# A Review of Data-Driven Discovery for Dynamic Systems

arXiv: https://arxiv.org/abs/2210.10663 · HTML: https://mlsanity.com/paper/2210.10663/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2022.

## Built on by (most cited first, 18 of 18)

- [Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis](https://mlsanity.com/paper/2503.01036/) (2025)
- [When is a System Discoverable from Data? Discovery Requires Chaos](https://mlsanity.com/paper/2511.08860/) (2025)
- [Statistical Mechanics of Dynamical System Identification](https://mlsanity.com/paper/2403.01723/) (2024)
- [Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networks](https://mlsanity.com/paper/2501.11350/) (2025)
- [Data-driven discovery of governing differential equations across physical systems](https://mlsanity.com/paper/2606.09638/) (2026)
- [Data-driven Discovery of Digital Twins in Biomedical Research](https://mlsanity.com/paper/2508.21484/) (2025)
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- [An evolutionary approach for discovering non-Gaussian stochastic dynamical systems based on nonlocal Kramers-Moyal formulas](https://mlsanity.com/paper/2409.19534/) (2024)
- [Invertible Koopman neural operator for data-driven modeling of partial differential equations](https://mlsanity.com/paper/2503.19717/) (2025)
- [Data Denoising and Derivative Estimation for Data-Driven Modeling of Nonlinear Dynamical Systems](https://mlsanity.com/paper/2509.14219/) (2025)
- [Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression](https://mlsanity.com/paper/2607.00257/) (2026)
- [Navigating Uncertainties in Machine Learning for Structural Dynamics: A Comprehensive Survey of Probabilistic and Non-Probabilistic Approaches in Forward and Inverse Problems](https://mlsanity.com/paper/2408.08629/) (2024)
- [Principled model selection for stochastic dynamics](https://mlsanity.com/paper/2501.10339/) (2025)
- [Optimizing Hard Thresholding for Sparse Model Discovery](https://mlsanity.com/paper/2504.20256/) (2025)
- [Scientific machine learning in Hydrology: a unified perspective](https://mlsanity.com/paper/2506.06308/) (2025)
- [From Data to Laws: Neural Discovery of Conservation Laws Without False Positives](https://mlsanity.com/paper/2603.20474/) (2026)
- [A Robust SINDy Autoencoder for Noisy Dynamical System Identification](https://mlsanity.com/paper/2604.04829/) (2026)
- [Watch your neighbors: Training statistically accurate chaotic systems with local phase space information](https://mlsanity.com/paper/2605.14405/) (2026)

## Abstract (arXiv)

Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations driving these complex nonlinear dynamic system using data-driven approaches. In this paper we review the current literature on data-driven discovery for dynamic systems. We provide a categorization to the different approaches for data-driven discovery and a unified mathematical framework to show the relationship between the approaches. Importantly, we discuss the role of statistics in the data-driven discovery field, describe a possible approach by which the problem can be cast in a statistical framework, and provide avenues for future work.