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

Author name not available (Why is that?)

Publication date: 14 June 2023

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. While PINNacle does not guarantee success in all real-world scenarios, it represents a significant contribution to the field by offering a robust, diverse, and comprehensive benchmark suite that will undoubtedly foster further research and development in PINNs.

Has companion code repository: https://github.com/i207m/pinnacle

This page was built for publication: PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6440356)