. Adv. doi: 10.1126/sciadv.1602614 – volume: 106 year: 2011 ident: 10.1016/j.jcp.2017.11.039_br0240 article-title: Predicting catastrophes in nonlinear dynamical systems by compressive sensing publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.106.154101 – volume: 113 start-page: 3932 year: 2016 ident: 10.1016/j.jcp.2017.11.039_br0220 article-title: Discovering governing equations from data by sparse identification of nonlinear dynamical systems publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.1517384113 – volume: 53 start-page: 920 issue: 4 year: 2015 ident: 10.1016/j.jcp.2017.11.039_br0300 article-title: Low-dimensional approach for reconstruction of airfoil data via compressive sensing publication-title: AIAA J. doi: 10.2514/1.J053287 – year: 2002 ident: 10.1016/j.jcp.2017.11.039_br0380 – volume: 10 year: 2015 ident: 10.1016/j.jcp.2017.11.039_br0120 article-title: Efficient inference of parsimonious phenomenological models of cellular dynamics using s-systems and alternating regression publication-title: PLoS ONE doi: 10.1371/journal.pone.0119821 – volume: 1 start-page: 211 year: 2001 ident: 10.1016/j.jcp.2017.11.039_br0390 article-title: Sparse Bayesian learning and the relevance vector machine publication-title: J. Mach. Learn. Res. – volume: 1 start-page: 715 year: 2003 ident: 10.1016/j.jcp.2017.11.039_br0040 article-title: Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis publication-title: Commun. Math. Sci. doi: 10.4310/CMS.2003.v1.n4.a5 – year: 2006 ident: 10.1016/j.jcp.2017.11.039_br0340 – volume: 110 start-page: 6634 year: 2013 ident: 10.1016/j.jcp.2017.11.039_br0250 article-title: Sparse dynamics for partial differential equations publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.1302752110 – volume: 110 start-page: 18368 year: 2013 ident: 10.1016/j.jcp.2017.11.039_br0260 article-title: Compressed modes for variational problems in mathematics and physics publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.1318679110 – ident: 10.1016/j.jcp.2017.11.039_br0460 – volume: 197 start-page: 2131 year: 2008 ident: 10.1016/j.jcp.2017.11.039_br0640 article-title: A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2007.08.014 – ident: 10.1016/j.jcp.2017.11.039_br0540 – ident: 10.1016/j.jcp.2017.11.039_br0580 – year: 1998 ident: 10.1016/j.jcp.2017.11.039_br0650 – volume: 78 start-page: 1481 year: 1990 ident: 10.1016/j.jcp.2017.11.039_br0420 article-title: Networks for approximation and learning publication-title: Proc. IEEE doi: 10.1109/5.58326 – year: 2012 ident: 10.1016/j.jcp.2017.11.039_br0350 – volume: 45 start-page: 357 year: 2013 ident: 10.1016/j.jcp.2017.11.039_br0170 article-title: Analysis of fluid flows via spectral properties of the Koopman operator publication-title: Annu. Rev. Fluid Mech. doi: 10.1146/annurev-fluid-011212-140652 – volume: 335 start-page: 736 year: 2017 ident: 10.1016/j.jcp.2017.11.039_br0320 article-title: Inferring solutions of differential equations using noisy multi-fidelity data publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2017.01.060 – year: 2013 ident: 10.1016/j.jcp.2017.11.039_br0370 – volume: 14 start-page: 23 year: 1986 ident: 10.1016/j.jcp.2017.11.039_br0570 article-title: Spectral and finite difference solutions of the Burgers equation publication-title: Comput. Fluids doi: 10.1016/0045-7930(86)90036-8 – volume: 112 start-page: E1569 year: 2015 ident: 10.1016/j.jcp.2017.11.039_br0080 article-title: Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.1417063112 – start-page: 379 year: 1995 ident: 10.1016/j.jcp.2017.11.039_br0680 article-title: Computer simulation of Lévy α-stable variables and processes |
| SSID | ssj0008548 |
| Score | 2.7107108 |
| Snippet | While there is currently a lot of enthusiasm about “big data”, useful data is usually “small” and expensive to acquire. In this paper, we present a new... While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new... |
| SourceID | proquest crossref elsevier |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 125 |
| SubjectTerms | Applications of mathematics Artificial intelligence Bayesian modeling Complexity Computational fluid dynamics Computational physics Data management Fractional equations Gaussian process Machine learning Mathematical models Navier-Stokes equations Nonlinear differential equations Nonlinear equations Normal distribution Partial differential equations Physics Probabilistic inference Probabilistic machine learning Small data System identification Time dependence Uncertainty quantification |
| Title | Hidden physics models: Machine learning of nonlinear partial differential equations |
| URI | https://dx.doi.org/10.1016/j.jcp.2017.11.039 https://www.proquest.com/docview/2030207139 |
| Volume | 357 |
| WOSCitedRecordID | wos000427393800006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1090-2716 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008548 issn: 0021-9991 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3db9MwELdg44GX8S0GA_mBJ1CqOE5ih7cJFQ0QExJD6ltke7a0aoSxdtPEX8_Zd85KJyZA4iVq08aOfOf78t3vGHthhDYmGFeoDnyTulKusE3lixC8BYer1a3VqdmE2t_Xs1n3iQL6i9ROQA2DvrjoTv4rqeEeEDuWzv4FucdB4QZ8BqLDFcgO1z8i_F4EBRkoZEGtblLe28eUN-lzo4iU7DwgUkbEu45DpRMb7JiSvvjvZysRvas2rEs9IXI8kaZcOTqCDYcFQT-OzJgF_CFObw6j6XoZlX81_boagBCpIg9LMDEqlitjfkncxNSPDjtxTTwK17Iri0phbWWWvhLxqUl-CqyCJlUsEBPripTHgMN8MncRcVSoScRhRUykNfDseBYdgRaEAEkWT4xvss1KNR2I8M3dd9PZ-1Fr66ZGrU3vnU_AUy7g2kS_s2HWtHkyUQ7usi2iC99FnrjHbvjhPrtDfgYnKb54wD4ji3CiF0cWec2JQXhmEP4t8JFBODEIX2UQPjLIQ_bl7fTgzV5BzTUKJ1u9LFoHxrpxoi1tG7TS0hqva2crIU1pTRd8KYPqAlg4oWqDlPYQLHsvvZZKgAaVj9gGvIJ_zLgQ3laNNabVZe0ab4L2RlsHZo90VeO2WZmXq3eEPB8boBz3OcVw3sMK93GFwSPtYYW32cvxkROEXbnuz3WmQU92I9qDPTDMdY_tZHr1tH8X8LsEB0qBX_Tk30Z9ym5fbpIdtrE8PfPP2C13vjxanD4nrvsJTXedig |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Hidden+physics+models%3A+Machine+learning+of+nonlinear+partial+differential+equations&rft.jtitle=Journal+of+computational+physics&rft.au=Raissi%2C+Maziar&rft.au=Karniadakis%2C+George+Em&rft.date=2018-03-15&rft.pub=Elsevier+Inc&rft.issn=0021-9991&rft.eissn=1090-2716&rft.volume=357&rft.spage=125&rft.epage=141&rft_id=info:doi/10.1016%2Fj.jcp.2017.11.039&rft.externalDocID=S0021999117309014 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0021-9991&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0021-9991&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0021-9991&client=summon |