Physics-informed neural networks for inverse problems in supersonic flows
Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data available for density gradients from Schlieren photography as well as data at the inflow and part of the wall...
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| Published in: | Journal of computational physics Vol. 466; p. 111402 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
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Elsevier Science Ltd
01.10.2022
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| ISSN: | 0021-9991, 1090-2716 |
| Online Access: | Get full text |
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| Abstract | Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data available for density gradients from Schlieren photography as well as data at the inflow and part of the wall boundaries. These inverse problems are notoriously difficult, and traditional methods may not be adequate to solve such ill-posed inverse problems. To this end, we employ the physics-informed neural networks (PINNs) and its extended version, extended PINNs (XPINNs), where domain decomposition allows to deploy locally powerful neural networks in each subdomain, which can provide additional expressivity in subdomains, where a complex solution is expected. Apart from the governing compressible Euler equations, we also enforce the entropy conditions in order to obtain viscosity solutions. Moreover, we enforce positivity conditions on density and pressure. We consider inverse problems involving two-dimensional expansion waves, two-dimensional oblique and bow shock waves. We compare solutions obtained by PINNs and XPINNs and invoke some theoretical results that can be used to decide on the generalization errors of the two methods. |
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| AbstractList | Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data available for density gradients from Schlieren photography as well as data at the inflow and part of the wall boundaries. These inverse problems are notoriously difficult, and traditional methods may not be adequate to solve such ill-posed inverse problems. To this end, we employ the physics-informed neural networks (PINNs) and its extended version, extended PINNs (XPINNs), where domain decomposition allows to deploy locally powerful neural networks in each subdomain, which can provide additional expressivity in subdomains, where a complex solution is expected. Apart from the governing compressible Euler equations, we also enforce the entropy conditions in order to obtain viscosity solutions. Moreover, we enforce positivity conditions on density and pressure. We consider inverse problems involving two-dimensional expansion waves, two-dimensional oblique and bow shock waves. We compare solutions obtained by PINNs and XPINNs and invoke some theoretical results that can be used to decide on the generalization errors of the two methods. |
| ArticleNumber | 111402 |
| Author | Adams, Nikolaus Mao, Zhiping Karniadakis, George Em Jagtap, Ameya D. |
| Author_xml | – sequence: 1 givenname: Ameya D. surname: Jagtap fullname: Jagtap, Ameya D. – sequence: 2 givenname: Zhiping surname: Mao fullname: Mao, Zhiping – sequence: 3 givenname: Nikolaus surname: Adams fullname: Adams, Nikolaus – sequence: 4 givenname: George Em surname: Karniadakis fullname: Karniadakis, George Em |
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| Cites_doi | 10.1016/j.jcp.2020.109345 10.1016/j.jcp.2021.110698 10.4007/annals.2005.161.223 10.1098/rspa.2020.0334 10.1137/20M1318043 10.1016/j.jcp.2021.110683 10.1016/j.cma.2019.112789 10.1016/0021-9991(82)90046-8 10.1126/science.aaw4741 10.1109/MSP.2021.3118904 10.1364/OE.384875 10.1137/0916069 10.1016/j.cma.2020.113028 10.1016/j.jcp.2021.110754 10.1016/j.jcp.2019.05.027 10.1016/j.jcp.2019.109136 10.1016/j.jcp.2018.10.045 10.4208/cicp.OA-2020-0164 10.1063/1.5139992 10.1016/j.oceaneng.2022.110775 10.1016/j.cma.2020.113547 10.1615/JMachLearnModelComput.2020033905 10.1017/jfm.2021.135 10.1016/j.jcp.2021.110324 10.1016/j.cma.2021.113741 |
