Physical Constraint Embedded Neural Networks for inference and noise regulation

TL;DR

This paper introduces neural networks embedded with physical constraints like symmetries and conservation laws, improving inference accuracy and noise regulation, especially with small or noisy datasets.

Contribution

It presents novel methods for embedding physical constraints into neural networks, including an even-odd decomposition architecture and conservation law integration for noise resilience.

Findings

Accurately infers symmetries without prior knowledge.

Demonstrates noise resilience and improved inference accuracy.

Outperforms baseline symbolic regression in physics-aligned modeling.

Abstract

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.