A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics

We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to inversion and surrogate modeling in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN, and explore in detail the application to linear e...

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Published in:	Computer methods in applied mechanics and engineering Vol. 379; p. 113741
Main Authors:	Haghighat, Ehsan, Raissi, Maziar, Moure, Adrian, Gomez, Hector, Juanes, Ruben
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.06.2021 Elsevier BV
Subjects:	Algorithms Artificial neural network Artificial neural networks Constitutive relationships Convergence Deep learning Elastoplasticity Finite element method Inversion Linear elasticity Machine learning Mathematical models Model testing Neural networks Parameters Physics Physics-informed deep learning Robustness (mathematics) Sensitivity analysis Solid mechanics Training Transfer learning Inversion Artificial neural network Physics-informed deep learning Elastoplasticity Transfer learning Linear elasticity
ISSN:	0045-7825, 1879-2138
Online Access:	Get full text
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Abstract	We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to inversion and surrogate modeling in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN, and explore in detail the application to linear elasticity, and illustrate its extension to nonlinear problems through an example that showcases von Mises elastoplasticity. While common PINN algorithms are based on training one deep neural network (DNN), we propose a multi-network model that results in more accurate representation of the field variables. To validate the model, we test the framework on synthetic data generated from analytical and numerical reference solutions. We study convergence of the PINN model, and show that Isogeometric Analysis (IGA) results in superior accuracy and convergence characteristics compared with classic low-order Finite Element Method (FEM). We also show the applicability of the framework for transfer learning, and find vastly accelerated convergence during network re-training. Finally, we find that honoring the physics leads to improved robustness: when trained only on a few parameters, we find that the PINN model can accurately predict the solution for a wide range of parameters new to the network—thus pointing to an important application of this framework to sensitivity analysis and surrogate modeling. •Application of Physics-Informed Neural Networks (PINNs) to solid mechanics.•Novel application to inversion, transfer learning, and surrogate modeling.•Formulation of PINNs for linear elasticity and von-Mises elastoplasticity.
AbstractList	We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to inversion and surrogate modeling in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN, and explore in detail the application to linear elasticity, and illustrate its extension to nonlinear problems through an example that showcases von Mises elastoplasticity. While common PINN algorithms are based on training one deep neural network (DNN), we propose a multi-network model that results in more accurate representation of the field variables. To validate the model, we test the framework on synthetic data generated from analytical and numerical reference solutions. We study convergence of the PINN model, and show that Isogeometric Analysis (IGA) results in superior accuracy and convergence characteristics compared with classic low-order Finite Element Method (FEM). We also show the applicability of the framework for transfer learning, and find vastly accelerated convergence during network re-training. Finally, we find that honoring the physics leads to improved robustness: when trained only on a few parameters, we find that the PINN model can accurately predict the solution for a wide range of parameters new to the network—thus pointing to an important application of this framework to sensitivity analysis and surrogate modeling. •Application of Physics-Informed Neural Networks (PINNs) to solid mechanics.•Novel application to inversion, transfer learning, and surrogate modeling.•Formulation of PINNs for linear elasticity and von-Mises elastoplasticity. We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to inversion and surrogate modeling in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN, and explore in detail the application to linear elasticity, and illustrate its extension to nonlinear problems through an example that showcases von Mises elastoplasticity. While common PINN algorithms are based on training one deep neural network (DNN), we propose a multi-network model that results in more accurate representation of the field variables. To validate the model, we test the framework on synthetic data generated from analytical and numerical reference solutions. We study convergence of the PINN model, and show that Isogeometric Analysis (IGA) results in superior accuracy and convergence characteristics compared with classic low-order Finite Element Method (FEM). We also show the applicability of the framework for transfer learning, and find vastly accelerated convergence during network re-training. Finally, we find that honoring the physics leads to improved robustness: when trained only on a few parameters, we find that the PINN model can accurately predict the solution for a wide range of parameters new to the network-thus pointing to an important application of this framework to sensitivity analysis and surrogate modeling.
