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The Vlasov-Poisson system is employed in its reduced form version (1D1V) as atest bed for the applicability of Physics Informed Neural Network (PINN) to thewave-particle resonance. Two examples are explored: the Landau damping and thebump-on-tail instability. PINN is first tested as a compression method for thesolution of the Vlasov-Poisson system and compared to the standard neuralnetworks. Second, the application of PINN to solving the Vlasov-Poisson systemis also presented with the special emphasis on the integral part, whichmotivates the implementation of a PINN variant, called Integrable PINN(I-PINN), based on the automatic-differentiation to solve the partialdifferential equation and on the automatic-integration to solve the integralequation.

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