# Physical Constraint Embedded Neural Networks for inference and noise regulation

arXiv: https://arxiv.org/abs/2105.09146 · HTML: https://mlsanity.com/paper/2105.09146/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 19 May 2021.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Physical Symmetries Embedded in Neural Networks](https://mlsanity.com/paper/1904.08991/) (2019)
- [Variational Integrator Networks for Physically Structured Embeddings](https://mlsanity.com/paper/1910.09349/) (2019)
- [Physics-Aware Neural Networks for Distribution System State Estimation](https://mlsanity.com/paper/1903.09669/) (2019)
- [Joint Parameter Discovery and Generative Modeling of Dynamic Systems](https://mlsanity.com/paper/2103.10905/) (2021)

## Built on by (most cited first, 1 of 1)

- [Discovering an interpretable mathematical expression for a full wind-turbine wake with artificial intelligence enhanced symbolic regression](https://mlsanity.com/paper/2406.00695/) (2024)

## Abstract (arXiv)

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.