Physics informed Neural Networks applied to the description of wave-particle resonance in kinetic simulations of fusion plasmas

TL;DR

This paper explores the use of Physics Informed Neural Networks (PINNs) to model wave-particle resonance phenomena in kinetic plasma simulations, focusing on Landau damping and bump-on-tail instability, and introduces a novel I-PINN variant.

Contribution

It demonstrates the application of PINNs to the Vlasov-Poisson system and develops the Integrable PINN (I-PINN) for improved handling of integral equations in plasma physics.

Findings

PINNs effectively approximate solutions to the Vlasov-Poisson system.

I-PINN enhances the solution of integral equations in plasma simulations.

PINNs outperform standard neural networks in solution compression.

Abstract

The Vlasov-Poisson system is employed in its reduced form version (1D1V) as a test bed for the applicability of Physics Informed Neural Network (PINN) to the wave-particle resonance. Two examples are explored: the Landau damping and the bump-on-tail instability. PINN is first tested as a compression method for the solution of the Vlasov-Poisson system and compared to the standard neural networks. Second, the application of PINN to solving the Vlasov-Poisson system is also presented with the special emphasis on the integral part, which motivates the implementation of a PINN variant, called Integrable PINN (I-PINN), based on the automatic-differentiation to solve the partial differential equation and on the automatic-integration to solve the integral equation.