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IMath Webinar Series: Dr. Won Chang and Dr. Mark Jason Celiz

You’re all invited to attend the 3rd installment of this semester’s IMath Webinar Series on Monday, November 14, 2022 at 2:00 PM. Dr Won Chang (of the University of Cincinnati, hosted by the Modelling and Applications Group) and Dr. Mark Jason Celiz (of the Optimization and Approximation Group) will be our speakers.

Dr. Won Chang (University of Cincinnati, hosted by the Modelling and Applications Group)
Title: Deep Learning-based Uncertainty Quantification for Mathematical Models
Abstract: Over the recent years, various methods based on deep neural networks have been developed and utilized in a wide range of scientific fields. Deep neural networks are highly suitable for analyzing time series or spatial data with complicated dependence structures, making them particularly useful for environmental sciences and biosciences where such type of simulation model output and observations are prevalent. In this talk, I will introduce my recent efforts in utilizing various deep learning methods for statistical analysis of mathematical simulations and observational data in those areas, including surrogate modeling, parameter estimation, and long-term trend reconstruction. Various scientific application examples will also be discussed, including ocean diffusivity estimation, WRF-hydro calibration, AMOC reconstruction, and SIR calibration.

Dr. Mark Jason Celiz (Optimization and Approximation Group)
Title: Spaces of Functions of Variable Bandwidth
Abstract: In this talk, we introduce the notion of variable bandwidth via spectral subspaces of a self-adjoint Sturm-Liouville operator \(f \mapsto -\left(pf^{\prime}\right)^{\prime}\) on \(\mathbb{R}\), where \(p>0\) a.e. is called a bandwidth-parametrizing function. Elements of these subspaces can be viewed as functions having local bandwidths roughly determined by \(1/\sqrt{p}\). We then present some properties and characterizations of functions of variable bandwidth, most of which resemble those known to classical bandlimited functions. We also show that spaces of functions of variable bandwidth admit sampling theorems as well as necessary density conditions for sampling and interpolation for some choices of \(p\). In addition, a critical density (Nyquist rate in engineering) that separates sets of stable sampling from sets of interpolation is found.