# Sparse Identification of Nonlinear Dynamics with Conformal Prediction

arXiv: https://arxiv.org/abs/2507.11739 · HTML: https://mlsanity.com/paper/2507.11739/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 52 references that are in the map.
- First posted on arXiv 15 Jul 2025.

## Builds on (most cited first, 24 of 24)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [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)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Predictive Inference Is Free with the Jackknife+-after-Bootstrap](https://mlsanity.com/paper/2002.09025/) (2020)
- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Data](https://mlsanity.com/paper/2009.08810/) (2020)
- [Predictive Inference with Feature Conformal Prediction](https://mlsanity.com/paper/2210.00173/) (2022)
- [Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics](https://mlsanity.com/paper/2302.13271/) (2023)
- [Benchmarking sparse system identification with low-dimensional chaos](https://mlsanity.com/paper/2302.10787/) (2023)
- [Bayesian System ID: Optimal management of parameter, model, and measurement uncertainty](https://mlsanity.com/paper/2003.02359/) (2020)
- [Bayesian differential programming for robust systems identification under uncertainty](https://mlsanity.com/paper/2004.06843/) (2020)
- [Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discovery](https://mlsanity.com/paper/2301.12649/) (2023)
- [Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data](https://mlsanity.com/paper/2402.15357/) (2024)
- [VENI, VINDy, VICI: a generative reduced-order modeling framework with uncertainty quantification](https://mlsanity.com/paper/2405.20905/) (2024)
- [Safe Physics-Informed Machine Learning for Dynamics and Control](https://mlsanity.com/paper/2504.12952/) (2025)
- [Statistical Mechanics of Dynamical System Identification](https://mlsanity.com/paper/2403.01723/) (2024)
- [EKF-SINDy: Empowering the extended Kalman filter with sparse identification of nonlinear dynamics](https://mlsanity.com/paper/2404.07536/) (2024)

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

- [Towards a data-scale independent regulariser for robust sparse identification of non-linear dynamics](https://mlsanity.com/paper/2603.05201/) (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)
- [PSI-SINDy: Post-Selection Inference for Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2610.11486/) (2026)

## Abstract (arXiv)

The Sparse Identification of Nonlinear Dynamics (SINDy) is a method for discovering nonlinear dynamical system models from data. Quantifying uncertainty in SINDy models is essential for assessing their reliability, particularly in safety-critical applications. While various uncertainty quantification methods exist for SINDy, including Bayesian and ensemble approaches, this work explores the integration of Conformal Prediction, a framework that can provide valid prediction intervals with coverage guarantees based on minimal assumptions like data exchangeability. We introduce three applications of conformal prediction with Ensemble-SINDy (E-SINDy): (1) quantifying uncertainty in time series prediction, (2) model selection based on library feature importance, and (3) quantifying the uncertainty of identified model coefficients using feature conformal prediction. We demonstrate the three applications on stochastic predator-prey dynamics and several chaotic dynamical systems. We show that conformal prediction methods integrated with E-SINDy can reliably achieve desired target coverage for time series forecasting, effectively quantify feature importance, and produce more robust uncertainty intervals for model coefficients, even under non-Gaussian noise, compared to standard E-SINDy coefficient estimates.