Solving inverse problems in stochastic models using deep neural networks and adversarial training

DOI10.1016/j.cma.2021.113976zbMath1506.65017OpenAlexW3166275749MaRDI QIDQ2237477

Eric Darve, Kailai Xu

Publication date: 27 October 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.2021.113976

zbMATH Keywords

neural networksautomatic differentiationadversarial training

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Probabilistic models, generic numerical methods in probability and statistics (65C20) Neural nets and related approaches to inference from stochastic processes (62M45)

Related Items (11)

Physics constrained learning for data-driven inverse modeling from sparse observations ⋮ Scientific machine learning through physics-informed neural networks: where we are and what's next ⋮ Isogeometric collocation method for the fractional Laplacian in the 2D bounded domain ⋮ Coupling of peridynamics and inverse finite element method for shape sensing and crack propagation monitoring of plate structures ⋮ On the use of neural networks for full waveform inversion ⋮ Uncertainty quantification in scientific machine learning: methods, metrics, and comparisons ⋮ Inferring parameters of pyramidal neuron excitability in mouse models of Alzheimer's disease using biophysical modeling and deep learning ⋮ A Mesh-Free Algorithm to Solve an Inverse Source Problem for Degenerate Two-Dimensional Parabolic Equation from Final Observations ⋮ Resolution-independent generative models based on operator learning for physics-constrained Bayesian inverse problems ⋮ AI in computational mechanics and engineering sciences ⋮ Learning viscoelasticity models from indirect data using deep neural networks

Uses Software

• L-BFGS-B
• L-BFGS
• LBFGS-B
• DiffSharp
• Adam
• ADCME
• Wasserstein GAN
• MMD GAN
• f-GAN

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Learning constitutive relations from indirect observations using deep neural networks
• On the limited memory BFGS method for large scale optimization
• An introduction to MCMC for machine learning
• Tutorial on maximum likelihood estimation
• A tutorial on Fisher information
• On the empirical estimation of integral probability metrics
• Circumventing the solution of inverse problems in mechanics through deep learning: application to elasticity imaging
• Adversarial uncertainty quantification in physics-informed neural networks
• 10.1162/153244302760185252
• Divergence measures based on the Shannon entropy
• Algorithm 778: L-BFGS-B
• On Choosing and Bounding Probability Metrics
• Large Sample Properties of Weighted Monte Carlo Estimators
• Data-Driven Identification of Parametric Partial Differential Equations
• Some Properties of CIR Processes
• Perception as Bayesian Inference

This page was built for publication: Solving inverse problems in stochastic models using deep neural networks and adversarial training