# LES-SINDy: Laplace-Enhanced Sparse Identification of Nonlinear Dynamical Systems

arXiv: https://arxiv.org/abs/2411.01719 · HTML: https://mlsanity.com/paper/2411.01719/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 45 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 17 of 17)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [Best Subset Selection via a Modern Optimization Lens](https://mlsanity.com/paper/1507.03133/) (2015)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [LNO: Laplace Neural Operator for Solving Differential Equations](https://mlsanity.com/paper/2303.10528/) (2023)
- [Data-driven discovery of intrinsic dynamics](https://mlsanity.com/paper/2108.05928/) (2021)
- [Learning Dissipative Dynamics in Chaotic Systems](https://mlsanity.com/paper/2106.06898/) (2021)
- [A Unified Framework for Sparse Relaxed Regularized Regression: SR3](https://mlsanity.com/paper/1807.05411/) (2018)
- [Neural Laplace: Learning diverse classes of differential equations in the Laplace domain](https://mlsanity.com/paper/2206.04843/) (2022)
- [SINDy with Control: A Tutorial](https://mlsanity.com/paper/2108.13404/) (2021)
- [Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2405.07839/) (2024)

## Built on by (most cited first, 4 of 4)

- [Ultra Fast PDE Solving via Physics Guided Few-step Diffusion](https://mlsanity.com/paper/2602.03627/) (2026)
- [Application of Reduced-Order Models for Temporal Multiscale Representations in the Prediction of Dynamical Systems](https://mlsanity.com/paper/2510.18925/) (2025)
- [MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data](https://mlsanity.com/paper/2604.00333/) (2026)
- [Symbolic Graph Networks for Robust PDE Discovery from Noisy Sparse Data](https://mlsanity.com/paper/2603.22380/) (2026)

## Abstract (arXiv)

Sparse Identification of Nonlinear Dynamical Systems (SINDy) is a powerful tool for the data-driven discovery of governing equations. However, it encounters challenges when modeling complex dynamical systems involving high-order derivatives or discontinuities, particularly in the presence of noise. These limitations restrict its applicability across various fields in applied mathematics and physics. To mitigate these, we propose Laplace-Enhanced SparSe Identification of Nonlinear Dynamical Systems (LES-SINDy). By transforming time-series measurements from the time domain to the Laplace domain using the Laplace transform and integration by parts, LES-SINDy enables more accurate approximations of derivatives and discontinuous terms. It also effectively handles unbounded growth functions and accumulated numerical errors in the Laplace domain, thereby overcoming challenges in the identification process. The model evaluation process selects the most accurate and parsimonious dynamical systems from multiple candidates. Experimental results across diverse ordinary and partial differential equations show that LES-SINDy achieves superior robustness, accuracy, and parsimony compared to existing methods.