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Computational and Applied Mathematics Seminar: Ke Chen, Maryland, Towards efficient deep operator learning for forward and inverse PDEs: theory and algorithms

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Deep neural networks (DNNs) have been a successful model across diverse machine learning tasks, increasingly capturing the interest for their potential in engineering problems where PDEs have long been the dominant model. This talk delves into efficient training for PDE operator learning in both the forward and the inverse problems setting. Firstly, we address the curse…

Geometry and Topology Seminar: Kai-Wei Zhao, University of Notre Dame, On the blowup of regularized solutions to the Jang equation and constant expansion surfaces

SAS 1216

Schoen-Yau proved the spacetime positive energy theorem by reducing it to the time-symmetric (Riemannian) case using the Jang equation. To acquire solutions to the Jang equation, they introduced a family of regularized equations and took the limit of regularized solutions, whereas a sequence of regularized solutions could blow up in some bounded regions enclosed by apparent horizons. They analyzed the blowup behavior near and outside the apparent horizons, but what happens inside…

Applied Math Graduate Student Seminar: Harley Hanes, NC State, Boundary Quantification and Optimal Sample Identification in Reduced-Order Models

SAS 4201

Reduced-order models (ROMs) are a critical tool for sensitivity analysis, parameter inference, and uncertainty quantification where high-fidelity models would be computationally intractable. Galerkin POD-ROMs are one particular class of ROMs which project high-fidelity model equations onto a set of model solutions to construct ROMs retaining original model parameters and physics, enabling accurate sensitivity analysis, parameter inference,…

Algebra and Combinatorics Seminar: Kyle Celano, Wake Forest University, Chromatic Symmetric Functions and RSK for (3 + 1)-free Posets

SAS 4201

In 1995, Stanley introduced the chromatic symmetric function of a graph, a symmetric function analog of the classical chromatic polynomial of a graph. The Stanley-Stembridge e-positivity conjecture is a long-standing conjecture that states that the chromatic symmetric function of a certain class of graphs, called incomparability graphs of (3+1)-free posets, has nonnegative coefficients when expanded…

Differential Equations and Nonlinear Analysis Seminar: Leon Bungert, University of Würzburg, Adversarial robustness in machine learning: from worst-case to probabilistic

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In this talk I will first review recent results which characterize adversarial training (AT) of binary classifiers as nonlocal perimeter regularization. Then I will speak about a probabilistic generalization of AT which also admits such a geometric interpretation, albeit with a different nonlocal perimeter. Using suitable relaxations one can prove the existence of solutions for…

Teaching and Learning Seminar: Maria Meehan, University College Dublin, Video recordings to complement, or substitute for, the first-year mathematics lecture: One lecturer’s journey

SAS 4201

As part of a professional development project aimed at engaging in the Discipline of Noticing as conceptualised by John Mason, some colleagues and I wrote and shared brief-but-vivid accounts of our practice. Evident in these accounts is the catalyst for the subsequent change in my practice of introducing short, pre-recorded videos to complement, or substitute…

Computational and Applied Mathematics Seminar: Gregory Ongie, Marquette University, A function space view of infinite-width neural networks

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It is well-known that nearly any function can be approximated arbitrarily-well by a neural network with non-linear activations. However, one cannot guarantee that the weights in the neural network remain bounded in norm as the approximation error goes to zero, which is an important consideration when practically training neural networks. This raises the question: What…

Biomathematics Seminar: TBA

Cox 306

All BMA seminars have a virtual option with the following Zoom Link: https://ncsu.zoom.us/j/93046132033?pwd=dkZiTjlKazgzK2Q3aXJra1g2R1Q0dz09 Meeting ID: 930 4613 2033 Passcode: 075251

Differential Equations and Nonlinear Analysis Seminar: Tu Nguyen Thai Son, Michigan State University, Generalized convergence of solutions for nonlinear Hamilton-Jacobi equations

SAS 4201

We examine the asymptotic behaviors of solutions to Hamilton-Jacobi equations while varying the underlying domains. We establish a connection between the convergence of these solutions and the regularity of the additive eigenvalues in relation to the domains. To accomplish this, we introduce a framework based on Mather measures that enables us to compute the one-sided derivative…

Computational and Applied Mathematics Seminar: Antoine Blanchard, Verisk, A Multi-Scale Deep Learning Framework for Projecting Weather Extremes

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Extreme weather events are of growing concern for societies because under climate change their frequency and intensity are expected to increase significantly. Unfortunately, general circulation models (GCMs)--currently the primary tool for climate projections--cannot characterize weather extremes accurately. Here, we report on advances in the application of a multi-scale deep learning framework, trained on reanalysis data,…

Geometry and Topology Seminar: Andrew Shedlock, NC State, Recovery of a complete Riemannian Manifold using the local source-to-solution operator for the Electro-Magnetic Wave Operator

SAS 1216

In this talk we consider an Electro-Magnetic Wave operator on a complete Riemannian manifold, which generalizes the standard wave equation to include first order and zeroth order terms.  The Cauchy Problem for the Electro-Magnetic Wave operator with zero initial values and a smooth compactly supported forcing function has a unique smooth solution. We study the…

Geometry and Topology Seminar: Lili Yan, University of Minnesota, Stable determination of time-dependent collision kernel in the nonlinear Boltzmann equation

SAS 1216

In this talk, we consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions 2 and higher. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional conditions. A uniqueness result is derived as an immediate consequence of the stability result. Our approach relies on…

Applied Math Graduate Student Seminar: Sam Thornton, NC State, Dual-Domain Clustering of Spatiotemporal Infectious Disease Data

SAS 4201

The purpose of this project is to develop, test, and document performance of dual-domain clustering algorithms for spatiotemporal datasets, tailored to pandemic preparedness and endgame challenges. Dual-domain clustering refers to the unsupervised learning clustering method performed on data with both application-specific attributes (e.g., number of infectious) and geographic information (e.g., latitude and longitude of data…

Colloquium: Christopher K.R.T. Jones, University of North Carolina at Chapel Hill, Do We Need to Adapt to a Changing Climate, or to the Rate at Which it is Changing?

SAS 4201

The climate is changing due to the heat trapping caused by the rapid increase in greenhouse gases, mainly carbon dioxide, in the atmosphere. One way to state the issue is that we cannot, as a species, adapt to the new conditions quickly enough. This is an example of rate-induced tipping for which the mathematics has…

Algebra and Combinatorics Seminar: Raymond Maresca, Brandeis University, Combinatorics of exceptional collections in type A-tilde

SAS 4201

We will define quivers of type A-tilde, their representations, and exceptional collections of these representations. We will then introduce a combinatorial model of these representations, based on the one constructed by Garver, Igusa, Matherne, and Ostroff for type A, by drawing strands on a copy of the integers. We will see that collections of strands…