Meta-learning PINN loss functions

DOI10.1016/j.jcp.2022.111121OpenAlexW3181235980MaRDI QIDQ2139042

Kenji Kawaguchi, Apostolos F. Psaros, George Em. Karniadakis

Publication date: 17 May 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.05544

zbMATH Keywords

meta-learningphysics-informed neural networksmeta-learned loss function

Mathematics Subject Classification ID

Artificial intelligence (68Txx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical analysis (65-XX)

Related Items (13)

A-PINN: auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations ⋮ Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part I: 1D Problems ⋮ VC-PINN: variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient ⋮ A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks ⋮ Phase-field DeepONet: physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionals ⋮ Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: error analysis and algorithms ⋮ Uncertainty quantification in scientific machine learning: methods, metrics, and comparisons ⋮ A metalearning approach for physics-informed neural networks (PINNs): application to parameterized PDEs ⋮ Physics-informed neural network methods based on Miura transformations and discovery of new localized wave solutions ⋮ Loss-attentional physics-informed neural networks ⋮ Learning Specialized Activation Functions for Physics-Informed Neural Networks ⋮ PINN training using biobjective optimization: the trade-off between data loss and residual loss ⋮ Optimization of physics-informed neural networks for solving the nolinear Schrödinger equation

Uses Software

• Adam
• DeepXDE
• DARTS
• NSFnets
• hp-VPINNs

Cites Work

• \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
• nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications
• B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
• NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations
• Parallel physics-informed neural networks via domain decomposition
• A composite neural network that learns from multi-fidelity data: application to function approximation and inverse PDE problems
• Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
• DeepXDE: A Deep Learning Library for Solving Differential Equations

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