DDPS | ‘DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein
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.
Bio: Z. Zhang received his B.S. degree and Ph.D. degree in mathematics from Tsinghua University, Beijing, P.R. China, in 2006 and 2011, respectively. After his graduation, he was a postdoctoral scholar at the California Institute of Technology from 2011 to 2015. He joined the University of Hong Kong as an Assistant Professor in 2015 and became an Associate Professor in 2021. Dr. Zhang’s research interests are scientific computation. Research topics include uncertainty quantification (UQ), i.e. numerical methods for stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs), and numerical methods for partial differential equations (PDEs) arising from quantum chemistry, wave propagation, multiscale porous media, nonlinear filtering, data assimilation, and stochastic fluid dynamics. Recently, he is also working on deep learning methods for solving SDEs and PDEs.
DDPS webinar: https://www.librom.net/ddps.html
💻 LLNL News: https://www.llnl.gov/news
📲 Instagram: / livermore_lab
🤳 Facebook: / livermore.lab
🐤 Twitter: / livermore_lab
About LLNL: Lawrence Livermore National Laboratory has a mission of strengthening the United States’ security through development and application of world-class science and technology to: 1) enhance the nation’s defense, 2) reduce the global threat from terrorism and weapons of mass destruction, and 3) respond with vision, quality, integrity and technical excellence to scientific issues of national importance. Learn more about LLNL: https://www.llnl.gov/.
LLNL-VIDEO-860342