Moju: A Physics Admissibility Auditing Framework for Scientific Machine Learning Surrogates
Description
Scientific machine learning models are often checked only against governing partial differential equations. A surrogate can keep PDE residuals small while still breaking constitutive relations, for example by predicting a thermal field that does not match the diffusivity implied by the same equation. This paper presents Moju, an open-source library for physics admissibility auditing with native support for JAX and PyTorch. Moju reports governing-law residuals and constitutive consistency separately, and assigns tiered admissibility scores (HIGH, MODERATE, LOW, and NON-ADMISSIBLE) so users can see which part of the physics fails.
The study uses one-dimensional transient slab cooling with Robin convection. Seven fully connected networks are trained for 14,000 L-BFGS steps, with hidden widths from 2 to 128. All models reach at least 99.99% governing-law admissibility on the Fourier conduction residual, but constitutive admissibility spans 17.8% to 93.2%. That gap is not visible from PDE loss alone. The paper reports training trajectories, worst-point constitutive diagnostics, and agreement between training and evaluation grids within 0.5 percentage points. It also discusses how capacity relates to constitutive admissibility in this benchmark.
The Moju software is available at https://github.com/IfimoAI/moju and on PyPI as moju. Companion Colab notebooks reproduce the paper training run and a fast audit-only demo from pre-exported states.
Files
moju_ai_surrogate_OS_auditing_tool.pdf
Files
(1.6 MB)
| Name | Size | Download all |
|---|---|---|
|
md5:a4c3945b17ffd818c45de748161c5bb7
|
1.6 MB | Preview Download |
Additional details
Software
- Repository URL
- https://github.com/IfimoAI/moju
- Programming language
- Python
- Development Status
- Active
References
- Andrea Beck and Marius Kurz. A perspective on machine learning methods in turbulence modeling. GAMM-Mitteilungen, 44(1):e202100002, 2021. doi: 10.1002/gamm.202100002.
- Steven L. Brunton, Bernd R. Noack, and Pierre Sagaut. Machine learning for fluid mechanics. Annual Review of Fluid Mechanics, 52:477–508, 2020. doi: 10.1146/ annurev-fluid-010719-060214.
- Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations. In International Conference on Learning Representations (ICLR), 2021.
- Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George E. Karniadakis. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nature Machine Intelligence, 3:218–229, 2021. doi: 10.1038/s42256-021-00302-5.
- Maziar Raissi, Paris Perdikaris, and George E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686–707, 2019. doi: 10.1016/j.jcp.2018.10.045.
- Sifan Wang, Yujun Teng, and Paris Perdikaris. Understanding and mitigating gradient flow pathologies in physics-informed neural networks. SIAM Journal on Scientific Computing, 43(5):A3055–A3081, 2021. doi: 10.1137/20M1318043.
- Sifan Wang, Xinling Yu, and Paris Perdikaris. When and why PINNs fail to train: A neural tangent kernel perspective. Journal of Computational Physics, 449:110768, 2022. doi: 10.1016/j.jcp.2021.110768.