Michael Abdelmalik - A Multi-Fidelity Framework for Rarefied Dynamics - IPAM at UCLA
Recorded 19 May 2026. Michael Abdelmalik of Technische Universiteit Eindhoven presents "A Multi-Fidelity Framework for Rarefied Dynamics: Hierarchical Models, Multi-Scale Closures and Acceleration with Neural Green's Operators" at IPAM's Multi-Fidelity Methods to Enable Robust Optimization and Real-Time Control of Fusion Processes Workshop.Abstract: Rarefied dynamics arising in non-equilibrium flow regimes pose a persistent challenge to computational modeling. Their multiple scales, nonlocal interactions, and high dimensionality require computational strategies that merge physical consistency with computational efficiency. This talk proposes a mulit-fidelity framework that connects structure-preserving moment hierarchies, variational multiscale closures, and computational acceleration with data-driven neural operators. We begin from the method of moments as a hierarchical modeling paradigm and show how invariances and thermodynamic laws guide the development of closure relations consistent with underlying physical symmetries [1]. Building on this, we extend the closure relations using variational multiscale methods to capture unresolved scales while maintaining thermodynamic constraints [2]. Finally, we demonstrate how Neural Green’s Operators can act as data-driven accelerators that can support multi-query problem solving [3].
[1] MRA Abdelmalik, EH van Brummelen. "Moment closure approximations of the Boltzmann equation based on φ-divergences" Journal of Statistical Physics 164.1 (2016): 77-104
[2] FA Baidoo, IM Gamba, TJR Hughes, MRA Abdelmalik. “Extensions to the Navier–Stokes–Fourier equations for rarefied transport: Variational multiscale moment methods for the Boltzmann equation” Mathematical Models and Methods in Applied Sciences 36.01 (2026): 111-172
[3] H Melchers, J Prins, MRA Abdelmalik. "Neural Green's Operators for Parametric Partial Differential Equations." Computer Methods in Applied Mechanics and Engineering 455 (2026): 118893
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iv-multi-fidelity-methods-to-enable-robust-optimization-and-real-time-control-of-fusion-processes/?tab=overview Receive SMS online on sms24.me
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