INO: Invariant Neural Operators for Learning Complex Physical Systems with Momentum Conservation

Understand

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.