Zu Chongzhi Mathematics Research Seminar

Date and Time (China standard time): Wednesday, February 12, 10:30 am – 11:30 am

Location: WDR 1100

Zoom: 994 3592 1412, Passcode: dkumath

Title: Random Batch Methods and Kinetic Monte Carlo for Interacting Particle Systems with Lévy Noise

Speaker: Yuliang Wang

Abstract: The Random Batch Method (RBM) is an efficient algorithm simulating large-scale interacting particle systems comprising N indistinguishable particles, which model diverse phenomena in natural and social sciences, ranging from molecular dynamics to collective behavior in biological and social contexts. The central idea of RBM involves randomly selecting small batches of size p<<N, where particles within a batch interact with each other over a short time. Consequently, the computational cost per time step is reduced from O(N^2) to O(pN), while maintaining an unbiased approximation of the force or velocity field in the original system. Remarkably, RBM with replacement has a fundamental equivalence with the well-established Kinetic Monte Carlo (KMC) method commonly used in particle simulations. Moreover, in many real-world scenarios, the underlying random fluctuations are non-Gaussian, particularly in contexts where heavy-tailed data distributions arise. Such phenomena call for Lévy noise, which accommodates jumps and extreme variations. The RBM framework seamlessly extends to handle systems driven by Lévy noise, offering robust theoretical guarantees for accuracy and convergence. In this talk, I will discuss the theoretical foundations and practical applications of RBMs, with a focus on the RBM with replacement (RBM-r) and RBM for interacting particle systems with Lévy noise (RBM- Lévy).

Bio: Yuliang Wang is currently a Ph.D. student at Shanghai Jiao Tong University under the supervision of Prof. Lei Li. Before that, he obtained his Bachelor’s degree in 2020 from Shanghai Jiao Tong University (Zhiyuan Honor Program). His research mainly focuses on applied and computational mathematics, including analysis and design of various random algorithms, functional optimization, interacting particle systems, particle filters, generative models, etc.