Micro-Macro Tensor Neural Surrogates for Uncertainty Quantification in Collisional Plasma

TL;DR

This paper introduces a variance-reduced Monte Carlo framework utilizing tensor neural surrogates for efficient uncertainty quantification in collisional plasma simulations, significantly reducing computational costs while maintaining accuracy.

Contribution

It develops a novel tensor neural network based on micro-macro decomposition, calibrated for asymptotic limits, to serve as an efficient surrogate in plasma UQ tasks.

Findings

Substantial variance reduction over standard Monte Carlo methods.

Accurate statistical results with fewer high-fidelity samples.

Lower computational time while maintaining robustness.

Abstract

Plasma kinetic equations exhibit pronounced sensitivity to microscopic perturbations in model parameters and data, making reliable and efficient uncertainty quantification (UQ) essential for predictive simulations. However, the cost of uncertainty sampling, the high-dimensional phase space, and multiscale stiffness pose severe challenges to both computational efficiency and error control in traditional numerical methods. These aspects are further emphasized in presence of collisions where the high-dimensional nonlocal collision integrations and conservation properties pose severe constraints. To overcome this, we present a variance-reduced Monte Carlo framework for UQ in the Vlasov--Poisson--Landau (VPL) system, in which neural network surrogates replace the multiple costly evaluations of the Landau collision term. The method couples a high-fidelity, asymptotic-preserving VPL solver with inexpensive, strongly correlated surrogates based on the Vlasov--Poisson--Fokker--Planck (VPFP) and Euler--Poisson (EP) equations. For the surrogate models, we introduce a generalization of the separable physics-informed neural network (SPINN), developing a class of tensor neural networks based on an anisotropic micro-macro decomposition, to reduce velocity-moment costs, model complexity, and the curse of dimensionality. To further increase correlation with VPL, we calibrate the VPFP model and design an asymptotic-preserving SPINN whose small- and large-Knudsen limits recover the EP and VP systems, respectively. Numerical experiments show substantial variance reduction over standard Monte Carlo, accurate statistics with far fewer high-fidelity samples, and lower wall-clock time, while maintaining robustness to stochastic dimension.