LR-RaNN: Lipschitz Regularized Randomized Neural Networks for System Identification

Chunyang Liao
Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:15-29, 2026.

Abstract

Approximating the governing equations from data is of great importance in studying the dynamical systems. In this paper, we propose randomized neural networks (RaNN) to investigate the problem of approximating the governing equations of the system of ordinary differential equations. In contrast with other neural networks based methods, training randomized neural network solves a least-squares problem, which significant reduces the computational complexity. Moreover, we introduce a regularization term to the loss function, which improves the generalization ability. We provide an estimation of Lipschitz constant for our proposed model and analyze its generalization error. Our empirical experiments on synthetic datasets demonstrate that our proposed method achieves good generalization performance and enjoys easy implementation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v321-liao26a, title = {LR-RaNN: Lipschitz Regularized Randomized Neural Networks for System Identification}, author = {Liao, Chunyang}, booktitle = {Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025)}, pages = {15--29}, year = {2026}, editor = {Bernardez Gil, Guillermo and Black, Mitchell and Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Garcı́a-Rodondo, Ińes and Holtz, Chester and Kotak, Mit and Kvinge, Henry and Mishne, Gal and Papillon, Mathilde and Pouplin, Alison and Rainey, Katie and Rieck, Bastian and Telyatnikov, Lev and Yeats, Eric and Wang, Qingsong and Wang, Yusu and Wayland, Jeremy}, volume = {321}, series = {Proceedings of Machine Learning Research}, month = {01--02 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v321/main/assets/liao26a/liao26a.pdf}, url = {https://proceedings.mlr.press/v321/liao26a.html}, abstract = {Approximating the governing equations from data is of great importance in studying the dynamical systems. In this paper, we propose randomized neural networks (RaNN) to investigate the problem of approximating the governing equations of the system of ordinary differential equations. In contrast with other neural networks based methods, training randomized neural network solves a least-squares problem, which significant reduces the computational complexity. Moreover, we introduce a regularization term to the loss function, which improves the generalization ability. We provide an estimation of Lipschitz constant for our proposed model and analyze its generalization error. Our empirical experiments on synthetic datasets demonstrate that our proposed method achieves good generalization performance and enjoys easy implementation.} }
Endnote
%0 Conference Paper %T LR-RaNN: Lipschitz Regularized Randomized Neural Networks for System Identification %A Chunyang Liao %B Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025) %C Proceedings of Machine Learning Research %D 2026 %E Guillermo Bernardez Gil %E Mitchell Black %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Ińes Garcı́a-Rodondo %E Chester Holtz %E Mit Kotak %E Henry Kvinge %E Gal Mishne %E Mathilde Papillon %E Alison Pouplin %E Katie Rainey %E Bastian Rieck %E Lev Telyatnikov %E Eric Yeats %E Qingsong Wang %E Yusu Wang %E Jeremy Wayland %F pmlr-v321-liao26a %I PMLR %P 15--29 %U https://proceedings.mlr.press/v321/liao26a.html %V 321 %X Approximating the governing equations from data is of great importance in studying the dynamical systems. In this paper, we propose randomized neural networks (RaNN) to investigate the problem of approximating the governing equations of the system of ordinary differential equations. In contrast with other neural networks based methods, training randomized neural network solves a least-squares problem, which significant reduces the computational complexity. Moreover, we introduce a regularization term to the loss function, which improves the generalization ability. We provide an estimation of Lipschitz constant for our proposed model and analyze its generalization error. Our empirical experiments on synthetic datasets demonstrate that our proposed method achieves good generalization performance and enjoys easy implementation.
APA
Liao, C.. (2026). LR-RaNN: Lipschitz Regularized Randomized Neural Networks for System Identification. Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), in Proceedings of Machine Learning Research 321:15-29 Available from https://proceedings.mlr.press/v321/liao26a.html.

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