Data-Driven Modeling of Landau Damping by Fourier Neural Operator

TL;DR

This paper uses Fourier Neural Operator to create surrogate models for Landau damping based on kinetic simulation data, achieving high accuracy in predicting heat flux from electron density.

Contribution

It introduces the application of Fourier Neural Operator to model Landau fluid closure, outperforming traditional MLP architectures in this context.

Findings

FNO accurately predicts heat flux from electron density.

FNO outperforms MLP in modeling physical quantities.

Surrogate models can effectively replicate kinetic simulation results.

Abstract

The development of machine learning techniques enables us to construct surrogate models from data of direct numerical simulations, which has important implications for modeling complex physical systems. In this paper, based on the output from 1D Vlasov-Ampere simulations, we adopt the Fourier Neural Operator (FNO) to build surrogate models of Landau fluid closure for multi-moment fluid equations from kinetic simulation data. The trained FNO is able to obtain the heat flux using electron density as input, in agreement with the true value from kinetic simulations. We compare the physical quantities obtained using the FNO and Multilayer Perceptron (MLP) architectures, and found that the results of FNO are significantly better than that of MLP.