2 results
Search Results
Now showing 1 - 2 of 2
- ItemData-Driven Discovery of Stochastic Differential Equations(Beijing : Engineering Sciences Press, 2022) Wang, Yasen; Fang, Huazhen; Jin, Junyang; Ma, Guijun; He, Xin; Dai, Xing; Yue, Zuogong; Cheng, Cheng; Zhang, Hai-Tao; Pu, Donglin; Wu, Dongrui; Yuan, Ye; Gonçalves, Jorge; Kurths, Jürgen; Ding, HanStochastic 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.
- ItemDynamical network size estimation from local observations([London] : IOP, 2020) Tang, Xiuchuan; Huo, Wei; Yuan, Ye; Li, Xiuting; Shi, Ling; Kurths, JürgenHere we present a method to estimate the total number of nodes of a network using locally observed response dynamics. The algorithm has the following advantages: (a) it is data-driven. Therefore it does not require any prior knowledge about the model; (b) it does not need to collect measurements from multiple stimulus; and (c) it is distributed as it uses local information only, without any prior information about the global network. Even if only a single node is measured, the exact network size can be correctly estimated using a single trajectory. The proposed algorithm has been applied to both linear and nonlinear networks in simulation, illustrating the applicability to real-world physical networks. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.