Sparse learning of stochastic dynamical equations.

By L. Boninsegna, Feliks Nuske, Cecilia Clementi. 2017

279 citations recorded by the source corpus.

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 stochastic 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.

Subfields: Artificial Intelligence, Molecular Biology, Statistical and Nonlinear Physics

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Citations in the corpus

Learning stable and predictive structures in kinetic systems (2018, methodology): “Even though we are not aware of any work that proposes this precise implementation, the idea of using `1-penalized procedures for model inference has been used extensively Boninsegna et al. [2018], Brunton et al.”
Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control (2021, methodology): “Extensions of the SINDy algorithm include accounting for control inputs [43] and rational functions [44, 45], enforcing known conservation laws and symmetries [27], promoting stability [46], improved noise robustness through the integral formulation [34, 47–51], generalizations for stochastic dynami”
Deep learning of physical laws from scarce data (2020, background): “…such as ﬂuid ﬂows (13, 14), structural systems (15, 16), biological and chemical systems (17–19), active matter (20), predictive control of nonlinear dynamics (21), multi-time-scale systems (22), a predator-prey system (23), and stochastic processes (24), just naming a few among many others.”
Identifying Causal Structure in Large-Scale Kinetic Systems (2018, background): “Brunton et al. [2016], Wu et al. [2014], for example, propose to apply `1-penalization, see the baseline implemented in the Section 5.1. Mikkelsen and Hansen [2017] introduce an extension called AIM, which combines the `1-penalization with direct minimization of the nonlinear optimization problem th”