NEOPIC: A Neural Operator Framework for Particle-based Kinetic Plasma Simulations
Abstract
We introduce NEOPIC, a framework for learning the field operator in particle-based methods applied to kinetic plasma simulations. Its key novelty is a neural operator that acts directly on the empirical measure of the particles, rather than on a grid, and is evaluated at the particle positions. No mesh or tree is needed and, unlike grid-based neural operators, no deposition onto a mesh takes place, so the particle noise that dominates the inputs of particle simulations is not aliased. Since it replaces only the field solve, it serves as a plug-and-play field solver for particle-based methods: it can be trained on data from particle-in-cell, particle-in-Fourier or tree codes, and combined with any time integrator, including implicit schemes. We prove that the discrete evaluation coincides with the continuous operator at any number of particles (representation equivalence) and derive an error analysis that separates sampling, learning and time-stepping errors: up to the learning error, NEOPIC has the error structure of standard Monte Carlo particle methods. We show that the particle noise in the training data acts as an implicit regularizer, which gives guidance on the number of training particles in relation to the particle numbers used at inference. A complexity analysis shows that NEOPIC is an O(Np) method whose constants are set by the architecture alone, independently of any mesh or tree. Numerical experiments on electrostatic benchmarks in two and three dimensions, including Landau damping, two-stream and bump-on-tail instabilities, a cyclotron mini-app and a Penning trap, confirm the theoretical findings. A single model trained on several mini-apps generated by different reference methods captures all of them and remains stable up to twice the training time window, which points towards foundation models for fields in particle-based methods.
Related
- On the diffusive-mean field limit of a kinetic weakly interacting particle system
- An implicit multiscale solver for steady kinetic equations based on wave-particle decomposition
- Wave-Particle Decomposition for Kinetic Equations II: Full Boltzmann equation
- A General Framework for Operator Continuity between Riesz Spaces
- An Analytical Framework for a Multi-Particle Oja Flow
BibTeX
@misc{muralikrishnan2026neopic,
title = {{NEOPIC: A Neural Operator Framework for Particle-based Kinetic Plasma Simulations}},
author = {Sriramkrishnan Muralikrishnan and Chelsea Maria John and Jeffrey Kelling and Michael Bussmann and Robert Speck and Paul Gibbon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40528},
eprint = {2610.40528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40528},
}
RIS
TY - UNPB
TI - NEOPIC: A Neural Operator Framework for Particle-based Kinetic Plasma Simulations
AU - Sriramkrishnan Muralikrishnan
AU - Chelsea Maria John
AU - Jeffrey Kelling
AU - Michael Bussmann
AU - Robert Speck
AU - Paul Gibbon
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40528
UR - https://arxiv.org/abs/2610.40528
AB - We introduce NEOPIC, a framework for learning the field operator in particle-based methods applied to kinetic plasma simulations. Its key novelty is a neural operator that acts directly on the empirical measure of the particles, rather than on a grid, and is evaluated at the particle positions. No mesh or tree is needed and, unlike grid-based neural operators, no deposition onto a mesh takes place, so the particle noise that dominates the inputs of particle simulations is not aliased. Since it replaces only the field solve, it serves as a plug-and-play field solver for particle-based methods: it can be trained on data from particle-in-cell, particle-in-Fourier or tree codes, and combined with any time integrator, including implicit schemes. We prove that the discrete evaluation coincides with the continuous operator at any number of particles (representation equivalence) and derive an error analysis that separates sampling, learning and time-stepping errors: up to the learning error, NEOPIC has the error structure of standard Monte Carlo particle methods. We show that the particle noise in the training data acts as an implicit regularizer, which gives guidance on the number of training particles in relation to the particle numbers used at inference. A complexity analysis shows that NEOPIC is an O(N_p) method whose constants are set by the architecture alone, independently of any mesh or tree. Numerical experiments on electrostatic benchmarks in two and three dimensions, including Landau damping, two-stream and bump-on-tail instabilities, a cyclotron mini-app and a Penning trap, confirm the theoretical findings. A single model trained on several mini-apps generated by different reference methods captures all of them and remains stable up to twice the training time window, which points towards foundation models for fields in particle-based methods.
ER -