国(境)外文教专家系列讲座一百七十六讲-鞠立力:A Deep Learning Method for the Dynamics of Classic and Conservative Allen-Chan equations based on Fully-Discrete Operators

时间:2023-06-16浏览:15

一、主讲人介绍:赵雁翔教授

鞠立力教授1995年毕业于武汉大学数学系获数学学士学位,1998年在中国科学院计算数学与科学工程计算研究所获得计算数学硕士学位,2002年在美国爱荷华州立大学获得应用数学博士学位。2002-2004年在美国明尼苏达大学数学与应用研究所从事博士后研究。随后进入美国南卡罗莱纳大学工作,历任数学系助理教授(2004-2008),副教授(2008-2012),和教授(2013-现在)。主要从事偏微分方程数值方法与分析,非局部模型与算法,计算机视觉,深度学习算法,高性能科学计算,及其在材料与地球科学中的应用等方面的研究工作。至今已发表科研论文140多篇,Google学术引用5000多次。自2006年起连续主持了十多项由美国国家科学基金会和能源部资助的科研项目。20122017年担任SIAM Journal on Numerical Analysis的副编辑,目前是JSC, NMPDE, NMTMA, AAMM等期刊的副编辑。与合作者关于合金微结构演化在“神威·太湖之光”超级计算机上的相场模拟工作入围2016年国际高性能计算应用领域“戈登·贝尔”奖提名。

 

二、讲座信息

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.

时间:202361409:00-10:00

地点:数学院424会议室

 

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