Mathematics Colloquium

Upcoming Colloquium

Fast prediction of plasma instabilities with sparse-grid-accelerated optimized dynamic mode decomposition
Dr. Ionut Farcas, Virginia Tech

April 27, 2026
12:30pm-1:30pm in FO3-200A

Abstract

Parametric data-driven reduced-order models (ROMs) that embed dependencies in many input parameters are essential for enabling many-query tasks in large-scale problems, and are key to the development of digital twins. However, generating training data to construct the ROMs using standard grid-based approaches is computationally infeasible due to the curse of dimensionality. This presentation introduces an efficient strategy for constructing parametric data-driven ROMs by leveraging sparse grid interpolation with (L)-Leja points. These points are nested and exhibit slow growth, resulting in sparse grids with low cardinality in low- to medium-dimensional settings, making them well-suited for computationally expensive, large-scale problems. As a representative real-world application, we consider gyrokinetic simulations of plasma micro-instabilities in fusion experiments. We construct parametric ROMs for the full five-dimensional gyrokinetic distribution function using optimized dynamic mode decomposition (optDMD) in combination with sparse grids. For an electron–temperature–gradient-driven micro-instability simulation with six input parameters, we demonstrate that a predictive parametric optDMD ROM can be built using only 28 high-fidelity simulations, while achieving evaluation costs up to three orders of magnitude lower. These results highlight the potential of sparse grid-based parametric ROMs in enabling otherwise intractable many-query tasks in large-scale applications.

Biosketch

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I am an Assistant Professor in the Department of Mathematics and the Division of Computational Modeling and Data Analytics at Virginia Tech. Prior to joining Virginia Tech, I was a Postdoctoral Fellow at the Oden Institute for Computational Engineering and Sciences at The University of Texas at Austin, where I worked with Dr. Karen Willcox and Dr. Frank Jenko on data-driven reduced modeling and uncertainty quantification for large-scale simulations in rocket combustion and fusion plasmas. I earned my Ph.D. summa cum laude from the Technical University of Munich (Germany) in 2020, with a thesis focused on numerical methods for efficient uncertainty quantification in large-scale problems. I was honored to receive the Romanian Student of the Year award (Postgraduate Level in Europe) in 2019, as well as the Heinz Schwaertzel Prize, awarded to the best Ph.D. thesis in the fundamentals of informatics submitted to any Munich university in the previous two years. I was also a recipient of the Engineering Research Visioning Alliance Idea Award from the National Academy of Engineering in 2026. My research interests lie at the intersection of data-driven learning, model reduction, uncertainty quantification, multi-fidelity methods, and high-performance computing, with applications to real-world problems.