一、主講人介紹：趙雁翔教授

鞠立力教授1995年畢業(yè)于武漢大學(xué)數(shù)學(xué)系獲數(shù)學(xué)學(xué)士學(xué)位，1998年在中國(guó)科學(xué)院計(jì)算數(shù)學(xué)與科學(xué)工程計(jì)算研究所獲得計(jì)算數(shù)學(xué)碩士學(xué)位，2002年在美國(guó)愛(ài)荷華州立大學(xué)獲得應(yīng)用數(shù)學(xué)博士學(xué)位。2002-2004年在美國(guó)明尼蘇達(dá)大學(xué)數(shù)學(xué)與應(yīng)用研究所從事博士后研究。隨后進(jìn)入美國(guó)南卡羅萊納大學(xué)工作，歷任數(shù)學(xué)系助理教授（2004-2008），副教授（2008-2012），和教授（2013-現(xiàn)在）。主要從事偏微分方程數(shù)值方法與分析，非局部模型與算法，計(jì)算機(jī)視覺(jué)，深度學(xué)習(xí)算法，高性能科學(xué)計(jì)算，及其在材料與地球科學(xué)中的應(yīng)用等方面的研究工作。至今已發(fā)表科研論文140多篇，Google學(xué)術(shù)引用5000多次。自2006年起連續(xù)主持了十多項(xiàng)由美國(guó)國(guó)家科學(xué)基金會(huì)和能源部資助的科研項(xiàng)目。2012至2017年擔(dān)任SIAM Journal on Numerical Analysis的副編輯，目前是JSC, NMPDE, NMTMA, AAMM等期刊的副編輯。與合作者關(guān)于合金微結(jié)構(gòu)演化在“神威·太湖之光”超級(jí)計(jì)算機(jī)上的相場(chǎng)模擬工作入圍2016年國(guó)際高性能計(jì)算應(yīng)用領(lǐng)域“戈登·貝爾”獎(jiǎng)提名。

二、講座信息

The Allen-Cahn equation is a well-known stiff semilinear parabolic partial differential equation (PDE) used to describe the process of phase separation and transition in multi-component physical systems, while the conservative Allen-Cahn equation is a modified version of the classic  Allen-Cahn equation that can additionally conserve the mass. As neural networks and deep learning techniques have achieved significant successes in recent years in scientific and engineering applications, there has been growing interest in developing deep learning algorithms for numerical solutions of PDEs.  In this paper, we propose  a deep learning method for predicting the dynamics of the classic and conservative Allen-Cahn equations. We design two types of convolutional neural network models, one for each of the Allen-Cahn equations, to learn the fully-discrete operators between two adjacent time steps. Specifically, the loss functions of the two models are defined using the residual of the fully-discrete systems, which result from applying the central finite difference discretization in space and the Crank–Nicolson approximation in time (second-order accurate in both time and space).  This approach enables us to train the models without requiring any ground-truth data. Moreover, we introduce a novel training strategy that automatically generates useful samples along the time evolution to facilitate effective training of the models. Finally, we conduct extensive experiments in two and three dimensions to demonstrate the outstanding performance of our proposed method, including its dynamics prediction and generalization ability under different scenarios.

時(shí)間：2023年6月14日09:00-10:00

地點(diǎn)：數(shù)學(xué)院424會(huì)議室

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