Data-driven closure learning for radiation transport and plasmas
Luis Chacon
Los Alamos National Laboratory
Theoretical Division
We consider the challenge of developing accurate, generalizable closures for out-of-equilibrium conditions in radiation transport and plasmas. Physical systems with infrequent collisions often depart from thermodynamic equilibrium, requiring augmented mathematical models including not only configuration space, but also velocity (or energy/angle) coordinates. Such physical models are high-dimensional (at least 6D+time), strongly nonlinear, and multiscale in time and space. For radiation and weakly coupled plasmas (the foci of this presentation), such models take the form of the Boltzmann and Vlasov-Fokker-Planck equations, respectively. Moment equations, derived by successive integration in phase-space variables, suffer from the so-called closure problem, in which a given moment equation depends on higher-order moments. If a suitable model is available for the higher-order moment terms (as in strongly collisional regimes), the moment system has been “closed” and if successful it may offer high fidelity at a fraction of computational cost. However, such models rarely exist for weakly collisional regimes.
In this presentation, we will explore developing data-driven closures for both radiative transfer [1] and plasma applications in weakly collisional regimes. For the radiation transport application, we will explore constructing interpretable closures for optically thin media from high-fidelity radiation transport simulations [2] using weak-form sparse identification of nonlinear dynamics (WSINDy). WSINDy performs equation discovery, whereby governing equations are identified symbolically from data from a specified operator library. We propose a WSINDy target library from physical arguments and required structure such as reflection symmetry (in 1D) and hyperbolicity. We show on a series of multifrequency radiation inflow problems that our proposed closures improve on the high-fidelity simulation by removing numerical artifacts and generalize well beyond their training data set, enabling extrapolation in spacetime and in parameter space, where drive temperature and opacity magnitude are treated as model parameters.
For plasmas, we consider the problem of developing closures for electron heat-flux in arbitrary collisionality regimes using a fractional-calculus approach. We mine data from fully kinetic Vlasov-Fokker-Planck simulations [3] and derive significant intuition from earlier closures in both collisionless [4] and collisional [5] regimes to postulate a convolution-kernel hypothesis for their generalization to arbitrary collisional regimes. The analysis confirms the validity of our hypothesis, opening the door for practical numerical implementations.
1. Messenger et al. “Learning interpretable closures for thermal radiation transport in optically thin media using WSINDy,” arXiv:2510.11840 (2025)
2. Hammer, Park, and Chacón, JCP 386:653-674 (2019)
3. Taitano et al., CPC 263:107861 (2021)
4. Hammett and Perkins, PRL 64(25):3019 (1990)
5. Luciani, Mora, Virmont, PRL 51(18):1664 (1983)