Adaptive Correction for Ensuring Conservation Laws in Neural Operators

ArXi:2505.24579v2 Announce Type: replace Physical laws, such as the conversation of mass and momentum, are fundamental principles in many physical systems. Neural operators have achieved promising performance in learning the solutions to those systems, but often fail to ensure conservation. Existing methods typically enforce strict conservation via hand-crafted post-processing or architectural constraints, leading to limited model flexibility and adaptability.