Adaptive sampling points based multi-scale residual network for solving partial differential equations (Q6585372)

scientific article; zbMATH DE number 7894800

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English	Adaptive sampling points based multi-scale residual network for solving partial differential equations	scientific article; zbMATH DE number 7894800

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instance of

scholarly article

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title

Adaptive sampling points based multi-scale residual network for solving partial differential equations (English)

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9 August 2024

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zbMATH Keywords

PINNs

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multi-scale Resnet

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adaptive sampling

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gradient-enhanced

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PDEs

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MaRDI profile type

Publication

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cites work

Solving high-dimensional partial differential equations using deep learning

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NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations

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A non-intrusive neural network model order reduction algorithm for parameterized parabolic PDEs

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Local randomized neural networks with discontinuous Galerkin methods for diffusive-viscous wave equation

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RPINNs: rectified-physics informed neural networks for solving stationary partial differential equations

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A super-convergence analysis of the Poisson solver with octree grids and irregular domains

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Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations

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DGM: a deep learning algorithm for solving partial differential equations

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

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Weak adversarial networks for high-dimensional 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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DeepXDE: A Deep Learning Library for Solving Differential Equations

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Physics-informed neural networks for 2nd order ODEs with sharp gradients

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Physics informed neural networks: a case study for gas transport problems

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Self-adaptive physics-informed neural networks

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Meta-learning PINN loss functions

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Adaptive transfer learning for PINN

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Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks

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Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

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Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems

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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

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Parallel physics-informed neural networks via domain decomposition

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Improved deep neural networks with domain decomposition in solving partial differential equations

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A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

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

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Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

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Physics and equality constrained artificial neural networks: application to forward and inverse problems with multi-fidelity data fusion

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When and why PINNs fail to train: a neural tangent kernel perspective

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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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On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks

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Deep Learning: An Introduction for Applied Mathematicians

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Linearized Learning with Multiscale Deep Neural Networks for Stationary Navier-Stokes Equations with Oscillatory Solutions

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Evaluation of various high‐order‐accuracy schemes with and without flux limiters

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An adaptive Rothe method for nonlinear reaction-diffusion systems

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published in

Computers & Mathematics with Applications

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Identifiers

DOI

10.1016/j.camwa.2024.06.029

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6585372