ArticleNumber	113741
Author	Juanes, Ruben Gomez, Hector Haghighat, Ehsan Moure, Adrian Raissi, Maziar
Author_xml	– sequence: 1 givenname: Ehsan orcidid: 0000-0003-2659-0507 surname: Haghighat fullname: Haghighat, Ehsan organization: Massachusetts Institute of Technology, Cambridge, MA, United States of America – sequence: 2 givenname: Maziar surname: Raissi fullname: Raissi, Maziar organization: University of Colorado Boulder, Boulder, CO, United States of America – sequence: 3 givenname: Adrian surname: Moure fullname: Moure, Adrian organization: Purdue University, West Lafayette, IN, United States of America – sequence: 4 givenname: Hector orcidid: 0000-0002-2553-9091 surname: Gomez fullname: Gomez, Hector organization: Purdue University, West Lafayette, IN, United States of America – sequence: 5 givenname: Ruben orcidid: 0000-0002-7370-2332 surname: Juanes fullname: Juanes, Ruben email: juanes@mit.edu organization: Massachusetts Institute of Technology, Cambridge, MA, United States of America
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Cites_doi	10.1016/j.ymssp.2019.06.003 10.1016/0895-7177(94)90095-7 10.1109/72.870037 10.1038/nature14539 10.1016/S0266-352X(97)00034-7 10.1007/978-3-642-27645-3_2 10.1038/srep02810 10.1016/j.cma.2004.10.008 10.1016/j.cma.2020.113552 10.4208/cicp.OA-2020-0164 10.1073/pnas.1911815116 10.1016/j.jcp.2018.10.045 10.1002/tal.1400 10.1137/18M1191944 10.25080/Majora-92bf1922-003 10.1007/s11837-011-0057-7 10.1038/nrg3920 10.1016/j.cma.2009.02.036 10.1103/PhysRevFluids.4.100501 10.1126/science.aau0323 10.1002/nme.1620010107 10.1088/2515-7639/ab291e 10.1126/sciadv.1501057 10.1038/s41586-018-0337-2 10.1073/pnas.1718942115 10.1785/0220180259 10.1029/2019GL082706 10.1016/j.jcp.2019.05.024 10.1109/72.712178 10.1073/pnas.1818555116 10.1038/s41586-018-0438-y 10.1073/pnas.1814058116 10.1146/annurev-fluid-010719-060214
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References	Bazilevs, Calo, Cottrell, Evans, Hughes, Lipton, Scott, Sederberg (b42) 2010; 199 Sen, Aghazadeh, Mousavi, Nagarajaiah, Baraniuk, Dabak (b17) 2019; 131 Wang, Wang, Perdikaris (b51) 2020 Rafiei, Adeli (b16) 2017; 26 Brunton, Noack, Koumoutsakos (b14) 2020; 52 Cottrell, Hughes, Bazilevs (b33) 2009 Goodfellow, Bengio, Courville (b3) 2016 Shi, Tsymbalov, Dao, Suresh, Shapeev, Li (b11) 2019; 116 Wang, Teng, Perdikaris (b46) 2020 Butler, Davies, Cartwright, Isayev, Walsh (b10) 2018; 559 Haghighat, Bekar, Madenci, Juanes (b50) 2020 Bergen, Johnson, de Hoop, Beroza (b5) 2019; 363 Simo, Hughes (b43) 1998; vol. 7 Baydin, Pearlmutter, Radul, Siskind (b35) 2017; 18 Haghighat, Juanes (b40) 2021; 373 Smith, Kindermans, Ying, Le (b45) 2017 Lange, Gabel, Riedmiller (b31) 2012; 12 Yoon, O’Reilly, Bergen, Beroza (b4) 2015; 1 Wang, Yu, Perdikaris (b47) 2020 LeCun, Bengio, Hinton (b2) 2015; 521 Bishop (b1) 2006 Hughes, Cottrell, Bazilevs (b32) 2005; 194 Ghaboussi, Sidarta (b18) 1998; 22 Zienkiewicz, Valliappan, King (b44) 1969; 1 Kalidindi, Niezgoda, Salem (b19) 2011; 63 Chen, Li, Li, Lin, Wang, Wang, Xiao, Xu, Zhang, Zhang (b36) 2015 (b41) 2020 Bar-Sinai, Hoyer, Hickey, Brenner (b24) 2019; 116 Meade, Fernandez (b26) 1994; 19 Kong, Trugman, Ross, Bianco, Meade, Gerstoft (b7) 2018; 90 Brunton, Kutz (b12) 2019; 2 Kingma, Ba (b38) 2014 Raissi, Perdikaris, Karniadakis (b22) 2019; 378 Lagaris, Likas, Papageorgiou (b28) 2000; 11 Taylor, Stone (b34) 2009; 10 Han, Jentzen, E (b23) 2018; 115 DeVries, Viégas, Wattenberg, Meade (b6) 2018; 560 Pilania, Wang, Jiang, Rajasekaran, Ramprasad (b9) 2013; 3 Libbrecht, Noble (b15) 2015; 16 Abadi, Barham, Chen, Chen, Davis, Dean, Devin, Ghemawat, Irving, Isard, Kudlur, Levenberg, Monga, Moore, Murray, Steiner, Tucker, Vasudevan, Warden, Wicke, Yu, Zheng (b30) 2016 Rahaman, Baratin, Arpit, Draxler, Lin, Hamprecht, Bengio, Courville (b48) 2019; vol. 97 J. Bergstra, O. Breuleux, F. Bastien, P. Lamblin, R. Pascanu, G. Desjardins, J. Turian, D. Warde-Farley, Y. Bengio, Theano: a CPU and GPU math expression compiler, in: Proceedings of the Python for Scientific Computing Conference (SciPy), Vol. 4, Austin, TX, 2010. Zhu, Zabaras, Koutsourelakis, Perdikaris (b25) 2019; 394 Brenner, Eldredge, Freund (b13) 2019; 4 Duchi, Hazan, Singer (b39) 2011; 12 Jagtap, Karniadakis (b49) 2020; 28 Lagaris, Likas, Fotiadis (b27) 1998; 9 Rudy, Alla, Brunton, Kutz (b21) 2019; 18 Chollet (b37) 2015 Mozaffar, Bostanabad, Chen, Ehmann, Cao, Bessa (b20) 2019; 116 Ren, Dorostkar, Rouet-Leduc, Hulbert, Strebel, Guyer, Johnson, Carmeliet (b8) 2019; 46 Simo (10.1016/j.cma.2021.113741_b43) 1998; vol. 7 Bishop (10.1016/j.cma.2021.113741_b1) 2006 Hughes (10.1016/j.cma.2021.113741_b32) 2005; 194 Rudy (10.1016/j.cma.2021.113741_b21) 2019; 18 Mozaffar (10.1016/j.cma.2021.113741_b20) 2019; 116 Smith (10.1016/j.cma.2021.113741_b45) 2017 Bergen (10.1016/j.cma.2021.113741_b5) 2019; 363 Taylor (10.1016/j.cma.2021.113741_b34) 2009; 10 Duchi (10.1016/j.cma.2021.113741_b39) 2011; 12 Kingma (10.1016/j.cma.2021.113741_b38) 2014 Han (10.1016/j.cma.2021.113741_b23) 2018; 115 Chollet (10.1016/j.cma.2021.113741_b37) 2015 Baydin (10.1016/j.cma.2021.113741_b35) 2017; 18 Wang (10.1016/j.cma.2021.113741_b47) 2020 10.1016/j.cma.2021.113741_b29 Rahaman (10.1016/j.cma.2021.113741_b48) 2019; vol. 97 (10.1016/j.cma.2021.113741_b41) 2020 DeVries (10.1016/j.cma.2021.113741_b6) 2018; 560 Meade (10.1016/j.cma.2021.113741_b26) 1994; 19 Haghighat (10.1016/j.cma.2021.113741_b50) 2020 Wang (10.1016/j.cma.2021.113741_b46) 2020 Ghaboussi (10.1016/j.cma.2021.113741_b18) 1998; 22 Jagtap (10.1016/j.cma.2021.113741_b49) 2020; 28 Lagaris (10.1016/j.cma.2021.113741_b27) 1998; 9 Abadi (10.1016/j.cma.2021.113741_b30) 2016 Wang (10.1016/j.cma.2021.113741_b51) 2020 Raissi (10.1016/j.cma.2021.113741_b22) 2019; 378 Zhu (10.1016/j.cma.2021.113741_b25) 2019; 394 Sen (10.1016/j.cma.2021.113741_b17) 2019; 131 Zienkiewicz (10.1016/j.cma.2021.113741_b44) 1969; 1 Lange (10.1016/j.cma.2021.113741_b31) 2012; 12 LeCun (10.1016/j.cma.2021.113741_b2) 2015; 521 Ren (10.1016/j.cma.2021.113741_b8) 2019; 46 Lagaris (10.1016/j.cma.2021.113741_b28) 2000; 11 Kalidindi (10.1016/j.cma.2021.113741_b19) 2011; 63 Bar-Sinai (10.1016/j.cma.2021.113741_b24) 2019; 116 Goodfellow (10.1016/j.cma.2021.113741_b3) 2016 Butler (10.1016/j.cma.2021.113741_b10) 2018; 559 Yoon (10.1016/j.cma.2021.113741_b4) 2015; 1 Bazilevs (10.1016/j.cma.2021.113741_b42) 2010; 199 Brunton (10.1016/j.cma.2021.113741_b14) 2020; 52 Kong (10.1016/j.cma.2021.113741_b7) 2018; 90 Brunton (10.1016/j.cma.2021.113741_b12) 2019; 2 Pilania (10.1016/j.cma.2021.113741_b9) 2013; 3 Chen (10.1016/j.cma.2021.113741_b36) 2015 Rafiei (10.1016/j.cma.2021.113741_b16) 2017; 26 Brenner (10.1016/j.cma.2021.113741_b13) 2019; 4 Shi (10.1016/j.cma.2021.113741_b11) 2019; 116 Libbrecht (10.1016/j.cma.2021.113741_b15) 2015; 16 Haghighat (10.1016/j.cma.2021.113741_b40) 2021; 373 Cottrell (10.1016/j.cma.2021.113741_b33) 2009
