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Journal Article

Data-Driven Discovery of Stochastic Differential Equations

Authors

Wang,  Yasen
External Organizations;

Fang,  Huazhen
External Organizations;

Jin,  Junyang
External Organizations;

Ma,  Guijun
External Organizations;

He,  Xin
External Organizations;

Dai,  Xing
External Organizations;

Yue,  Zuogong
External Organizations;

Cheng,  Cheng
External Organizations;

Zhang,  Hai-Tao
External Organizations;

Pu,  Donglin
External Organizations;

Wu,  Dongrui
External Organizations;

Yuan,  Ye
External Organizations;

Gonçalves,  Jorge
External Organizations;

/persons/resource/Juergen.Kurths

Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

Ding,  Han
External Organizations;

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Citation

Wang, Y., Fang, H., Jin, J., Ma, G., He, X., Dai, X., Yue, Z., Cheng, C., Zhang, H.-T., Pu, D., Wu, D., Yuan, Y., Gonçalves, J., Kurths, J., Ding, H. (2022): Data-Driven Discovery of Stochastic Differential Equations. - Engineering, 17, 244-252.
https://doi.org/10.1016/j.eng.2022.02.007


Cite as: https://publications.pik-potsdam.de/pubman/item/item_27972
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.