DAS-PINNs: a deep adaptive sampling method for solving high-dimensional partial differential equations (Q2681099)

scientific article; zbMATH DE number 7652779

Language	Label	Description	Also known as
English	DAS-PINNs: a deep adaptive sampling method for solving high-dimensional partial differential equations	scientific article; zbMATH DE number 7652779

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instance of

scholarly article

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title

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

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Journal of Computational Physics

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publication date

10 February 2023

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full work available at URL

https://arxiv.org/abs/2112.14038

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zbMATH Keywords

deep learning

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numerical approximation of PDEs

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adaptive sampling

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deep generative models

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describes a project that uses

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Solving high-dimensional partial differential equations using deep learning

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The Dawning of a New Era in Applied Mathematics

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

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

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\textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition

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DGM: a deep learning algorithm for solving partial differential equations

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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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fPINNs: Fractional Physics-Informed Neural Networks

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Neural‐network‐based approximations for solving partial differential equations

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Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations

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PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain

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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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Weak adversarial networks for high-dimensional partial differential equations

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Foundations of Data Science

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High-Dimensional Probability

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Adaptive deep density approximation for Fokker-Planck equations

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SelectNet: self-paced learning for high-dimensional partial differential equations

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Convergence of Adaptive Finite Element Methods

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Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs

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Finite elements and fast iterative solvers. With applications in incompressible fluid dynamics

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VAE-KRnet and Its Applications to Variational Bayes

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Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling

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Optimization Methods for Large-Scale Machine Learning

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Approximation by superpositions of a sigmoidal function

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Multilayer feedforward networks are universal approximators

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Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems

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Active learning based sampling for high-dimensional nonlinear partial differential equations

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From Knothe's Transport to Brenier's Map and a Continuation Method for Optimal Transport

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A tutorial on the cross-entropy method

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DeepXDE: A Deep Learning Library for Solving Differential Equations

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A collection of 2D elliptic problems for testing adaptive grid refinement algorithms

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Identifiers

Mathematics Subject Classification ID

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10.1016/J.JCP.2022.111868

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Sitelinks

Mathematics(1 entry)

mardi Publication:2681099