References_xml	– volume: 363 year: 2019 ident: b5 article-title: Machine learning for data-driven discovery in solid earth geoscience publication-title: Science – volume: 4 year: 2019 ident: b13 article-title: Perspective on machine learning for advancing fluid mechanics publication-title: Phys. Rev. Fluids – year: 2020 ident: b41 article-title: COMSOL Multiphysics User’s Guide – year: 2020 ident: b46 article-title: Understanding and mitigating gradient pathologies in physics-informed neural networks – year: 2009 ident: b33 article-title: Isogeometric Analysis: Toward Integration of CAD and FEA – volume: 9 start-page: 987 year: 1998 end-page: 1000 ident: b27 article-title: Artificial neural networks for solving ordinary and partial differential equations publication-title: IEEE Trans. Neural Netw. – volume: 116 start-page: 26414 year: 2019 end-page: 26420 ident: b20 article-title: Deep learning predicts path-dependent plasticity publication-title: Proc. Natl. Acad. Sci. – volume: 11 start-page: 1041 year: 2000 end-page: 1049 ident: b28 article-title: Neural-network methods for boundary value problems with irregular boundaries publication-title: IEEE Trans. Neural Netw. – start-page: 265 year: 2016 end-page: 283 ident: b30 article-title: TensorFlow: A system for large-scale machine learning publication-title: 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI 16) – volume: 28 start-page: 2002 year: 2020 end-page: 2041 ident: b49 article-title: Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations publication-title: Commun. Comput. Phys. – volume: 46 start-page: 7395 year: 2019 end-page: 7403 ident: b8 article-title: Machine learning reveals the state of intermittent frictional dynamics in a sheared granular fault publication-title: Geophys. Res. Lett. – volume: 19 start-page: 1 year: 1994 end-page: 25 ident: b26 article-title: The numerical solution of linear ordinary differential equations by feed-forward neural networks publication-title: Math. Comput. Modelling – volume: 560 start-page: 632 year: 2018 end-page: 634 ident: b6 article-title: Deep learning of aftershock patterns following large earthquakes publication-title: Nature – volume: vol. 7 year: 1998 ident: b43 publication-title: Computational Inelasticity – year: 2014 ident: b38 article-title: Adam: A method for stochastic optimization – volume: 521 start-page: 436 year: 2015 end-page: 444 ident: b2 article-title: Deep learning publication-title: Nature – start-page: 800 year: 2016 ident: b3 article-title: Deep Learning – year: 2015 ident: b36 article-title: MXNet: A flexible and efficient machine learning library for heterogeneous distributed systems – volume: 22 start-page: 29 year: 1998 end-page: 52 ident: b18 article-title: New nested adaptive neural networks (NANN) for constitutive modeling publication-title: Comput. Geotech. – reference: J. Bergstra, O. Breuleux, F. Bastien, P. Lamblin, R. Pascanu, G. Desjardins, J. Turian, D. Warde-Farley, Y. Bengio, Theano: a CPU and GPU math expression compiler, in: Proceedings of the Python for Scientific Computing Conference (SciPy), Vol. 4, Austin, TX, 2010. – year: 2017 ident: b45 article-title: Don’t decay the learning rate, increase the batch size – volume: 90 start-page: 3 year: 2018 end-page: 14 ident: b7 article-title: Machine learning in seismology: turning data into insights publication-title: Seismol. Res. Lett. – volume: 199 start-page: 229 year: 2010 end-page: 263 ident: b42 article-title: Isogeometric analysis using T-splines publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 131 start-page: 524 year: 2019 end-page: 537 ident: b17 article-title: Data-driven semi-supervised and