applied math

Joint Inverse Problems/Data Sciences/Applied Math Seminar at Colorado State University

Thursday 3:30-4:30PM, Weber 223

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Zoom Meeting link  
Meeting ID: 981 7030 4471

Spring 2023

Feb 02   Mar 23   Mar 30   Apr 06   Apr 20   Apr 27  

Feb 02   Back to top

Round Table

All applied math faculty and graduate students



Mar 23   Back to top

Michael Perlmutter

Department of Mathematics, University of California Los Angeles

Title  Geometric Scattering on Measure Spaces

Abstract  Geometric Deep Learning is an emerging field of research that aims to extend the success of convolutional neural networks (CNNs) to data with non-Euclidean geometric structure. Despite being in its relative infancy, this field has already found great success in many applications such as recommender systems, computer graphics, and traffic navigation. In order to improve our understanding of the networks used in this new field, several works have proposed novel versions of the scattering transform, a wavelet-based model of CNNs for graphs, manifolds, and more general measure spaces. In a similar spirit to the original Euclidean scattering transform, these geometric scattering transforms provide a mathematically rigorous framework for understanding the stability and invariance of the networks used in geometric deep learning.Additionally, they also have many interesting applications such as drug discovery, solving combinatorial optimization problems, and predicting patient outcomes from single-cell data. In particular, motivated by these applications to single-cell data, I will also discuss recent work proposing a diffusion maps style algorithm with quantitative convergence guarantees for implementing the manifold scattering transform from finitely many samples of an unknown manifold.

Mar 30   Back to top

Pablo Lucero

Department of Applied Mathematics, University of Colorado at Boulder

Title  Direct parallel solvers for a variable coefficient Helmholtz equation applied to 3D wave propagation problems.

Abstract  We present an efficient parallel solver for the linear system that arises from the Hierarchical Poincare-Steklov (HPS) discretization of three dimensional variable coefficient Helmholtz problems. We tackle problems of 100 wavelengths in each direction that require more than a billion unknowns to achieve approximately 4 digits of accuracy in less than 20 minutes. Additionally, we show results on a parallel Direct solver for the same problem and explore the potential of both techniques for inverse problems. This work was funded by Total Energies and NSF.

Apr 06   Back to top

Troy Butler

Department of Mathematics, University of Colorado Denver

Tim Wildey

Sandia National Labs



Apr 20   Back to top

Dustin Mixon

Department of Mathematics, The Ohio State University



Apr 27   Back to top

Keaton Hamm

Department of Mathematics, University of Texas at Arlington