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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Vydáno v:	Computer methods in applied mechanics and engineering Ročník 379; s. 113741
Hlavní autoři:	Haghighat, Ehsan, Raissi, Maziar, Moure, Adrian, Gomez, Hector, Juanes, Ruben
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 01.06.2021 Elsevier BV
Témata:	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
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

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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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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