Data-Driven Discovery of Stochastic Differential Equations
Yasen Wang,
Huazhen Fang,
Junyang Jin,
Guijun Ma,
Xin He,
Xing Dai,
Zuogong Yue,
Cheng Cheng,
Hai-Tao Zhang,
Donglin Pu,
Dongrui Wu,
Ye Yuan,
Jorge Gonçalves,
Jürgen Kurths,
Han Ding
Affiliations
Yasen Wang
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
Huazhen Fang
Department of Mechanical Engineering, University of Kansas, Lawrence, KS 66045, USA
Junyang Jin
HUST-Wuxi Research Institute, Wuxi 214174, China
Guijun Ma
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
Xin He
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Xing Dai
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; HUST-Wuxi Research Institute, Wuxi 214174, China
Zuogong Yue
Key Laboratory of Image Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China
Cheng Cheng
Key Laboratory of Image Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China
Hai-Tao Zhang
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China
Donglin Pu
HUST-Wuxi Research Institute, Wuxi 214174, China
Dongrui Wu
Key Laboratory of Image Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China
Ye Yuan
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Corresponding author.
Jorge Gonçalves
Key Laboratory of Image Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK; Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Belvaux 4367, Luxembourg
Jürgen Kurths
Department of Physics, Humboldt University of Berlin, Berlin 12489, Germany; Department of Complexity Science, Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
Han Ding
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China; HUST-Wuxi Research Institute, Wuxi 214174, China
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.