supervised learning algorithms for health monitoring of pipes publication-title: Mech. Syst. Signal Process. – year: 2015 ident: b37 article-title: Keras – year: 2020 ident: b51 article-title: On the eigenvector bias of fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks – volume: 18 start-page: 643 year: 2019 end-page: 660 ident: b21 article-title: Data-driven identification of parametric partial differential equations publication-title: SIAM J. Appl. Dyn. Syst. – volume: 52 start-page: 477 year: 2020 end-page: 508 ident: b14 article-title: Machine learning for fluid mechanics publication-title: Annu. Rev. Fluid Mech. – volume: 26 start-page: 1 year: 2017 end-page: 11 ident: b16 article-title: A novel machine learning-based algorithm to detect damage in high-rise building structures publication-title: Struct. Des. Tall Special Build. – volume: 394 start-page: 56 year: 2019 end-page: 81 ident: b25 article-title: Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data publication-title: J. Comput. Phys. – volume: 10 start-page: 1633 year: 2009 end-page: 1685 ident: b34 article-title: Transfer learning for reinforcement learning domains: A survey publication-title: J. Mach. Learn. Res. – volume: 18 start-page: 5595 year: 2017 end-page: 5637 ident: b35 article-title: Automatic differentiation in machine learning: a survey publication-title: J. Mach. Learn. Res. – volume: 116 start-page: 4117 year: 2019 end-page: 4122 ident: b11 article-title: Deep elastic strain engineering of bandgap through machine learning publication-title: Proc. Natl. Acad. Sci. – volume: 3 start-page: 1 year: 2013 end-page: 6 ident: b9 article-title: Accelerating materials property predictions using machine learning publication-title: Sci. Rep. – volume: 12 start-page: 2121 year: 2011 end-page: 2159 ident: b39 article-title: Adaptive subgradient methods for online learning and stochastic optimization publication-title: J. Mach. Learn. Res. – year: 2006 ident: b1 article-title: Pattern Recognition and Machine Learning – volume: vol. 97 start-page: 5301 year: 2019 end-page: 5310 ident: b48 article-title: On the spectral bias of neural networks publication-title: Proceedings of the 36th International Conference on Machine Learning – volume: 194 start-page: 4135 year: 2005 end-page: 4195 ident: b32 article-title: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 559 start-page: 547 year: 2018 end-page: 555 ident: b10 article-title: Machine learning for molecular and materials science publication-title: Nature – volume: 12 start-page: 45 year: 2012 end-page: 73 ident: b31 article-title: Reinforcement learning publication-title: Adaptation, Learning, and Optimization – volume: 378 start-page: 686 year: 2019 end-page: 707 ident: b22 article-title: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations publication-title: J. Comput. Phys. – volume: 2 year: 2019 ident: b12 article-title: Methods for data-driven multiscale model discovery for materials publication-title: J. Phys. Mater. – volume: 116 start-page: 15344 year: 2019 end-page: 15349 ident: b24 article-title: Learning data-driven discretizations for partial differential equations publication-title: Proc. Natl. Acad. Sci. – year: 2020 ident: b50 article-title: A nonlocal physics-informed deep learning framework using the peridynamic differential operator – volume: 373 start-page: 113552 year: 2021 ident: b40 article-title: SciANN: A keras/tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks publication-title: Comput. Methods