Physical Constraint Embedded Neural Networks for inference and noise regulation
This addresses the challenge of applying neural networks to experimental data with physical constraints, offering incremental improvements for domain-specific applications in physics and engineering.
The paper tackled the problem of neural networks violating physics when trained on small, noisy datasets by embedding symmetries and conservation laws into architectures, resulting in accurate symmetry inference without prior knowledge and improved symbolic regression that outperformed a baseline.
Neural networks often require large amounts of data to generalize and can be ill-suited for modeling small and noisy experimental datasets. Standard network architectures trained on scarce and noisy data will return predictions that violate the underlying physics. In this paper, we present methods for embedding even--odd symmetries and conservation laws in neural networks and propose novel extensions and use cases for physical constraint embedded neural networks. We design an even--odd decomposition architecture for disentangling a neural network parameterized function into its even and odd components and demonstrate that it can accurately infer symmetries without prior knowledge. We highlight the noise resilient properties of physical constraint embedded neural networks and demonstrate their utility as physics-informed noise regulators. Here we employed a conservation of energy constraint embedded network as a physics-informed noise regulator for a symbolic regression task. We showed that our approach returns a symbolic representation of the neural network parameterized function that aligns well with the underlying physics while outperforming a baseline symbolic regression approach.