A Physics-Constrained Deep Learning Treatment of Runaway Electron Dynamics

TL;DR

This paper introduces a physics-informed neural network framework using an adjoint formulation to efficiently model the time evolution of runaway electron densities in plasmas, maintaining kinetic accuracy and enabling rapid predictions.

Contribution

It presents a novel adjoint-based PINN approach for projecting runaway electron densities forward in time across various plasma conditions, with a trained model offering rapid, accurate predictions.

Findings

The PINN framework accurately matches traditional Fokker-Planck solver results.

Once trained, the model predicts RE density evolution with minimal online computation.

The method effectively handles different initial conditions and plasma parameters.

Abstract

An adjoint formulation leveraging a physics-informed neural network (PINN) is employed to advance the density moment of a runaway electron (RE) distribution forward in time. A distinguishing feature of this approach is that once the adjoint problem is solved, its solution can be used to project the RE density forward in time for an arbitrary initial momentum space distribution of REs. Furthermore, by employing a PINN, a parametric solution to the adjoint problem can be learned. Thus, once trained, this adjoint-deep learning framework is able to efficiently project the RE density forward in time across various plasma conditions while still including a fully kinetic description of RE dynamics. As an example application, the temporal evolution of the density of primary electrons is studied, with particular emphasis on evaluating the decay of a RE population when below threshold. Predictions from the adjoint-deep learning framework are found to be in good agreement with a traditional relativistic electron Fokker-Planck solver, for several distinct initial conditions, and across an array of physics parameters. Once trained the PINN thus provides a means of generating RE density time histories with exceptionally low online execution time.