High dimensional partial differential equations (PDE) are challenging to compute by traditional mesh-based methods especially when their solutions have large gradients or concentrations at unknown locations. Mesh-free methods are more appealing; however, they remain slow and expensive when a long time and resolved computation is necessary. In this talk, we present DeepParticle, an integrated deep learning (DL), optimal transport (OT), and interacting particle (IP) approach through a case study of Fisher-Kolmogorov-Petrovsky-Piskunov front speeds in incompressible flows. PDE analysis reduces the problem to the computation of the principal eigenvalue of an advection-diffusion operator. Stochastic representation via the Feynman-Kac formula makes possible a genetic interacting particle algorithm that evolves particle distribution to a large time-invariant measure from which the front speed is extracted. The invariant measure is parameterized by a physical parameter (the Peclet number). We learn this family of invariant measures by training a physically parameterized deep neural network on affordable data from IP computation at moderate Peclet numbers, then predict at a larger Peclet number when IP computation is expensive. Our methodology extends to a more general context of deep learning stochastic particle dynamics. For instance, we can learn and generate aggregation patterns in Keller-Segel chemotaxis systems.

6月23日
3pm - 4pm
地點
Room 4503 (Lifts 25/26)
講者/表演者
Prof. Zhiwen ZHANG
The University of Hong Kong
主辦單位
Department of Mathematics
聯絡方法
付款詳情
對象
Alumni, Faculty and staff, PG students, UG students
語言
英語
其他活動
5月24日
研討會, 演講, 講座
IAS / School of Science Joint Lecture - Confinement Controlled Electrochemistry: Nanopore beyond Sequencing
Abstract Nanopore electrochemistry refers to the promising measurement science based on elaborate pore structures, which offers a well-defined geometric confined space to adopt and characterize sin...
5月13日
研討會, 演講, 講座
IAS / School of Science Joint Lecture – Expanding the Borders of Chemical Reactivity
Abstract The lecture will demonstrate how it has been possible to expand the borders of cycloadditions beyond the “classical types of cycloadditions” applying organocatalytic activation principles....