標題：Computational Quantum Mechanics in Phase Space — An Attempt to Break the Curse of Dimensionality
報告時間：2024年04月03日(星期三)10:00-11:00
報告地點：人民大街校區數學與統計學院二樓會議室
主講人：邵嗣烘
主辦單位：數學與統計學院
報告內容簡介：
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.
主講人簡介：
邵嗣烘，北京大學博雅特聘教授，畢業于北京大學數學科學學院并獲得理學學士和博士學位，先后到訪過北卡羅萊那大學夏洛特分校，香港科技大學，普林斯頓大學、塞維利亞大學和香港中文大學等。主講《數學分析I-III》，《數學模型》，《高維數值方法》，《組合最優化算法》，《譜方法》和《計算流體力學》等課程。主要開展面向智能、量子和計算的交叉融合研究，落腳點在基礎的數學理論和高效的算法設計，強調離散數學結構的設計、分析和應用。具體研究領域包括：高維數值方法、離散建模與組合優化、計算量子力學、圖譜理論及算法、微分方程數值解和計算復雜性等，是國家級高層次領軍人才，獲國家自然科學基金面上和青年等項目資助。2019年入選北京智源人工智能研究院“智源青年科學家”。2020年獲北京大學優秀博士學位論文指導老師。2021年獲北京大學黃廷芳/信和青年杰出學者獎。曾獲中國計算數學學會優秀青年論文一等獎，北京大學學術類創新獎，北京大學優秀博士學位論文三等獎，寶潔教師獎和北京大學優秀班主任等。
