Deep finite volume method for partial differential equations (Q6615033)

scientific article; zbMATH DE number 7922813

Language	Label	Description	Also known as
English	Deep finite volume method for partial differential equations	scientific article; zbMATH DE number 7922813

Statements

instance of

scholarly article

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title

Deep finite volume method for partial differential equations (English)

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Journal of Computational Physics

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publication date

8 October 2024

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zbMATH Keywords

finite volume method

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high-dimensional PDEs

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neural network

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second order differential operator

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Learning phase field mean curvature flows with neural networks

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Q4215355

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Quasi-Monte Carlo Sampling for Solving Partial Differential Equations by Deep Neural Networks

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The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems

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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

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Failure-Informed Adaptive Sampling for PINNs

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Solving many-electron Schrödinger equation using deep neural networks

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A derivative-free method for solving elliptic partial differential equations with deep neural networks

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Q5755052

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Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions

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DeepXDE: A Deep Learning Library for Solving Differential Equations

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MIM: a deep mixed residual method for solving high-order partial differential equations

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A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations

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The Divergence Theorem

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Learning representations by back-propagating errors

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wPINNs: Weak Physics Informed Neural Networks for Approximating Entropy Solutions of Hyperbolic Conservation Laws

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PFNN: a penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries

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DGM: a deep learning algorithm for solving partial differential equations

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Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordès coefficients

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DAS-PINNs: a deep adaptive sampling method for solving high-dimensional partial differential equations

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Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

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Analysis of linear and quadratic simplicial finite volume methods for elliptic equations

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Weak adversarial networks for high-dimensional partial differential equations

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Adaptive deep neural networks methods for high-dimensional partial differential equations

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Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.JCP.2024.113307

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Sitelinks

Mathematics(1 entry)

mardi Publication:6615033