Appl. Mech. Engrg. – year: 2020 ident: b47 article-title: When and why PINNs fail to train: A neural tangent kernel perspective – volume: 115 start-page: 8505 year: 2018 end-page: 8510 ident: b23 article-title: Solving high-dimensional partial differential equations using deep learning publication-title: Proc. Natl. Acad. Sci. – volume: 63 start-page: 34 year: 2011 end-page: 41 ident: b19 article-title: Microstructure informatics using higher-order statistics and efficient data-mining protocols publication-title: JOM – volume: 16 start-page: 321 year: 2015 end-page: 332 ident: b15 article-title: Machine learning applications in genetics and genomics publication-title: Nature Rev. Genet. – volume: 1 year: 2015 ident: b4 article-title: Earthquake detection through computationally efficient similarity search publication-title: Sci. Adv. – volume: 1 start-page: 75 year: 1969 end-page: 100 ident: b44 article-title: Elasto-plastic solutions of engineering problems ‘initial stress’, finite element approach publication-title: Internat. J. Numer. Methods Engrg. – year: 2015 ident: 10.1016/j.cma.2021.113741_b36 – volume: vol. 97 start-page: 5301 year: 2019 ident: 10.1016/j.cma.2021.113741_b48 article-title: On the spectral bias of neural networks – volume: 131 start-page: 524 year: 2019 ident: 10.1016/j.cma.2021.113741_b17 article-title: Data-driven semi-supervised and supervised learning algorithms for health monitoring of pipes publication-title: Mech. Syst. Signal Process. doi: 10.1016/j.ymssp.2019.06.003 – volume: 19 start-page: 1 issue: 12 year: 1994 ident: 10.1016/j.cma.2021.113741_b26 article-title: The numerical solution of linear ordinary differential equations by feed-forward neural networks publication-title: Math. Comput. Modelling doi: 10.1016/0895-7177(94)90095-7 – volume: 11 start-page: 1041 issue: 5 year: 2000 ident: 10.1016/j.cma.2021.113741_b28 article-title: Neural-network methods for boundary value problems with irregular boundaries publication-title: IEEE Trans. Neural Netw. doi: 10.1109/72.870037 – volume: 521 start-page: 436 issue: 7553 year: 2015 ident: 10.1016/j.cma.2021.113741_b2 article-title: Deep learning publication-title: Nature doi: 10.1038/nature14539 – volume: 22 start-page: 29 issue: 1 year: 1998 ident: 10.1016/j.cma.2021.113741_b18 article-title: New nested adaptive neural networks (NANN) for constitutive modeling publication-title: Comput. Geotech. doi: 10.1016/S0266-352X(97)00034-7 – volume: 12 start-page: 45 year: 2012 ident: 10.1016/j.cma.2021.113741_b31 article-title: Reinforcement learning doi: 10.1007/978-3-642-27645-3_2 – volume: 3 start-page: 1 year: 2013 ident: 10.1016/j.cma.2021.113741_b9 article-title: Accelerating materials property predictions using machine learning publication-title: Sci. Rep. doi: 10.1038/srep02810 – volume: 194 start-page: 4135 issue: 39 year: 2005 ident: 10.1016/j.cma.2021.113741_b32 article-title: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2004.10.008 – start-page: 265 year: 2016 ident: 10.1016/j.cma.2021.113741_b30 article-title: TensorFlow: A system for large-scale machine learning – year: 2020 ident: 10.1016/j.cma.2021.113741_b50 – volume: 373 start-page: 113552 year: 2021 ident: 10.1016/j.cma.2021.113741_b40 article-title: SciANN: A keras/tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2020.113552 – volume: 28 start-page: 2002 issue: 5 year: 2020 ident: 10.1016/j.cma.2021.113741_b49 article-title: Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations publication-title: