Papers › Sparse learning of stochastic dynamic equations
Sparse learning of stochastic dynamic equations
Lorenzo Boninsegna, Feliks Nüske, Cecilia Clementi
With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems, which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastics SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy, and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential, and the projected dynamics of a two-dimensional diffusion process.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Denoising | Darmstadt Noise Dataset | SINDy | PSNR | 81 | #1 of 10 | Archive leaderboard | report |
| Sparse Learning | ImageNet | SINDy | Top-1 Accuracy | 6 | #9 of 9 | Archive leaderboard | report |
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