Learning Heat Transport Kernels Using a Nonlocal Heat Transport Theory-Informed Neural Network

TL;DR

This paper introduces a neural network-based model that learns dynamic, nonlocal heat transport kernels directly from kinetic plasma simulations, improving upon classical static models and capturing complex plasma behaviors.

Contribution

The paper presents a novel neural network framework that learns time-evolving heat flux kernels from simulation data, extending nonlocal heat transport modeling beyond traditional static kernel approaches.

Findings

Strong agreement with kinetic benchmarks across regimes

Captures dynamic, time-dependent heat transport behaviors

Outperforms classical static kernel models

Abstract

We present a data-driven framework for the modeling of nonlocal heat transport in plasmas using a nonlocal theory informed neural network trained on kinetic Particle-in-Cell simulations that span both local and nonlocal regimes. The model learns spatiotemporal heat flux kernels directly from simulation data, capturing dynamic transport behaviors beyond the reach of classical formulations. Unlike time-independent kernel models such as Luciani Mora Virmont and Schurtz Nicola\"i Busquet models, our approach yields physically grounded, time-evolving kernels that adapt to varying plasma conditions. The resulting predictions show strong agreement with kinetic benchmarks across regimes. This offers a promising direction for data-driven modeling of nonlocal heat transport and contributes to a deeper understanding of plasma dynamics.