Learning collision operators from plasma phase space data using differentiable simulators

Abstract

We propose a methodology to infer collision operators from phase space data of plasma dynamics. Our approach combines a differentiable kinetic simulator, whose core component in this work is a differentiable Fokker-Planck solver, with a gradient-based optimisation method to learn the collisional operators that best describe the phase space dynamics. We test our method using data from two-dimensional Particle-in-Cell simulations of spatially uniform thermal plasmas, and learn the collision operator that captures the self-consistent electromagnetic interaction between finite-size charged particles over a wide variety of simulation parameters. We demonstrate that the learned operators are more accurate than alternative estimates based on particle tracks, while making no prior assumptions about the relevant time scales of the processes and significantly reducing memory requirements. We find that the retrieved operators, obtained in the non-relativistic regime, are in excellent agreement with theoretical predictions derived for electrostatic scenarios. Our results show that differentiable simulators offer a powerful and computational efficient approach to infer novel operators for a wide rage of problems, such as electromagnetically dominated collisional dynamics and stochastic wave-particle interactions.

accepted for publication in Journal of Plasma Physics, code available at https://github.com/diogodcarvalho/ml-pic-collision-operators

References in corpus (18)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Dense plasmas in astrophysics: from giant planets to neutron stars
• Solving Fokker-Planck equation using deep learning
• First-principles demonstration of diffusive-advective particle acceleration in kinetic simulations of relativistic plasma turbulence
• Differential Form of the Collision Integral for a Relativistic Plasma
• Extending plasma transport theory to strong coupling through the concept of an effective interaction potential
• Low-temperature plasma simulation based on physics-informed neural networks: frameworks and preliminary applications
• Trend to Equilibrium for the Kinetic Fokker-Planck Equation via the Neural Network Approach
• Using neural networks to accelerate the solution of the Boltzmann equation
• Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)
• RelaxNet: A structure-preserving neural network to approximate the Boltzmann collision operator
• Unsupervised Discovery of Inertial-Fusion Plasma Physics using Differentiable Kinetic Simulations and a Maximum Entropy Loss Function
• opPINN: Physics-Informed Neural Network with operator learning to approximate solutions to the Fokker-Planck-Landau equation
• A Physics-Informed Deep Learning Model of the Hot Tail Runaway Electron Seed
• Kinetic theory of particle-in-cell simulation plasma and the ensemble averaging technique
• Separable Physics-informed Neural Networks for Solving the BGK Model of the Boltzmann Equation
• Energy Diffusion and Advection Coefficients in Kinetic Simulations of Relativistic Plasma Turbulence
• FourierSpecNet: Neural Collision Operator Approximation Inspired by the Fourier Spectral Method for Solving the Boltzmann Equation