Learning heat transport kernels using a nonlocal heat transport theory-informed neural network

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 spatio-temporal 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-Nicolaï-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.