Variational physics informed neural networks: the role of quadratures and test functions

DOI10.1007/s10915-022-01950-4OpenAlexW3196894304MaRDI QIDQ2162334

Stefano Berrone, Moreno Pintore, Claudio Canuto

Publication date: 5 August 2022

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.02035

zbMATH Keywords

convergence ratesquadrature formulasinf-sup conditionelliptic problemsa priori error estimatevariational physics informed neural networks

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Numerical optimization and variational techniques (65K10) A priori estimates in context of PDEs (35B45) Variational methods for second-order elliptic equations (35J20) PDEs in connection with control and optimization (35Q93) Numerical analysis (65-XX) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (4)

Randomized neural network with Petrov-Galerkin methods for solving linear and nonlinear partial differential equations ⋮ Finite element interpolated neural networks for solving forward and inverse problems ⋮ An overview on deep learning-based approximation methods for partial differential equations ⋮ Solving PDEs by variational physics-informed neural networks: an a posteriori error analysis

Uses Software

• DiffSharp
• Adam
• PhyGeoNet
• VarNet
• Stiff-PINN
• hp-VPINNs

Cites Work

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• Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
• Transfinite interpolation over implicitly defined sets
• On the approximation of functions by tanh neural networks

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