The invariant distribution, which is characterized by the stationary Fokker-Planck equation, is an important object in the study of randomly perturbed dynamical systems. Traditional numerical methods for computing the invariant distribution based on the Fokker-Planck equation, such as finite difference or finite element methods, are limited to low-dimensional systems due to the curse of dimensionality. In this work, we propose a deep learning based method to compute the generalized potential, i.e. the negative logarithm of the invariant distribution multiplied by the noise. The idea of the method is to learn a decomposition of the force field, as specified by the Fokker-Planck equation, from the noisy trajectory data.



 



In the second part of the talk, we introduce a similar method to learn the quasi-potential for dynamical systems perturbed by small noise. The effectiveness of the proposed methods is demonstrated by numerical examples.

21 Jul 2023
11:00am - 12:00pm
Where
Room 2302 (Lifts 17/18)
Speakers/Performers
Prof. Weiqing REN
National University of Singapore
Organizer(S)
Department of Mathematics
Contact/Enquiries
Payment Details
Audience
Alumni, Faculty and staff, PG students, UG students
Language(s)
English
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