Stabilizing PDE--ML coupled systems
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Abstract (arXiv)
A long-standing obstacle in the use of machine-learnt surrogates with larger PDE systems is the onset of instabilities when solved numerically. Efforts towards ameliorating these have mostly concentrated on improving the accuracy of the surrogates or imbuing them with additional structure, and have garnered limited success. In this article, we study a prototype problem and draw insights that can help with more complex systems. In particular, we focus on a viscous Burgers'-ML system and, after identifying the cause of the instabilities, prescribe strategies to stabilize the coupled system. To improve the accuracy of the stabilized system, we next explore methods based on the Mori--Zwanzig formalism.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 7 of its 27 references that are in the map. First posted on arXiv 24 Jun 2025.
Builds on
7 of 27 references.
References · 7
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
- 2018On the Spectral Bias of Neural Networkscited by 1,341
- 2018Deep learning to represent sub-grid processes in climate modelscited by 156
- 2023Multi-stage Neural Networks: Function Approximator of Machine Precisioncited by 48
- 2018Deep Neural Networks for Data-Driven Turbulence Modelscited by 35
- 2020A Fortran-Keras Deep Learning Bridge for Scientific Computingcited by 16
- 2023A Multifidelity deep operator network approach to closure for multiscale systemscited by 11
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Citing papers per year: 2026: 1.
1 paper.