Physics Informed Neural Networks to solve the Boltzmann Transport Equation (Ref: 4741)

Plasma physics presents a number of physical challenges. In some regimes the physics is best described by the Boltzmann equation. This models the gas in a 6 dimensional space of spatial coordinates and velocity components; the evolution of the state of the plasma corresponds to the transport of the particles in this 6-d space. The plasma can be collisionless, or collisions can be represented by an additional term in the equation. The solution of this is challenging due to the high dimensionality of the phase space, and standard techniques such as finite difference methods quickly explode in memory and computational cost.

Machine Learning techniques are making significant impacts in all areas of physical modelling. In applying a Neural Network to a physics problem, the objective is for the NN to "learn" the behaviour of the system. In "physics informed Neural Networks" (PINNs), the structure of the ODE or PDE to be solved is built into the NN. This can be highly advantageous for high dimensional systems. The objective of the project is to apply PINN to solve the Boltzmann equation and extend this to complex domains; after training the NN could provide almost instantaneous solution to this very challenging equation.