Commun. Comput. Phys. doi: 10.4208/cicp.OA-2020-0164 – volume: 10 start-page: 1633 issue: Jul year: 2009 ident: 10.1016/j.cma.2021.113741_b34 article-title: Transfer learning for reinforcement learning domains: A survey publication-title: J. Mach. Learn. Res. – volume: 18 start-page: 5595 issue: 1 year: 2017 ident: 10.1016/j.cma.2021.113741_b35 article-title: Automatic differentiation in machine learning: a survey publication-title: J. Mach. Learn. Res. – year: 2020 ident: 10.1016/j.cma.2021.113741_b46 – year: 2006 ident: 10.1016/j.cma.2021.113741_b1 – year: 2014 ident: 10.1016/j.cma.2021.113741_b38 – volume: 116 start-page: 26414 issue: 52 year: 2019 ident: 10.1016/j.cma.2021.113741_b20 article-title: Deep learning predicts path-dependent plasticity publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.1911815116 – year: 2020 ident: 10.1016/j.cma.2021.113741_b51 – year: 2015 ident: 10.1016/j.cma.2021.113741_b37 – year: 2017 ident: 10.1016/j.cma.2021.113741_b45 – volume: 378 start-page: 686 year: 2019 ident: 10.1016/j.cma.2021.113741_b22 article-title: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2018.10.045 – volume: 26 start-page: 1 issue: 18 year: 2017 ident: 10.1016/j.cma.2021.113741_b16 article-title: A novel machine learning-based algorithm to detect damage in high-rise building structures publication-title: Struct. Des. Tall Special Build. doi: 10.1002/tal.1400 – volume: 18 start-page: 643 issue: 2 year: 2019 ident: 10.1016/j.cma.2021.113741_b21 article-title: Data-driven identification of parametric partial differential equations publication-title: SIAM J. Appl. Dyn. Syst. doi: 10.1137/18M1191944 – ident: 10.1016/j.cma.2021.113741_b29 doi: 10.25080/Majora-92bf1922-003 – volume: 63 start-page: 34 issue: 4 year: 2011 ident: 10.1016/j.cma.2021.113741_b19 article-title: Microstructure informatics using higher-order statistics and efficient data-mining protocols publication-title: JOM doi: 10.1007/s11837-011-0057-7 – volume: 12 start-page: 2121 issue: Jul year: 2011 ident: 10.1016/j.cma.2021.113741_b39 article-title: Adaptive subgradient methods for online learning and stochastic optimization publication-title: J. Mach. Learn. Res. – volume: 16 start-page: 321 issue: 6 year: 2015 ident: 10.1016/j.cma.2021.113741_b15 article-title: Machine learning applications in genetics and genomics publication-title: Nature Rev. Genet. doi: 10.1038/nrg3920 – volume: 199 start-page: 229 issue: 5–8 year: 2010 ident: 10.1016/j.cma.2021.113741_b42 article-title: Isogeometric analysis using T-splines publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/j.cma.2009.02.036 – year: 2020 ident: 10.1016/j.cma.2021.113741_b47 – volume: 4 issue: 10 year: 2019 ident: 10.1016/j.cma.2021.113741_b13 article-title: Perspective on machine learning for advancing fluid mechanics publication-title: Phys. Rev. Fluids doi: 10.1103/PhysRevFluids.4.100501 – volume: 363 issue: 6433 year: 2019 ident: 10.1016/j.cma.2021.113741_b5 article-title: Machine learning for data-driven discovery in solid earth geoscience publication-title: Science doi: 10.1126/science.aau0323 – volume: 1 start-page: 75 issue: 1 year: 1969 ident: 10.1016/j.cma.2021.113741_b44 article-title: Elasto-plastic solutions of engineering problems ‘initial stress’, finite element approach publication-title: Internat. J. Numer. Methods Engrg. doi: 10.1002/nme.1620010107 – volume: 2 issue: 4 year: 2019 ident: 10.1016/j.cma.2021.113741_b12 article-title: Methods for data-driven multiscale model discovery for materials publication-title: