报告题目：Robust PDE Identification from a Noisy Data Set

报告人：刘皓助理教授香港浸会大学

报告时间：2026年06月24日10：00—11：00

报告地点：正新楼313

校内联系人：吕俊良 [email protected]

报告摘要：

    Partial differential equations (PDEs) are fundamental tools for modeling physical phenomena across science and engineering. Traditionally derived from empirical observation, PDEs can now be discovered directly from data -- thanks to the rapid growth in data collection and storage capabilities. This presentation introduces our recent work on data-driven identification of parametric PDEs. A central challenge in this field is handling data corrupted by heavy noise, which many existing methods fail to address effectively. We tackle this by proposing a successively denoised differentiation strategy that improves both noise removal and the accuracy of computed partial derivatives. Building on this foundation, we develop two subspace pursuit-based methods for identifying parametric PDEs. We further extend this framework to PDEs with spatially and temporally varying coefficients. By incorporating B-spline representations, we formulate the problem as one of block sparse recovery and introduce a group subspace pursuit algorithm with theoretical guarantees. Finally, we present a weak-form based algorithm for the varying-coefficient setting, which achieves significantly improved robustness against noise.

报告人简介：

    刘皓，香港浸会大学数学系助理教授。其于2018年在香港科技大学取得博士学位，并于2018-2021年在佐治亚理工大学做博士后。在2021年，其加入香港浸会大学。其主要研究方向包括图像处理，深度学习理论，偏微分方程识别以及数值偏微分方程。