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%  HYKE-Hwarang 세미나
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일시: 2026년 8월 21일 (금) 16:00 - 17:00
장소: 27동 116호
연사:  ZHOU, Xiang (City Univ. of Hong Kong)
강연 제목 : Weak Form Makes Generative Model Stronger for Fokker-Planck equation.
초록 : Current deep learning‑based generative models, such as normalizing flows, have provided a new approach for solving high‑dimensional PDEs of probability density functions and, once trained, can generate independent and identically distributed (i.i.d.) samples very efficiently. However, one fundamental numerical bottleneck lies in the Jacobian determinant and the invertibility constraint. In this work, we introduce the Weak Generative Sampler (https://doi.org/10.1137/24M1665271), which employs a weak form of the Fokker–Planck equation to construct a novel loss function with randomized test functions, thereby circumventing the need for mini‑max optimization in traditional weak adversarial formulations. Our method requires neither the computationally intensive calculation of the Jacobian determinant nor the invertibility of the transformation map. A key component of our framework is the adaptively chosen family of test functions—specifically, Gaussian kernels whose centers are tied to the generated data samples. Experimental results on several benchmark examples demonstrate the effectiveness and scalability of our approach, which achieves low computational cost and exhibits excellent capability in exploring multiple metastable states.