# Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data

arXiv: https://arxiv.org/abs/2402.15357 · HTML: https://mlsanity.com/paper/2402.15357/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 46 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 11 of 11)

- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [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)
- [On the Convergence of the SINDy Algorithm](https://mlsanity.com/paper/1805.06445/) (2018)
- [Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Data](https://mlsanity.com/paper/2009.08810/) (2020)
- [A Unified Framework for Sparse Relaxed Regularized Regression: SR3](https://mlsanity.com/paper/1807.05411/) (2018)
- [On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression](https://mlsanity.com/paper/2012.01937/) (2020)
- [Benchmarking sparse system identification with low-dimensional chaos](https://mlsanity.com/paper/2302.10787/) (2023)
- [SINDy with Control: A Tutorial](https://mlsanity.com/paper/2108.13404/) (2021)
- [Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discovery](https://mlsanity.com/paper/2301.12649/) (2023)
- [Dynamical System Identification, Model Selection and Model Uncertainty Quantification by Bayesian Inference](https://mlsanity.com/paper/2401.16943/) (2024)

## Built on by (most cited first, 15 of 15)

- [BINDy -- Bayesian identification of nonlinear dynamics with reversible-jump Markov-chain Monte-Carlo](https://mlsanity.com/paper/2408.08062/) (2024)
- [Statistical Mechanics of Dynamical System Identification](https://mlsanity.com/paper/2403.01723/) (2024)
- [Sparse Identification of Nonlinear Dynamics with Conformal Prediction](https://mlsanity.com/paper/2507.11739/) (2025)
- [Data-driven Discovery of Digital Twins in Biomedical Research](https://mlsanity.com/paper/2508.21484/) (2025)
- [Physics-Informed Neural Networks for Biological 2D+t Reaction-Diffusion Systems](https://mlsanity.com/paper/2604.18548/) (2026)
- [Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification](https://mlsanity.com/paper/2604.20141/) (2026)
- [Machine learning for cerebral blood vessels' malformations](https://mlsanity.com/paper/2411.16349/) (2024)
- [BLADE: Bayesian Langevin Active Discovery with Replica Exchange for Identification of Complex Systems](https://mlsanity.com/paper/2503.02983/) (2025)
- [VeMo: A Lightweight Data-Driven Approach to Model Vehicle Dynamics](https://mlsanity.com/paper/2510.07447/) (2025)
- [A joint optimization approach to identifying sparse dynamics using least squares kernel collocation](https://mlsanity.com/paper/2511.18555/) (2025)
- [From STLS to Projection-based Dictionary Selection in Sparse Regression for System Identification](https://mlsanity.com/paper/2512.14404/) (2025)
- [Open datasets and machine learning for two-phase heat transfer: a review following a spatial-temporal taxonomy](https://mlsanity.com/paper/2605.23037/) (2026)
- [How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit](https://mlsanity.com/paper/2606.12182/) (2026)
- [An Introduction to Sparse Identification of Nonlinear Dynamics for Engineering Applications](https://mlsanity.com/paper/2607.15077/) (2026)
- [Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers](https://mlsanity.com/paper/2608.02662/) (2026)

## Abstract (arXiv)

We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to speed up computation. The resulting method, Bayesian-SINDy, not only quantifies uncertainty in the parameters estimated but also is more robust when learning the correct model from limited and noisy data. Using both synthetic and real-life examples such as Lynx-Hare population dynamics, we demonstrate the effectiveness of the new framework in learning correct model equations and compare its computational and data efficiency with existing methods. Because Bayesian-SINDy can quickly assimilate data and is robust against noise, it is particularly suitable for biological data and real-time system identification in control. Its probabilistic framework also enables the calculation of information entropy, laying the foundation for an active learning strategy.