J. Phys. Mater. doi: 10.1088/2515-7639/ab291e – volume: 1 issue: 11 year: 2015 ident: 10.1016/j.cma.2021.113741_b4 article-title: Earthquake detection through computationally efficient similarity search publication-title: Sci. Adv. doi: 10.1126/sciadv.1501057 – volume: 559 start-page: 547 issue: 7715 year: 2018 ident: 10.1016/j.cma.2021.113741_b10 article-title: Machine learning for molecular and materials science publication-title: Nature doi: 10.1038/s41586-018-0337-2 – volume: 115 start-page: 8505 issue: 34 year: 2018 ident: 10.1016/j.cma.2021.113741_b23 article-title: Solving high-dimensional partial differential equations using deep learning publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.1718942115 – volume: 90 start-page: 3 issue: 1 year: 2018 ident: 10.1016/j.cma.2021.113741_b7 article-title: Machine learning in seismology: turning data into insights publication-title: Seismol. Res. Lett. doi: 10.1785/0220180259 – volume: 46 start-page: 7395 issue: 13 year: 2019 ident: 10.1016/j.cma.2021.113741_b8 article-title: Machine learning reveals the state of intermittent frictional dynamics in a sheared granular fault publication-title: Geophys. Res. Lett. doi: 10.1029/2019GL082706 – volume: 394 start-page: 56 year: 2019 ident: 10.1016/j.cma.2021.113741_b25 article-title: Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2019.05.024 – volume: 9 start-page: 987 issue: 5 year: 1998 ident: 10.1016/j.cma.2021.113741_b27 article-title: Artificial neural networks for solving ordinary and partial differential equations publication-title: IEEE Trans. Neural Netw. doi: 10.1109/72.712178 – volume: vol. 7 year: 1998 ident: 10.1016/j.cma.2021.113741_b43 – year: 2009 ident: 10.1016/j.cma.2021.113741_b33 – year: 2020 ident: 10.1016/j.cma.2021.113741_b41 – volume: 116 start-page: 4117 issue: 10 year: 2019 ident: 10.1016/j.cma.2021.113741_b11 article-title: Deep elastic strain engineering of bandgap through machine learning publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.1818555116 – volume: 560 start-page: 632 issue: 7720 year: 2018 ident: 10.1016/j.cma.2021.113741_b6 article-title: Deep learning of aftershock patterns following large earthquakes publication-title: Nature doi: 10.1038/s41586-018-0438-y – volume: 116 start-page: 15344 issue: 31 year: 2019 ident: 10.1016/j.cma.2021.113741_b24 article-title: Learning data-driven discretizations for partial differential equations publication-title: Proc. Natl. Acad. Sci. doi: 10.1073/pnas.1814058116 – start-page: 800 year: 2016 ident: 10.1016/j.cma.2021.113741_b3 – volume: 52 start-page: 477 issue: 1 year: 2020 ident: 10.1016/j.cma.2021.113741_b14 article-title: Machine learning for fluid mechanics publication-title: Annu. Rev. Fluid Mech. doi: 10.1146/annurev-fluid-010719-060214
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Snippet	We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to inversion and surrogate modeling in solid...
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SubjectTerms	Algorithms Artificial neural network Artificial neural networks Constitutive relationships Convergence Deep learning Elastoplasticity Finite element method Inversion Linear elasticity Machine learning Mathematical models Model testing Neural networks Parameters Physics Physics-informed deep learning Robustness (mathematics) Sensitivity analysis Solid mechanics Training Transfer learning
Title	A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
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