PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs

2023/06/15 by Zhongkai Hao, Jiachen Yao, Hao, Zhongkai +19 · 15 citations
Physics and Astronomy · #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2306.08827

Abstract

While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, a benchmarking tool designed to fill this gap. PINNacle provides a diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These PDEs encapsulate key challenges inherent to real-world problems, such as complex geometry, multi-scale phenomena, nonlinearity, and high dimensionality. PINNacle also offers a user-friendly toolbox, incorporating about 10 state-of-the-art PINN methods for systematic evaluation and comparison. We have conducted extensive experiments with these methods, offering insights into their strengths and weaknesses. In addition to providing a standardized means of assessing performance, PINNacle also offers an in-depth analysis to guide future research, particularly in areas such as domain decomposition methods and loss reweighting for handling multi-scale problems and complex geometry. To the best of our knowledge, it is the largest benchmark with a diverse and comprehensive evaluation that will undoubtedly foster further research in PINNs.

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• Lang-PINN: From Language to Physics-Informed Neural Networks via a Multi-Agent Framework
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• A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
• HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions
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• Re4: Scientific Computing Agent with Rewriting, Resolution, Review and Revision
• Physics-informed Multiresolution Wavelet Neural Network Method for Solving Partial Differential Equations

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