期刊
JOURNAL OF CHEMICAL PHYSICS
卷 148, 期 24, 页码 -出版社
AIP Publishing
DOI: 10.1063/1.5018409
关键词
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资金
- National Science Foundation [CHE-1265929, CHE-1738990, PHY-1427654]
- Welch Foundation [C-1570]
- Big-Data Private-Cloud Research Cyberinfrastructure MRI-award (NSF) [CNS-1338099]
- Division Of Chemistry
- Direct For Mathematical & Physical Scien [1265929] Funding Source: National Science Foundation
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. Published by AIP Publishing.
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