2022, Volume 17, Issue 10
Engineering >> 2022, Volume 17, Issue 10 doi: 10.1016/j.eng.2022.02.007
Data-Driven Discovery of Stochastic Differential Equations
a School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
b State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
c Department of Mechanical Engineering, University of Kansas, Lawrence, KS 66045, USA
d HUST-Wuxi Research Institute, Wuxi 214174, China
e Key Laboratory of Image Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China
f Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK
g Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Belvaux 4367, Luxembourg
h Department of Physics, Humboldt University of Berlin, Berlin 12489, Germany
i Department of Complexity Science, Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
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Abstract
Stochastic differential equations (SDEs) are mathematical models that are widely used to describe complex processes or phenomena perturbed by random noise from different sources. The identification of SDEs governing a system is often a challenge because of the inherent strong stochasticity of data and the complexity of the system’s dynamics. The practical utility of existing parametric approaches for identifying SDEs is usually limited by insufficient data resources. This study presents a novel framework for identifying SDEs by leveraging the sparse Bayesian learning (SBL) technique to search for a parsimonious, yet physically necessary representation from the space of candidate basis functions. More importantly, we use the analytical tractability of SBL to develop an efficient way to formulate the linear regression problem for the discovery of SDEs that requires considerably less time-series data. The effectiveness of the proposed framework is demonstrated using real data on stock and oil prices, bearing variation, and wind speed, as well as simulated data on well-known stochastic dynamical systems, including the generalized Wiener process and Langevin equation. This framework aims to assist specialists in extracting
stochastic mathematical models from random phenomena in the natural sciences, economics, and engineering fields for analysis, prediction, and decision making.
Keywords
Data-driven method ; System identification ; Sparse Bayesian learning ; Stochastic differential equations ; Random phenomena
SupplementaryMaterials
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