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.
| Repository | Role | Ran |
|---|---|---|
| i207m/pinnacle | canonical | 0 of 11 |
| Function | Status | Where 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") |
Some links come from the archived Papers with Code dataset (CC BY-SA 4.0): attribution and licence.
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.
The same record, over MCP at https://syntology.ai/mcp:
get_harvested_code_for_paper("2306.08827")
get_code_for_paper("2306.08827")
have("2306.08827")
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