Stochastic differential equations(SDEs)are mathematical models that are widely used to describe com-plex 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 iden-tifying 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 gen-eralized 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 engi-neering fields for analysis,prediction,and decision making.

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 Gonalves;Jürgen Kurths;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;Department of Mechanical Engineering,University of Kansas,Lawrence,KS 66045,USA;HUST-Wuxi Research Institute,Wuxi 214174,China;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;g Luxembourg Centre for Systems Biomedicine,University of Luxembourg,Belvaux 4367,Luxembourg;Department of Physics,Humboldt University of Berlin,Berlin 12489,Germany;Department of Complexity Science,Potsdam Institute for Climate Impact Research,Potsdam 14473,Germany

工程（英文）

[1]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 Gonalves;Jürgen Kurths;Han Ding-.Data-Driven Discovery of Stochastic Differential Equations)[J].工程（英文）,2022(10):244-252

tractability

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