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Paper · 2306.08827 · 2023

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

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 11 functions out of this paper's own repositories and ran 0 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
i207m/pinnacle canonical 0 of 11
FunctionStatusWhere it lives
accuracy Not yet run i207m/pinnacle/deepxde/metrics.py
code served (permissive licence) · get_code("88820f35c43353d2")
hessian Not yet run i207m/pinnacle/deepxde/gradients.py
code served (permissive licence) · get_code("6c180f0e3803ab62")
jacobian Not yet run i207m/pinnacle/deepxde/gradients.py
code served (permissive licence) · get_code("22a4e56acdba95d0")
l1_loss Not yet run i207m/pinnacle/fbpinns/losses.py
code served (permissive licence) · get_code("3a51bac0fdd1fd7d")
l2_loss Not yet run i207m/pinnacle/fbpinns/losses.py
code served (permissive licence) · get_code("7664a629a07157a1")
l2_rel_err Not yet run i207m/pinnacle/fbpinns/losses.py
code served (permissive licence) · get_code("33cd904bcb4227f1")
l2_relative_error Not yet run i207m/pinnacle/deepxde/metrics.py
code served (permissive licence) · get_code("32c851eacf652fb9")
mean_absolute_error Not yet run i207m/pinnacle/deepxde/losses.py
code served (permissive licence) · get_code("b43df4ef25c604d7")
mean_absolute_percentage_error Not yet run i207m/pinnacle/deepxde/losses.py
code served (permissive licence) · get_code("642a817822586843")
mean_squared_error Not yet run i207m/pinnacle/deepxde/losses.py
code served (permissive licence) · get_code("e2fd023945751163")
nanl2_relative_error Not yet run i207m/pinnacle/deepxde/metrics.py
code served (permissive licence) · get_code("bf03a7838198a933")

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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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