  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.
