11月演講

Colloquium, 國家理論科學研究中心　Dr. Marco Sutti Thursday, November 2, 16:10—17:00 數學系3174 Title: Numerical Optimization on Matrix Manifolds Abstract:In this talk, we will showcase several fundamental ideas and tools needed to perform numerical optimization on matrix manifolds. We will start with a brief overview of the steepest descent method, a classical optimization algorithm in Euclidean space. Then, we will introduce the main tools from Riemannian geometry that allow us to extend the steepest descent to matrix manifolds, with particular emphasis on retraction mapping, and present some numerical examples. To keep the presentation more concrete, we will fix our ideas on the Stiefel manifold, but the concepts discussed herein would remain valid for any embedded submanifold. If time permits, we will also discuss the manifold of fixed-rank matrices and some related applications.

Colloquium, 教學發展中心 Teacher Beth Godle Thursday, November 9, 15:10—16:00 數學系3174 Title: 研究生英語口說寫作工作坊：Technical Writing Abstract:研究生通識課程

Colloquium, 教學發展中心 Teacher Valerie Harden Thursday, November 9, 16:10—17:00 數學系3174 Title: 研究生英語口說寫作工作坊：How to Give a Great Power Point Abstract:研究生通識課程

Colloquium, 國立高雄大學應用數學系　曾昱豪教授 Thursday, November 16, 16:10—17:00 數學系3174 Title: A Machine Learning Method for Solving Stokes Interface Problems Abstract:In this talk, we present a physics-informed neural network called the Discontinuity-Cusps Capturing Physics-Informed Neural Network for solving piecewise-constant viscosity Stokes interface problems. The network consists of two fully connected sub-networks that handle the pressure and velocity vectors separately. These sub-networks share the same primary input arguments but have different augmented features: the Discontinuity-Capturing Shallow Neural Network (DCSNN) uses an indicator function to capture the discontinuities, while the Cusp-Capturing Neural Network (CuspNN) employs a cusp-enforced level set function to capture cusp-like velocity profiles caused by jumps in viscous stresses. The main objective of this study is to explore the use of the stress balance formulation directly in the training process for obtaining accurate predictions, as opposed to the force formulation used in the Immersed Interface Method (IIM). We perform a series of numerical experiments to solve two- and three-dimensional Stokes interface problems and demonstrate the effectiveness and accuracy of the proposed network model. Our results indicate that even a shallow network with a moderate number of neurons and sufficient training data points can achieve prediction accuracy comparable to that of immersed interface methods.

Colloquium, 國立成功大學數學系　許瑞麟教授 Thursday, November 23, 16:10—17:00 數學系3174 Title: 成功大學數學系112學年圖書教育訓練 Abstract: 為使全國數學圖書、期刊及相關電子資源使用最大化， 此次圖書服務推廣講座針對本系師生所需之數學圖書資源做詳盡介紹， 其包含 1. 校內、外圖書及期刊資源之取得管道 2. 校外數學資源取得申請方式 3. 中央研究院數學所「 圖書期刊計畫」可提供的資源及線上便捷的合作服務 4. 數學各領域相關圖書之介紹 盼其圖書、期刊及電子資源能提供本系師生學習、研究所需。

Colloquium, 國立台灣大學數學系　陳宜良教授 Thursday, November 30, 16:10—17:00 數學系3174 Title: Introduction to Singularity Extraction Abstract:1990 年代起，應用數學界的幾波研究熱潮：小波理論、影像處理、壓縮感知，及近年的穩健型的主成分分析和最佳運輸等；這些理論的基礎都有共同的思維，就是L1優化和TV正則化。而如何從奇異集偵測與擷取的觀點，透過L1優化和TV正則化，貫穿上述幾個研究課題，我們將透過三場演講，讓大家可以由淺入深了解背後的運作原理。此為第一場演講，簡介Singularity Extraction，星期五還有Optimal transport and minimal currents及Variational principles in fluid mechanics兩大應用主題。也歡迎所有同學繼續參加12/1星期五及12/2星期六兩天的大師演講喔！