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

• URL: http://arxiv.org/abs/2308.12312v1
• Date: Wed, 23 Aug 2023 07:00:56 GMT
• Title: Physics informed Neural Networks applied to the description of wave-particle resonance in kinetic simulations of fusion plasmas
• Authors: Jai Kumar (IRFM), David Zarzoso (M2P2), Virginie Grandgirard (IRFM), Jan Ebert, Stefan Kesselheim
• Abstract summary: PINN is first tested as a compression method for the solution of the Vlasov-Poisson system. The application of PINN to solving the Vlasov-Poisson system is also presented with the special emphasis on the integral part.
• Score: 0.06316710659541969
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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