主講人：周濤 中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院研究員

時(shí)間：2025年10月9日15：30

地點(diǎn)：徐匯校區(qū)三號(hào)樓332室

舉辦單位：數(shù)理學(xué)院

主講人介紹：周濤，中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院研究員。主要研究方向?yàn)椴淮_定性量化、偏微分方程數(shù)值方法以及時(shí)間并行算法，在國(guó)際權(quán)威期刊發(fā)表論文 80 余篇，先后受邀為 SIAM Review 和 Acta Numerica 撰寫(xiě)綜述論文。2018 年擔(dān)任國(guó)防科工局《核挑戰(zhàn)專(zhuān)題》不確定性量化方向首席科學(xué)家。2022 年獲第三屆王選杰出青年學(xué)者獎(jiǎng)，2025 年榮獲中國(guó)數(shù)學(xué)會(huì)陳省身獎(jiǎng)?，F(xiàn)擔(dān)任 SIAM J Numer Anal.、SIAM J Sci Comput.、J Sci Comput.等十余種國(guó)內(nèi)外權(quán)威期刊編委，并擔(dān)任東亞工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)主席及學(xué)會(huì)期刊EAJAM 主編。

內(nèi)容介紹：Solving high-dimensional PDEs with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation to compute large Hessian matrices. We propose a deep random difference method (DRDM) that addresses these issues by approximating the convection-diffusion operator using first-order random differences, avoiding explicit Hessian computation. When incorporated into a Galerkin framework, the DRDM eliminates the need for pointwise evaluation of expectations, resulting in very efficient training procedure. Rigorous error estimates for DRDM are presented for linear PDEs. We further extend the approach to the Hamilton-Jacobi-Bellman (HJB) equations in stochastic optimal control. Numerical experiments demonstrate the efficiency of DRDM for solving quasilinear parabolic PDEs and HJB equations in dimensions up to 100000.