主講人：金石 上海交通大學(xué)教授

時(shí)間：2022年6月2日15：30

地點(diǎn)：騰訊會(huì)議 208 500 303

舉辦單位：數(shù)理學(xué)院

主講人介紹：金石，歐洲人文和自然科學(xué)院外籍院士和歐洲科學(xué)院院士，國(guó)際數(shù)學(xué)家大會(huì)45分鐘報(bào)告者、上海交通大學(xué)講席教授、博士生導(dǎo)師?，F(xiàn)任上海交通大學(xué)自然科學(xué)院院長(zhǎng),CSIAM會(huì)士、AMS會(huì)士、SIAM會(huì)士。曾獲馮康科學(xué)計(jì)算獎(jiǎng)、第四屆世界華人數(shù)學(xué)家大會(huì)晨興數(shù)學(xué)獎(jiǎng)銀獎(jiǎng)；在計(jì)算流體力學(xué)，動(dòng)力學(xué)方程，雙曲型守恒律方程高頻波計(jì)算，計(jì)算物理和多尺度問(wèn)題的計(jì)算方法等領(lǐng)域發(fā)表了200余篇SCI論文。

內(nèi)容介紹：Nonlinear partial differential equations (PDEs) are crucial to modelling important problems in science but they are computationally expensive and suffer from the curse of dimensionality. Since quantum algorithms have the potential to resolve the curse of dimensionality in certain instances, some quantum algorithms for nonlinear PDEs have been developed. However, they are fundamentally bound either to weak nonlinearities,valid to only short times,or display no quantum advantage. We construct new quantum algorithms--based on level sets --for nonlinear Hamilton-Jacobi and scalar hyperbolic PDEs that can be performed with quantum advantages on various critical numerical parameters, even for computing the physical observables, for arbitrary nonlinearity and are valid globally in time. These PDEs are important for many appli- cations like optimal control,machine learning, semi-classical limit of Schrodinger equations, mean-field games and many more. Depending on the details of the initial data, it can display up to exponential advantage in both the dimension of the PDE and the error in computing its observables. For general nonlinear PDEs, quantum advantage with respect to M,for computing the ensemble averages of solutions corresponding to M different initial data,is possible in the large $M$ limit. This is a joint work with Nana Liu.