主題演講

大會主講 1：10:00～10:50

講  者：馬國鳳  Kau-Fonq Ma 

單  位：中央研究院特聘研究員/國家講座教授 

講  題：How to Better Measure Seismic Hazard: Insights from Earthquake Kinematics and Dynamics

摘  要：
Earthquakes have long been understood as the release of energy resulting from the interaction and collision of tectonic plates. Taiwan is situated along an active tectonic plate boundary, making it highly prone to frequent and intense shaking caused by moderate to large earthquakes both inland and offshore. Recent advances in seismology have enhanced our ability to identify potential seismic hazard zones and explore the mechanisms of energy partitioning during earthquakes. While earthquake prediction remains a major scientific challenge, the most effective way to reduce the devastating impacts of severe earthquakes is through comprehensive seismic risk mitigation strategies.

In Taiwan, significant crustal damage from earthquakes is often attributed to complex fault systems rather than single fault segments. To better understand these systems, the Taiwan Earthquake Model (TEM) and TEMPSHA2015 integrated extensive studies of seismogenic mechanisms into the framework of seismic hazard analysis. This evolving knowledge is now shaping the next generation of probabilistic seismic hazard assessments. To further our understanding, we employed rupture kinematic modeling to simulate ground motion behavior. This approach helps forecast shaking patterns from seismogenic structures, assess the interactions within fault systems, and evaluate their potential effects on buildings and infrastructure. In parallel, Taiwan successfully implemented a state-of-the-art Earthquake Early Warning (EEW) system in 2015, which has demonstrated excellent performance in providing timely alerts to reduce earthquake risks.

Our ongoing efforts aim to bridge the gap between seismotectonic research and seismic hazard assessments. By applying knowledge gained from past earthquakes, we seek to refine probabilistic seismic hazard analyses and create a more holistic framework that incorporates insights from seismology, earthquake engineering, and seismo-tectonics. This integrated approach not only advances scientific understanding but also informs government policies and societal practices for improved earthquake preparedness and risk management. Despite the many unknowns that persist in earthquake science, our mission remains clear: to expand the frontiers of knowledge and translate it into actionable strategies that safeguard lives, infrastructure, and communities against future seismic events.

大會主講 2：14:00～14:50

講  者：王振男  Jenn-Nan Wang 

單  位：國立臺灣大學數學系特聘教授/教育部傑出獎教授 

講  題：Characterization of non-radiating sources and statistical aspect of identifying radiating sources  

摘  要：

I plan to discuss two themes about the determination of sources in this talk. Firstly, I would like to discuss the characterization of non-radiating volume and surface (faulting) sources for the elastic waves in anisotropic inhomogeneous media. Each type of the source can be decomposed into a radiating part and a non-radiating part. The non-radiating part does not induce scattered waves at a certain frequency. In other words, such non-radiating source can not be detected by measuring field at one single frequency in a region outside of the domain where the source is located. On the other hand, one can uniquely determine a radiating source by the near-field measurement. However, this problem is severely ill-posed. I will explain its implication on the consistency of Bayesian inference.

講者1：邱普照 Pu Zhao Kow 

單  位：國立政治大學應用數學系助理教授

講  題：Stability of linear inverse problems: a singular value decomposition approach

摘  要：

The main theme of this paper is to explain a general principle that the stability of linear inverse problem can be known from the decay asymptotic of single values. For simplicity, we consider the problem of recovering the density of a Herglotz wave function, based on [https://arxiv.org/abs/2404.18482]. We also exhibit some results in [https://arxiv.org/abs/2501.01650], which is a part of Helsinki Speech Challenge 2024 (https://arxiv.org/abs/2406.04123).

講者2：薛名成 Ming-Cheng Shiue 

單  位：國立陽明交通大學應用數學系副教授 

講  題：On the long-time stability of a class of second order time-stepping schemes based on blended BDF methods for the two-dimensional Navier-Stokes equations

摘  要：

This talk explores the long-time stability of a class of second-order time-stepping schemes designed for the two-dimensional Navier-Stokes equations. The algorithm employs blended BDF methods, combining the BDF2 and BDF3 schemes. This approach offers the advantage of preserving A-stability while potentially reducing the truncation error compared to the classical BDF2 discretization. 

For initial data in H, the scheme’s long-time L2-stability is established without requiring a small time step size, thus improving upon existing results that demand higher regularity of the initial data. Additionally, for initial data in V , the algorithm achieves long-time H1-stability, also without imposing constraints on the time step size.

講者1：曾昱豪 Yu-Hau Tseng 

單  位：國立高雄大學應用數學系副教授  

講  題：A discontinuity-cusp capturing neural network for Stokes interface problems

摘  要：

This talk briefly reviews DCSNN and CuspNN, forming the foundation of a discontinuity- and cusp-capturing physics-informed neural network (PINN) for solving static Stokes interface problems. Unlike the immersed boundary method, we reformulate the governing equations in each fluid domain separately and replace the singular force effect with the traction balance equation along the interface. To address discontinuities in pressure and velocity derivatives across the interface, our approach employs two fully connected sub-networks for pressure and velocity. These sub-networks share the same coordinate inputs but use distinct augmented features derived from a presumed level set function indicating the interface position. The pressure sub-network uses an indicator function to capture discontinuities, whereas the velocity sub-network incorporates a cusp-enforced level set function to handle derivative discontinuities via the traction balance equation. We conduct numerical experiments for two- and three-dimensional Stokes interface problems, comparing the accuracy of our method with augmented immersed interface methods. Results demonstrate that even shallow networks with moderate neurons and sufficient training data can achieve comparable prediction accuracy to traditional methods. In the last part of this talk, the DC-CuspNN incorporating a graphic representation for a droplet is presented to simulate droplet dynamics under a quiescent or a shear flow.

講者2：王辰樹 Chern-Shuh Wang

單  位：國立成功大學數學系副教授

講  題：敬獻吳宗芳教授