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Nonparametric inference of stochastic differential equations based on the relative entropy rate
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  • Min Dai,
  • Jinqiao Duan,
  • jianyu Hu,
  • Xiangjun Wang
Min Dai
Wuhan University of Technology

Corresponding Author:[email protected]

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Jinqiao Duan
Illinois Institute of Technology
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jianyu Hu
Huazhong University of Science and Technology
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Xiangjun Wang
Huazhong University of Science and Technology - Wuchang Campus
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The information detection of complex systems from data is currently undergoing a revolution,driven by the emergence of big data and machine learning methodology. Discovering governingequations and quantifying dynamical properties of complex systems are among central challenges. Inthis work, we devise a nonparametric approach to learn the relative entropy rate from observationsof stochastic differential equations with different drift functions. The estimator corresponding tothe relative entropy rate then is presented via the Gaussian process kernel theory. Meanwhile, thisapproach enables to extract the governing equations. We illustrate our approach in several examples.Numerical experiments show the proposed approach performs well for rational drift functions, notonly polynomial drift functions.
12 Nov 2021Submitted to Mathematical Methods in the Applied Sciences
14 Nov 2021Submission Checks Completed
14 Nov 2021Assigned to Editor
19 Nov 2021Reviewer(s) Assigned
10 Jul 2022Review(s) Completed, Editorial Evaluation Pending
10 Jul 2022Editorial Decision: Revise Minor
19 Jul 20221st Revision Received
19 Jul 2022Submission Checks Completed
19 Jul 2022Assigned to Editor
19 Jul 2022Reviewer(s) Assigned
12 Aug 2022Review(s) Completed, Editorial Evaluation Pending
12 Aug 2022Editorial Decision: Accept