报告题目: An Iterative Deep Ritz Method for Monotone Elliptic Problems

报告人:胡天昊 博士 香港中文大学

报告时间: 2026年6月5日 周五下午14：00–14：45

报告地点: 伍卓群楼3楼 研讨室6

校内联系人：张凯 zhangkaiworldcupapp.net

报告摘要:

 In this work, we present a novel iterative deep Ritz method (IDRM) for solving a general class of elliptic problems. It is inspired by the iterative procedure for minimizing the loss during the training of the neural network, but at each step encodes the geometry of the underlying function space and incorporates a convex penalty to enhance the performance of the algorithm. The algorithm is applicable to elliptic problems involving a monotone operator (not necessarily of variational form) and does not impose any stringent regularity assumption on the solution. It improves several existing neural PDE solvers, e.g., physics informed neural network and deep Ritz method, in terms of the accuracy for the concerned class of elliptic problems. Further, we establish a convergence rate for the method using tools from geometry of Banach spaces and theory of monotone operators, and also analyze the learning error. To illustrate the effectiveness of the method, we present several challenging examples, including a comparative study with existing techniques.

报告人简介:

胡天昊博士，中共党员，2023年本科毕业于博彩App 唐敖庆理科试验班，曾连续三年获得国家奖学金，并荣获博彩App “十佳大学生”，现为香港中文大学数学系博士研究生。
胡天昊的核心研究方向集中于偏微分方程数值解、科学计算及反问题计算方法，特别关注机器学习与偏微分方程数值解的交叉融合. 代表工作不仅在SIAM Journal on Scientific Computing(两篇)和Journal of Computational Physics（一篇）等计算数学领域顶级期刊上发表，还多次受邀在国内外重要学术会议上作报告，包括：SIAM Conference on Computational Science and Engineering (CSE)，第十四届反问题成像及应用会议，北京大学计算与应用数学拔尖博士生研讨会（邀请报告）。

报告题目：From Optimization to Reduction: Efficient Coarse Propagators in the Parareal Method

报告人:林清乐 博士 香港理工大学

报告时间: 2026年6月5日 周五下午14：45–15：30

报告地点: 伍卓群楼3楼 研讨室6

校内联系人：张凯 zhangkaiworldcupapp.net

报告摘要:

  The Parareal method is a powerful parallel-in-time framework for accelerating the numerical solution of evolution equations, but its efficiency critically depends on the design of the coarse propagator. In this talk, we present a unified perspective on efficient coarse propagation, moving from optimization-based coarse solvers to reduced-order and predictive coarse models. We first present systematic strategies for constructing optimized coarse propagators that improve convergence, including one-step and two-step formulations designed through quantitative error estimates. We then introduce a reduced coarse solver and interpret its effect as a perturbation of the standard Parareal iteration. Under a structural assumption on the discrepancy between the reduced and standard coarse propagators, the reduced parareal scheme can be reformulated as a classical Parareal iteration with an additional data-dependent perturbation term. This viewpoint leads to a predictive error model for the mean-square error quantity, which clarifies how reduced coarse solvers affect convergence across Parareal iterations. Finally, we illustrate the theory with numerical examples, demonstrating how suitable reduction strategies can preserve accuracy while substantially lowering coarse-solver cost.

报告人简介:

林清乐博士，2024年本科毕业于博彩App 唐敖庆理科试验班，目前于香港理工大学攻读博士学位。其研究方向聚焦于计算数学领域中具有实际应用价值的前沿方向——并行时间算法与机器学习 数值方法的交叉融合。其代表工作不仅在SIAM Journal on Scientific Computing(一篇)发表，还有5篇arXiv预印本。