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報(bào)告題目：Deep adaptive sampling for numerical PDEs

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

時(shí)間：2023年3月9日（周四）15:30 p.m.

地點(diǎn)：北院卓遠(yuǎn)樓305會(huì)議室

主辦單位：統(tǒng)計(jì)與數(shù)學(xué)學(xué)院

摘要：Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive method with applications. Then, we shall propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared to the neural network approximation obtained with uniformly distributed collocation points, the developed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.

主講人簡(jiǎn)介：

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,。曾于瑞士洛桑聯(lián)邦理工大學(xué)從事博士后研究,。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)間并行算法等,。在國(guó)際權(quán)威期刊SIAM Review,、SINUM、JCP等發(fā)表論文70余篇,。2016年獲CSIAM青年科技獎(jiǎng),，2018年獲優(yōu)秀青年科學(xué)基金資助,，2022年獲中組部高層次人才專項(xiàng)資助，并獲得第三屆王選杰出青年學(xué)者獎(jiǎng),。2018年曾擔(dān)任國(guó)防科工局《核挑戰(zhàn)專題》不確定性量化方向首席科學(xué)家,，并在2021年被授予“挑戰(zhàn)英才”稱號(hào)。現(xiàn)擔(dān)任SIAM J Sci Comput,、J Sci Comput,、Commun. Comput. Phys. 等多個(gè)國(guó)際權(quán)威期刊編委，國(guó)際不確定性量化期刊（International Journal for UQ）副主編,。周濤研究員目前擔(dān)任東亞工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)副主席,，并擔(dān)任學(xué)會(huì)期刊East Asian Journal on Applied Mathematics主編。