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| References | Wang (10.1016/j.jcp.2022.111402_br0440) 2021; 43 Glorot (10.1016/j.jcp.2022.111402_br0380) 2010 Mishra (10.1016/j.jcp.2022.111402_br0170) 2021 Kingma (10.1016/j.jcp.2022.111402_br0420) Jagtap (10.1016/j.jcp.2022.111402_br0150) 2022; 248 Dafermos (10.1016/j.jcp.2022.111402_br0330) 2016; vol. 325 Courant (10.1016/j.jcp.2022.111402_br0300) 1999 Fuks (10.1016/j.jcp.2022.111402_br0230) 2020; 1 Bianchini (10.1016/j.jcp.2022.111402_br0340) 2005 Abadi (10.1016/j.jcp.2022.111402_br0400) 2016 Shukla (10.1016/j.jcp.2022.111402_br0070) 2022; 39 Cai (10.1016/j.jcp.2022.111402_br0130) 2021; 915 10.1016/j.jcp.2022.111402_br0410 De Ryck (10.1016/j.jcp.2022.111402_br0180) He (10.1016/j.jcp.2022.111402_br0290) 2020; 127 Baydin (10.1016/j.jcp.2022.111402_br0390) 2018; 18 Shukla (10.1016/j.jcp.2022.111402_br0080) 2021; 447 Raissi (10.1016/j.jcp.2022.111402_br0040) 2020; 367 Yang (10.1016/j.jcp.2022.111402_br0120) 2019; 394 Chen (10.1016/j.jcp.2022.111402_br0090) 2020; 28 Mao (10.1016/j.jcp.2022.111402_br0270) 2021; 447 Karpuk (10.1016/j.jcp.2022.111402_br0460) Monfort (10.1016/j.jcp.2022.111402_br0280) 2017 Godlewski (10.1016/j.jcp.2022.111402_br0350) 1996 Jagtap (10.1016/j.jcp.2022.111402_br0370) 2020; 476 Patel (10.1016/j.jcp.2022.111402_br0220) 2022; 449 Shin (10.1016/j.jcp.2022.111402_br0160) Zucker (10.1016/j.jcp.2022.111402_br0320) 2002 Raissi (10.1016/j.jcp.2022.111402_br0010) 2019; 378 bin Waheed (10.1016/j.jcp.2022.111402_br0100) 2021 Jagtap (10.1016/j.jcp.2022.111402_br0060) 2020; 365 Magiera (10.1016/j.jcp.2022.111402_br0250) 2020; 409 Bezgin (10.1016/j.jcp.2022.111402_br0260) 2021; 437 Hall (10.1016/j.jcp.2022.111402_br0210) 1981 Jagtap (10.1016/j.jcp.2022.111402_br0050) 2020; 28 Jagtap (10.1016/j.jcp.2022.111402_br0450) Haghighat (10.1016/j.jcp.2022.111402_br0110) 2021; 379 Kharazmi (10.1016/j.jcp.2022.111402_br0140) 2021; 374 Liepmann (10.1016/j.jcp.2022.111402_br0310) 2001 Hu (10.1016/j.jcp.2022.111402_br0240) Raissi (10.1016/j.jcp.2022.111402_br0020) Jagtap (10.1016/j.jcp.2022.111402_br0360) 2020; 404 Mao (10.1016/j.jcp.2022.111402_br0030) 2020; 360 Bayliss (10.1016/j.jcp.2022.111402_br0200) 1982; 48 Byrd (10.1016/j.jcp.2022.111402_br0430) 1995; 16 Anderson (10.1016/j.jcp.2022.111402_br0190) 1995 |
| References_xml | – volume: 409 year: 2020 ident: 10.1016/j.jcp.2022.111402_br0250 article-title: Constraint-aware neural networks for Riemann problems publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2020.109345 – volume: 447 year: 2021 ident: 10.1016/j.jcp.2022.111402_br0270 article-title: Deepm&mnet for hypersonics: predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2021.110698 – start-page: 223 year: 2005 ident: 10.1016/j.jcp.2022.111402_br0340 article-title: Vanishing viscosity solutions of nonlinear hyperbolic systems publication-title: Ann. Math. doi: 10.4007/annals.2005.161.223 – volume: 476 issue: 2239 year: 2020 ident: 10.1016/j.jcp.2022.111402_br0370 article-title: Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks publication-title: Proc. R. Soc. A doi: 10.1098/rspa.2020.0334 – volume: 43 start-page: A3055 issue: 5 year: 2021 ident: 10.1016/j.jcp.2022.111402_br0440 article-title: Understanding and mitigating gradient flow pathologies in physics-informed neural networks publication-title: SIAM J. Sci. Comput. doi: 10.1137/20M1318043 – volume: 447 year: 2021 ident: 10.1016/j.jcp.2022.111402_br0080 article-title: Parallel physics-informed neural networks via domain decomposition publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2021.110683 – year: 1999 ident: 10.1016/j.jcp.2022.111402_br0300 – volume: 360 year: 2020 ident: 10.1016/j.jcp.2022.111402_br0030 article-title: Physics-informed neural networks for high-speed flows publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2019.112789 – volume: 48 start-page: 182 issue: 2 year: 1982 ident: 10.1016/j.jcp.2022.111402_br0200 article-title: Far field boundary conditions for compressible flows publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(82)90046-8 – ident: 10.1016/j.jcp.2022.111402_br0180 – start-page: 375 year: 2017 ident: 10.1016/j.jcp.2022.111402_br0280 article-title: A deep learning approach to identifying shock locations in turbulent combustion tensor fields – year: 1995 ident: 10.1016/j.jcp.2022.111402_br0190 – year: 1996 ident: 10.1016/j.jcp.2022.111402_br0350 – volume: 367 start-page: 1026 issue: 6481 year: 2020 ident: 10.1016/j.jcp.2022.111402_br0040 article-title: Hidden fluid mechanics: learning velocity and pressure fields from flow visualizations publication-title: Science doi: 10.1126/science.aaw4741 – ident: 10.1016/j.jcp.2022.111402_br0240 – volume: 39 start-page: 68 issue: 1 year: 2022 ident: 10.1016/j.jcp.2022.111402_br0070 article-title: A physics-informed neural network for quantifying the microstructural properties of polycrystalline nickel using ultrasound data: a promising approach for solving inverse problems publication-title: IEEE Signal Process. Mag. doi: 10.1109/MSP.2021.3118904 – volume: 28 start-page: 11618 issue: 8 year: 2020 ident: 10.1016/j.jcp.2022.111402_br0090 article-title: Physics-informed neural networks for inverse problems in nano-optics and metamaterials publication-title: Opt. Express doi: 10.1364/OE.384875 – volume: vol. 325 year: 2016 ident: 10.1016/j.jcp.2022.111402_br0330 article-title: Hyperbolic Conservation Laws in Continuum Physics – ident: 