Variational Physics-Informed Neural Networks For Solving Partial Differential Equations | Paper Citation Record

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Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems cites this paper.

Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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Deep learning applied to computational mechanics: A comprehensive review, state of the art, and the classics cites this paper.

Deep learning applied to computational mechanics: A comprehensive review, state of the art, and the classics Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 285

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Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems cites this paper.

Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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FE-PINNs: finite-element-based physics-informed neural networks for surrogate modeling cites this paper.

FE-PINNs: finite-element-based physics-informed neural networks for surrogate modeling Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 14

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A data-driven learned discretization approach in finite volume schemes for hyperbolic conservation laws and varying boundary conditions cites this paper.

A data-driven learned discretization approach in finite volume schemes for hyperbolic conservation laws and varying boundary conditions Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 23

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DeepVIVONet: Using deep neural operators to optimize sensor locations with application to vortex-induced vibrations cites this paper.

DeepVIVONet: Using deep neural operators to optimize sensor locations with application to vortex-induced vibrations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 24

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PINN-FEM: A Hybrid Approach for Enforcing Dirichlet Boundary Conditions in Physics-Informed Neural Networks cites this paper.

PINN-FEM: A Hybrid Approach for Enforcing Dirichlet Boundary Conditions in Physics-Informed Neural Networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 18

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Convex Physics Informed Neural Networks for the Monge-Amp\`ere Optimal Transport Problem cites this paper.

Convex Physics Informed Neural Networks for the Monge-Amp\`ere Optimal Transport Problem Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 17

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The Finite Element Neural Network Method: One Dimensional Study cites this paper.

The Finite Element Neural Network Method: One Dimensional Study Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 10

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Combining physics-based and data-driven models: advancing the frontiers of research with Scientific Machine Learning cites this paper.

Combining physics-based and data-driven models: advancing the frontiers of research with Scientific Machine Learning Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 130

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Sub-Sequential Physics-Informed Learning with State Space Model cites this paper.

Sub-Sequential Physics-Informed Learning with State Space Model Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 20

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Development and optimization of physics-informed neural networks for solving partial differential equations cites this paper.

Development and optimization of physics-informed neural networks for solving partial differential equations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 5

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DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modeling cites this paper.

DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modeling Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 18

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A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations cites this paper.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 19

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PINNs Algorithmic Framework for Simulation of Nonlinear Burgers' Type Models cites this paper.

PINNs Algorithmic Framework for Simulation of Nonlinear Burgers' Type Models Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 23

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Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs cites this paper.

Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 34

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Rank Inspired Neural Network for solving linear partial differential equations cites this paper.

Rank Inspired Neural Network for solving linear partial differential equations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 10

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Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks cites this paper.

Numerical simulation of transient heat conduction with moving heat source using Physics Informed Neural Networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 20

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A posteriori analysis of neural network approximations cites this paper.

A posteriori analysis of neural network approximations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 16

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Discontinuity-aware KAN-based physics-informed neural networks cites this paper.

Discontinuity-aware KAN-based physics-informed neural networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 29

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Data-Driven Adaptive Gradient Recovery for Unstructured Finite Volume Computations cites this paper.

Data-Driven Adaptive Gradient Recovery for Unstructured Finite Volume Computations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 24

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A Learning-based Domain Decomposition Method cites this paper.

A Learning-based Domain Decomposition Method Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 11

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Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems cites this paper.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 7

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Physics-informed Multiresolution Wavelet Neural Network Method for Solving Partial Differential Equations cites this paper.

Physics-informed Multiresolution Wavelet Neural Network Method for Solving Partial Differential Equations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 16

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Prediction error certification for PINNs: Theory, computation, and application to Stokes flow cites this paper.

Prediction error certification for PINNs: Theory, computation, and application to Stokes flow Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 30

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A Practitioner's Guide to Kolmogorov-Arnold Networks cites this paper.

A Practitioner's Guide to Kolmogorov-Arnold Networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 4

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HYCO: A Formalism for Hybrid-Cooperative PDE Modelling cites this paper.

HYCO: A Formalism for Hybrid-Cooperative PDE Modelling Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 4

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Python library supporting Discrete Variational Formulations and training solutions with Collocation-based Robust Variational Physics Informed Neural Networks (DVF-CRVPINN) cites this paper.

Python library supporting Discrete Variational Formulations and training solutions with Collocation-based Robust Variational Physics Informed Neural Networks (DVF-CRVPINN) Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 12

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Robust Deep FOSLS for Transmission Problems cites this paper.

Robust Deep FOSLS for Transmission Problems Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 7

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On Physics-Based Loss Scaling for MF-PINNs applied to the neutron diffusion equation cites this paper.

On Physics-Based Loss Scaling for MF-PINNs applied to the neutron diffusion equation Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 23

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Physics-informed neural networks for form-finding of unilateral membrane structures cites this paper.

Physics-informed neural networks for form-finding of unilateral membrane structures Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 27

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Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 33

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Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks cites this paper.

Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 33

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Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks cites this paper.

Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 17

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jNO: A JAX Library for Neural Operator and Foundation Model Training cites this paper.

jNO: A JAX Library for Neural Operator and Foundation Model Training Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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NPSolver: Neural Poisson Solver with Iterative Physics Supervision cites this paper.

NPSolver: Neural Poisson Solver with Iterative Physics Supervision Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 12

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Towards a Foundation Model for the Martian Atmosphere cites this paper.

Towards a Foundation Model for the Martian Atmosphere Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 141

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A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentials cites this paper.

A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentials Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 44

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Exact Boundary Enforcement Along Implicit Geometries for Physics-Informed, Deep Learning Problems in Continuum Mechanics cites this paper.

Exact Boundary Enforcement Along Implicit Geometries for Physics-Informed, Deep Learning Problems in Continuum Mechanics Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 32

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Learning light scattering from operator parameter spaces to Galerkin-consistent solution spaces cites this paper.

Learning light scattering from operator parameter spaces to Galerkin-consistent solution spaces Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 14

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INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities cites this paper.

INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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Neural network approximation in discrete dual norms with adaptive test spaces cites this paper.

Neural network approximation in discrete dual norms with adaptive test spaces Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 32

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Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning cites this paper.

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs cites this paper.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws cites this paper.

HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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Double screening in the training dynamics of variational physics-informed neural networks for heterogeneous coupled parabolic systems cites this paper.

Double screening in the training dynamics of variational physics-informed neural networks for heterogeneous coupled parabolic systems Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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Efficient Weak-Entropy PINN for Solving Hyperbolic Conservation Laws cites this paper.

Efficient Weak-Entropy PINN for Solving Hyperbolic Conservation Laws Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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