Towards fast weak adversarial training to solve high dimensional parabolic partial differential equations using XNODE-WAN

DOI10.1016/j.jcp.2022.111233OpenAlexW4226311057WikidataQ114163300 ScholiaQ114163300MaRDI QIDQ2671351

Paul Valsecchi Oliva, Yue Wu, Hao Ni, Cuiyu He

Publication date: 3 June 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.07812

zbMATH Keywords

parabolic partial differential equationgenerative adversarial networkneural ordinary differential equationweak adversarial network

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Parabolic equations and parabolic systems (35Kxx)

Related Items (1)

Weak adversarial networks for solving forward and inverse problems involving 2D incompressible Navier-Stokes equations

Uses Software

• DeepXDE
• torchdiffeq
• DGM

Cites Work

• Unnamed Item
• Orientation-matching minimization for image denoising and inpainting
• Weak adversarial networks for high-dimensional partial differential equations
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• DGM: a deep learning algorithm for solving partial differential equations
• Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs
• An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• A Primer on Neural Network Models for Natural Language Processing
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• Solving high-dimensional partial differential equations using deep learning
• Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations
• DeepXDE: A Deep Learning Library for Solving Differential Equations
• Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
• Computational Methods for Option Pricing

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