標(biāo)題：Computational Quantum Mechanics in Phase Space — An Attempt to Break the Curse of Dimensionality
報(bào)告時(shí)間：2024年04月03日(星期三)10:00-11:00
報(bào)告地點(diǎn)：人民大街校區(qū)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院二樓會(huì)議室
主講人：邵嗣烘
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告內(nèi)容簡(jiǎn)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(jiǎn)介：
邵嗣烘，北京大學(xué)博雅特聘教授，畢業(yè)于北京大學(xué)數(shù)學(xué)科學(xué)學(xué)院并獲得理學(xué)學(xué)士和博士學(xué)位，先后到訪(fǎng)過(guò)北卡羅萊那大學(xué)夏洛特分校，香港科技大學(xué)，普林斯頓大學(xué)、塞維利亞大學(xué)和香港中文大學(xué)等。主講《數(shù)學(xué)分析I-III》，《數(shù)學(xué)模型》，《高維數(shù)值方法》，《組合最優(yōu)化算法》，《譜方法》和《計(jì)算流體力學(xué)》等課程。主要開(kāi)展面向智能、量子和計(jì)算的交叉融合研究，落腳點(diǎn)在基礎(chǔ)的數(shù)學(xué)理論和高效的算法設(shè)計(jì)，強(qiáng)調(diào)離散數(shù)學(xué)結(jié)構(gòu)的設(shè)計(jì)、分析和應(yīng)用。具體研究領(lǐng)域包括：高維數(shù)值方法、離散建模與組合優(yōu)化、計(jì)算量子力學(xué)、圖譜理論及算法、微分方程數(shù)值解和計(jì)算復(fù)雜性等，是國(guó)家級(jí)高層次領(lǐng)軍人才，獲國(guó)家自然科學(xué)基金面上和青年等項(xiàng)目資助。2019年入選北京智源人工智能研究院“智源青年科學(xué)家”。2020年獲北京大學(xué)優(yōu)秀博士學(xué)位論文指導(dǎo)老師。2021年獲北京大學(xué)黃廷芳/信和青年杰出學(xué)者獎(jiǎng)。曾獲中國(guó)計(jì)算數(shù)學(xué)學(xué)會(huì)優(yōu)秀青年論文一等獎(jiǎng)，北京大學(xué)學(xué)術(shù)類(lèi)創(chuàng)新獎(jiǎng)，北京大學(xué)優(yōu)秀博士學(xué)位論文三等獎(jiǎng)，寶潔教師獎(jiǎng)和北京大學(xué)優(yōu)秀班主任等。
