数学科学研究所
Insitute of Mathematical Science

Applied Mathematical Seminar 63: Weak Generative Adversarial Network to Sample Invariant Distribution

Seminar| Institute of Mathematical Sciences

Time: Monday, Apirl 01th, 2024 , 16:00-17:00

Location:IMS, RS408

Speaker: Xiang Zhou, City University of Hong Kong

AbstractEfficient sampling of invariant distributions for diffusion processes has long been a significant area of research since the convergence usually takes a long time of simulation. For irreversible systems, the Metropolis adjust after the Langevin dynamics is not applicable in MCMC. Recently, deep learning-based solvers focus on determining the invariant probability  density function by using the neural networks only provides a high dimensional pdf and leaves the sampling as a separate second-stage problem. We aim to direclty generate samples of the invariant pdf which is the solution of the stationary Fokker Planck equation, without resolving the pdf.  By using the normalizing flow as the tool for sampling, our method is based on the weak formulation of the Fokker Planck equation and relies on the family of data-driven test functions to train the flow. This new weak adversarial approach has no compuation of the Jacobian determinant as in other methods and shows the state-of-the-art performance in the meta-stable systems with multiple modes.



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