  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.
