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 zhangkaicrzbpingtai.com

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，本科毕业于成人直播平台 ，目前于香港中文大学攻读博士学位。

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 zhangkaicrzbpingtai.com

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，本科毕业于成人直播平台 ，目前于香港理工大学攻读博士学位。