INO: Invariant Neural Operators for Learning Complex Physical Systems with Momentum Conservation
This work addresses the challenge of incorporating physical laws into neural operators for complex material behaviors, offering improved generalizability and performance for researchers in computational physics and machine learning.
The authors tackled the problem of learning physical systems with neural operators while preserving fundamental conservation laws, resulting in a model that automatically guarantees translation and rotation invariance and achieves state-of-the-art accuracy and efficiency.
Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator applications has thus far been data-driven, which neglects the intrinsic preservation of fundamental physical laws in data. In this paper, we introduce a novel integral neural operator architecture, to learn physical models with fundamental conservation laws automatically guaranteed. In particular, by replacing the frame-dependent position information with its invariant counterpart in the kernel space, the proposed neural operator is by design translation- and rotation-invariant, and consequently abides by the conservation laws of linear and angular momentums. As applications, we demonstrate the expressivity and efficacy of our model in learning complex material behaviors from both synthetic and experimental datasets, and show that, by automatically satisfying these essential physical laws, our learned neural operator is not only generalizable in handling translated and rotated datasets, but also achieves state-of-the-art accuracy and efficiency as compared to baseline neural operator models.