Computational Mathematics and Applications Seminar

Lorenzo Pareschi is going to talk about; 'Bridging high-order numerics and machine learning for kinetic plasma simulation'

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

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Professor Sara Shashaani is going to talk about: 'Adaptive Sampling and Regularization for Stochastic Trust-region Methods'

Trust-region methods have proven highly effective for unconstrained nonconvex stochastic optimization problems where objective and gradient information are available only through noisy stochastic oracles. ASTRO is a class of adaptive sampling trust-region methods that dynamically determine sampling effort while constructing local quadratic models from noisy function and gradient observations. By exploiting dependence among samples and the stochastic structure of the problem, ASTRO achieves strong convergence and complexity guarantees. Its derivative-free variant, ASTRO-DF, relies solely on noisy function evaluations and also enjoys almost-sure convergence guarantees.

Dr Peter Braam is going to talk about; 'State time geometry: causal performance profiles and optimal data transport in parallel execution'

The increasing complexity of parallel architectures and heterogeneous microarchitectures makes predicting and optimising program performance notoriously difficult. For Optimal Data Transport, we present a discrete variant of the Wasserstein–Fisher–Rao metric that quantifies the true cost of data layout transformations and movement across memory hierarchies. For Causal Performance Profiles, we introduce the Lyons–Gregg Signature, which combines the ideas of Terry Lyons' rough path signatures with hardware performance counters (eBPF) to capture cross-correlated, causal bottlenecks in execution streams. Both arose from State Time Geometry (STG), a model for stateful program execution on computing infrastructure, first modelled as a dynamical system governing state-values over the space of memory addresses. The address space generalises to geometric objects defining infrastructure and leads to the metric. The state transitions of parallel executions become a Grothendieck quantum field theory over the infrastructure and carry the statistical model for the Lyons-Gregg Signature. The central theme is that an intuitive faithful model is not doomed by complexity but forms a geometric domain in which both theoretical and engineering perspectives are simplified.

(In a companion lecture in the Computing Laboratory at 11:00 on Nov 13, we will discuss STG's underlying categorical and geometric structure and its relationship to programming languages and formal methods)

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