报告题目：Computational Quantum Mechanics in Phase Space — An Attempt to Break the Curse of Dimensionality
报 告 人：邵嗣烘 教授
所在单位：北京大学
报告时间：2024年4月3日 10:00-12:00
报告地点：正新楼209
校内联系人：贾继伟 jiajiwei@jlu.edu.cn
报告摘要：As a permanent goal and a tireless direction of computational mathematics, developing an accurate and stable high-dimensional solver has been attracting more and more attentions in recent years due to the urgent need in e.g., quantum science and high energy density physics. This talk represents our preliminary attempts to break the curse of dimensionality (CoD) which poses a fundamental obstacle to high-dimensional numerical simulations. More specifically, we will report some recent progress in both grid-based deterministic and particle-based stochastic methods for simulating high-dimensional Wigner quantum dynamics. A massively parallel solver, termed the characteristic-spectral-mixed scheme, is proposed to evolve the Wigner-Coulomb system in 6-D phase space. Within particle-based stochastic simulations, CoD, causing the unattainable exponential wall, reappears as the numerical sign problem. To this end, we propose a SPA (Stationary Phase Approximation) + SPADE (Sequential-clustering Particle Annihilation via Discrepancy Estimation) strategy is to overcome the numerical sign problem where it has been translated into a NP-hard problem that may have approximate solutions. Simulations of the proton-electron couplings in 6-D and 12-D phase space demonstrate the accuracy and the efficiency of our particle-based stochastic methods.
报告人简介： 邵嗣烘，北京大学博雅特聘教授，毕业于北京大学数学科学学院并获得理学学士和博士学位，先后到访过北卡罗莱那大学夏洛特分校，香港科技大学，普林斯顿大学、塞维利亚大学和香港中文大学等。主讲《数学分析I-III》，《数学模型》，《高维数值方法》，《组合最优化算法》，《谱方法》和《计算流体力学》等课程。主要开展面向智能、量子和计算的交叉融合研究，落脚点在基础的数学理论和高效的算法设计，强调离散数学结构的设计、分析和应用。具体研究领域包括：高维数值方法、离散建模与组合优化、计算量子力学、图谱理论及算法、微分方程数值解和计算复杂性等，获国家自然科学基金杰青、优青、面上和青年等项目资助。2019年入选北京智源人工智能研究院“智源青年科学家”。2020年获北京大学优秀博士学位论文指导老师。2021年获北京大学黄廷芳/信和青年杰出学者奖。曾获中国计算数学学会优秀青年论文一等奖，北京大学学术类创新奖，北京大学优秀博士学位论文三等奖，宝洁教师奖和北京大学优秀班主任等。
