# System Identification Through Lipschitz Regularized Deep Neural Networks

arXiv: https://arxiv.org/abs/2009.03288 · HTML: https://mlsanity.com/paper/2009.03288/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2020.

## Built on by (most cited first, 3 of 3)

- [Synthesis of Stabilizing Recurrent Equilibrium Network Controllers](https://mlsanity.com/paper/2204.00122/) (2022)
- [A Neural Network Ensemble Approach to System Identification](https://mlsanity.com/paper/2110.08382/) (2021)
- [Parameter Inference of Time Series by Delay Embeddings and Learning Differentiable Operators](https://mlsanity.com/paper/2203.06269/) (2022)

## Abstract (arXiv)

In this paper we use neural networks to learn governing equations from data. Specifically we reconstruct the right-hand side of a system of ODEs dotx(t) = f(t, x(t)) directly from observed uniformly time-sampled data using a neural network. In contrast with other neural network based approaches to this problem, we add a Lipschitz regularization term to our loss function. In the synthetic examples we observed empirically that this regularization results in a smoother approximating function and better generalization properties when compared with non-regularized models, both on trajectory and non-trajectory data, especially in presence of noise. In contrast with sparse regression approaches, since neural networks are universal approximators, we don't need any prior knowledge on the ODE system. Since the model is applied component wise, it can handle systems of any dimension, making it usable for real-world data.