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Neural networks often require large amounts of data to generalize and can beill-suited for modeling small and noisy experimental datasets. Standard networkarchitectures trained on scarce and noisy data will return predictions thatviolate the underlying physics. In this paper, we present methods for embeddingeven--odd symmetries and conservation laws in neural networks and propose novelextensions and use cases for physical constraint embedded neural networks. Wedesign an even--odd decomposition architecture for disentangling a neuralnetwork parameterized function into its even and odd components and demonstratethat it can accurately infer symmetries without prior knowledge. We highlightthe noise resilient properties of physical constraint embedded neural networksand demonstrate their utility as physics-informed noise regulators. Here weemployed a conservation of energy constraint embedded network as aphysics-informed noise regulator for a symbolic regression task. We showed thatour approach returns a symbolic representation of the neural networkparameterized function that aligns well with the underlying physics whileoutperforming a baseline symbolic regression approach.

Physical Constraint Embedded Neural Networks for inference and noise regulation