Computational Mathematics and Applications Seminar

Reliable uncertainty quantification is a central challenge in kinetic plasma simulation, where high dimensionality, multiple physical scales, and sensitivity to uncertain inputs make repeated high-fidelity computations prohibitively expensive. This is particularly relevant in fusion-oriented applications, for which accurate predictions require sophisticated numerical solvers but direct sampling is often out of reach.

In this talk, I will present a multifidelity framework for the Vlasov–Poisson–Landau system designed to combine, rather than replace, high-order numerical simulation with machine learning. At the high-fidelity level, asymptotic-preserving and structure-aware solvers provide accurate kinetic descriptions across different regimes. These are coupled with reduced plasma models and tensor neural surrogates constructed through a micro–macro decomposition, so that the dominant physical structure is treated analytically and numerically, while learning is used only for the lower-complexity kinetic correction.  The resulting hierarchy produces inexpensive low-fidelity samples that remain strongly correlated with the high-fidelity kinetic solution.  When used as control variates, these models yield substantial variance reduction and computational savings while retaining the high-order solver as the reference description.

Beyond the specific plasma application, the main message is that classical numerical analysis and machine learning need not be competing approaches. High-order solvers can provide structure, reliability, and asymptotic consistency, while learned models provide efficient approximations that can be exploited within rigorous multifidelity estimators. This interaction offers a general route toward trustworthy machine learning for computational science.
 

Ruth Misener will talk about: 'Optimizing over graphs: Challenges, Formulations, and Applications'

Applications involving optimization over graphs include molecular design, graph neural network verification, neural architecture search, etc. This talk discusses formulating graph spaces using mixed-integer optimization and incorporating application-specific constraints. We discuss computational challenges with these mixed-integer optimization formulations and zoom in on the practical implications for these applications. We mention what has been done (by both ourselves and others) and what other research still needs to be done.

Co-authors: Shiqiang Zhang, Yilin Xie, Christopher Hojny, Juan Campos, Jixiang Qing, Christian Feldmann, David Walz, Frederik Sandfort, Miriam Mathea, Calvin Tsay

This talk is hosted by Rutherford Appleton Laboratory, Harwell Campus

TBA; the speaker is visiting during term and this date can be flexible. 

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