Modeling Unknown Stochastic Dynamical System via Autoencoder
Speaker: Zhongshu Xu (OSU) Dates: 2024/10/03 Location: MW 154 Abstract: This talk presents a novel data-driven method for modeling unknown stochastic dynamical systems using autoencoders. The approach focuses on learning the flow map of an underlying system by identifying unobserved…
The Impact of Multiscale Dataset and a Multi-Rate Gradient Descent Approach
Speaker: Liangchen Liu (UT Austin) Dates: 2024/10/24 Location: MW 154 Abstract: Data embedded in high-dimensional spaces often follows intrinsic low-dimensional structures, but assuming a consistent scale across all directions may be too idealized. Indeed, empirical observations suggest that data distributions tend…
Frenet immersed finite element methods for interface problems: Design, analysis and future directions
Speaker: Haroun Meghaichi (OSU) Dates: 2024/08/29 Location: MW 154 Abstract: In this talk, I will go over a brief survey of unfitted methods for interface problems with an emphasis on the immersed finite element method. Next, I will describe a…
Discrete fracture models for fluid flow in fracture porous media
Speaker: Ziyao Xu (UND) Dates: 2024/04/05 Location: zoom, link Abstract: As a result of geological processes and human activities, fractures are widely distributed in subsurface rocks. Depending on the degree of precipitation, fractures can act either as highly permeable, flow-preferential…
On the Activation Function Dependence of the Spectral Bias of Neural Networks
Speaker: Qinguo Hong (Missouri S&T) Dates: 2024/03/22 Location: MW 154 Abstract: Neural networks are universal function approximators which are known to generalize well despite being dramatically overparameterized. We study this phenomenon from the point of view of the spectral bias…
A High Order Geometry Conforming Immersed Finite Element for Elliptic Interface Problems
Speaker: Haroun Meghaichi (VT) Dates: 2024/02/08 Location: zoom Abstract:We present a high order immersed finite element (IFE) method for solving the elliptic interface problem with interface-independent meshes. The IFE functions developed here satisfy the interface conditions exactly and they have…