Learning viscoelasticity models from indirect data using deep neural networks

DOI10.1016/j.cma.2021.114124OpenAlexW3199752695MaRDI QIDQ2246355

Kailai Xu, Eric Darve, Jeff Burghardt, Alexandre M. Tartakovsky

Publication date: 16 November 2021

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2021.114124

zbMATH Keywords

neural networksviscoelasticitydeep learninggeomechanics and multi-phase flow

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Nonlinear constitutive equations for materials with memory (74D10) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) PDE constrained optimization (numerical aspects) (49M41)

Related Items (6)

RI-IGABEM for 3D viscoelastic problems with body force ⋮ Model-free data-driven viscoelasticity in the frequency domain ⋮ Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations ⋮ JAX-FEM: a differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science ⋮ The anisotropic graph neural network model with multiscale and nonlinear characteristic for turbulence simulation ⋮ Simulation of Maxwell equation based on an ADI approach and integrated radial basis function-generalized moving least squares (IRBF-GMLS) method with reduced order algorithm based on proper orthogonal decomposition

Uses Software

• LBFGS-B
• SciPy
• Python
• TensorFlow
• DiffSharp
• ForwardDiff
• Adept
• PyTorch
• AMGCL

Cites Work

• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
• The implicit function theorem. History, theory, and applications
• Learning constitutive relations from indirect observations using deep neural networks
• Linear and nonlinear programming.
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• Learning constitutive relations using symmetric positive definite neural networks
• Isogeometric collocation method for the fractional Laplacian in the 2D bounded domain
• Solving inverse problems in stochastic models using deep neural networks and adversarial training
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• AMGCL: an efficient, flexible, and extensible algebraic multigrid implementation
• An inverse model and mathematical solution for inferring viscoelastic properties and dynamic deformations of heterogeneous structures
• Convergence of the generalized-\(\alpha\) scheme for constrained mechanical systems
• Inverse Modeling
• Optimal Solvers for PDE-Constrained Optimization
• Line search algorithms with guaranteed sufficient decrease
• Large-Scale PDE-Constrained Optimization: An Introduction
• Inverse Problem Theory and Methods for Model Parameter Estimation
• Scaling of temperature- and stress-dependent viscosity convection
• A Limited Memory Algorithm for Bound Constrained Optimization
• Solving high-dimensional partial differential equations using deep learning
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