10.1016/j.jcp.2022.111402_br0020 – start-page: 45 year: 1981 ident: 10.1016/j.jcp.2022.111402_br0210 article-title: Implementation of nonreflective boundary condition at the outflow boundary – year: 2021 ident: 10.1016/j.jcp.2022.111402_br0100 article-title: Pinneik: Eikonal solution using physics-informed neural networks publication-title: Comput. Geosci. – volume: 16 start-page: 1190 issue: 5 year: 1995 ident: 10.1016/j.jcp.2022.111402_br0430 article-title: A limited memory algorithm for bound constrained optimization publication-title: SIAM J. Sci. Comput. doi: 10.1137/0916069 – ident: 10.1016/j.jcp.2022.111402_br0160 – volume: 365 year: 2020 ident: 10.1016/j.jcp.2022.111402_br0060 article-title: Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2020.113028 – volume: 449 year: 2022 ident: 10.1016/j.jcp.2022.111402_br0220 article-title: Thermodynamically consistent physics-informed neural networks for hyperbolic systems publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2021.110754 – ident: 10.1016/j.jcp.2022.111402_br0420 – volume: 394 start-page: 136 year: 2019 ident: 10.1016/j.jcp.2022.111402_br0120 article-title: Adversarial uncertainty quantification in physics-informed neural networks publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2019.05.027 – volume: 404 year: 2020 ident: 10.1016/j.jcp.2022.111402_br0360 article-title: Adaptive activation functions accelerate convergence in deep and physics-informed neural networks publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2019.109136 – ident: 10.1016/j.jcp.2022.111402_br0410 – start-page: 265 year: 2016 ident: 10.1016/j.jcp.2022.111402_br0400 article-title: Tensorflow: a system for large-scale machine learning – volume: 378 start-page: 686 year: 2019 ident: 10.1016/j.jcp.2022.111402_br0010 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: 28 start-page: 2002 issue: 5 year: 2020 ident: 10.1016/j.jcp.2022.111402_br0050 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: 127 issue: 12 year: 2020 ident: 10.1016/j.jcp.2022.111402_br0290 article-title: Inverting shock-wave temperatures via artificial neural networks publication-title: J. Appl. Phys. doi: 10.1063/1.5139992 – volume: 248 year: 2022 ident: 10.1016/j.jcp.2022.111402_br0150 article-title: Deep learning of inverse water waves problems using multi-fidelity data: application to Serre–Green–Naghdi equations publication-title: Ocean Eng. doi: 10.1016/j.oceaneng.2022.110775 – volume: 374 year: 2021 ident: 10.1016/j.jcp.2022.111402_br0140 article-title: hp-vpinns: variational physics-informed neural networks with domain decomposition publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2020.113547 – volume: 1 issue: 1 year: 2020 ident: 10.1016/j.jcp.2022.111402_br0230 article-title: Limitations of physics informed machine learning for nonlinear two-phase transport in porous media publication-title: J. Mach. Learn. Model. Comput. doi: 10.1615/JMachLearnModelComput.2020033905 – volume: 915 year: 2021 ident: 10.1016/j.jcp.2022.111402_br0130 article-title: Flow over an espresso cup: inferring 3-d velocity and pressure fields from tomographic background oriented schlieren via physics-informed neural networks publication-title: J. Fluid Mech. doi: 10.1017/jfm.2021.135 – volume: 437 year: 2021 ident: 10.1016/j.jcp.2022.111402_br0260 article-title: A data-driven physics-informed finite-volume scheme for nonclassical undercompressive shocks publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2021.110324 – volume: 379 year: 2021 ident: 10.1016/j.jcp.2022.111402_br0110 article-title: A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2021.113741 – year: 2002 ident: 10.1016/j.jcp.2022.111402_br0320 – ident: 10.1016/j.jcp.2022.111402_br0460 – year: 2021 ident: 10.1016/j.jcp.2022.111402_br0170 article-title: Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for pdes publication-title: IMA J. Numer. Anal. – ident: 10.1016/j.jcp.2022.111402_br0450 – volume: 18 start-page: 1 year: 2018 ident: 10.1016/j.jcp.2022.111402_br0390 article-title: Automatic differentiation in machine learning: a survey publication-title: J. Mach. Learn. Res. – year: 2001 ident: 10.1016/j.jcp.2022.111402_br0310 – start-page: 249 year: 2010 ident: 10.1016/j.jcp.2022.111402_br0380 article-title: Understanding the difficulty of training deep feedforward neural networks |
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| SubjectTerms | Aerospace engineering Aerospace vehicles Compressible flow Computational physics Density gradients Elastic waves Euler-Lagrange equation Inverse problems Neural networks Schlieren photography Shock waves Supersonic flow |
| Title | Physics-informed neural networks for inverse problems in supersonic flows |
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