Discrete gradient flow approximations of high dimensional evolution partial differential equations via deep neural networks

DOI10.1016/j.cnsns.2022.106893OpenAlexW4305071438WikidataQ115358519 ScholiaQ115358519MaRDI QIDQ2108629

Asterios Tsiourvas, Michail Loulakis, Emmanuil H. Georgoulis

Publication date: 20 December 2022

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.00290

zbMATH Keywords

partial differential equationsnumerical analysisdeep neural networks

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Probabilistic methods, stochastic differential equations (65Cxx)

Uses Software

• DGM

Cites Work

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• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• DGM: a deep learning algorithm for solving partial differential equations
• PFNN: a penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
• The Sinkhorn–Knopp Algorithm: Convergence and Applications
• The Variational Formulation of the Fokker--Planck Equation
• Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions
• Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions
• On Atomistic-to-Continuum Couplings without Ghost Forces in Three Dimensions

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