![[2602.15184] Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledge](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2602.15184] Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledge
Summary
This paper presents a framework for enhancing data efficiency and generalization in neural operators by integrating fundamental physics knowledge, improving predictive accuracy across various PDE problems.
Why It Matters
As machine learning increasingly intersects with scientific domains, this research highlights the importance of incorporating fundamental principles into models, which can lead to better performance in real-world applications. The proposed framework could significantly advance the field of scientific machine learning by addressing common challenges in data efficiency and generalization.
Key Takeaways
- The proposed multiphysics training framework improves data efficiency and predictive accuracy.
- Incorporating fundamental physics knowledge enhances the generalization of neural operators.
- The method shows consistent improvements across various dimensional PDE problems.
Computer Science > Machine Learning arXiv:2602.15184 (cs) [Submitted on 16 Feb 2026] Title:Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledge Authors:Siying Ma, Mehrdad M. Zadeh, Mauricio Soroco, Wuyang Chen, Jiguo Cao, Vijay Ganesh View a PDF of the paper titled Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledge, by Siying Ma and 4 other authors View PDF HTML (experimental) Abstract:Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While existing approaches focus primarily on learning simulations from the target PDE, they often overlook more fundamental physical principles underlying these equations. Inspired by how numerical solvers are compatible with simulations of different settings of PDEs, we propose a multiphysics training framework that jointly learns from both the original PDEs and their simplified basic forms. Our framework enhances data efficiency, reduces predictive errors, and improves out-of-distribution (OOD) generalization, particularly in scenarios involving shifts of physical parameters and synthetic-to-real transfer. Our method is architecture-agnostic and demonstrates consistent improvements in normalized root mean square error (nRMSE) across a wide range of 1D/2D/3D PDE problems. Through exten...
