# Data-Driven Reconstruction of Spatially Resolved Electron and Ion Energy Distributions from Macroscopic Plasma Quantities with Deep Neural Networks

arXiv: https://arxiv.org/abs/2608.16519 · HTML: https://mlsanity.com/paper/2608.16519/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 70 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Builds on (most cited first, 7 of 7)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Extracting Electron Scattering Cross Sections from Swarm Data using Deep Neural Networks](https://mlsanity.com/paper/2011.14711/) (2020)
- [Deep Learning Architecture Based Approach For 2D-Simulation of Microwave Plasma Interaction](https://mlsanity.com/paper/2206.01263/) (2022)
- [Deep Learning assisted microwave-plasma interaction based technique for plasma density estimation](https://mlsanity.com/paper/2304.14807/) (2023)
- [Benchmarking and Parallelization of Electrostatic Particle-In-Cell for low-temperature Plasma Simulation by particle-thread Binding](https://mlsanity.com/paper/2506.21524/) (2025)

## Abstract (arXiv)

Spatially resolved EEDFs/IEDFs provide essential kinetic information about low-temperature plasmas (LTPs) and play a central role in determining transport, chemical reaction rates, and plasma surface interactions. While kinetic simulations directly resolve these distributions, experimental measurements remain challenging and are often invasive, spatially limited, or require assumptions regarding the distribution shape such as a Maxwellian. However, several macroscopic plasma observables can be measured non-invasively using advanced diagnostic techniques, providing spatially resolved information about the plasma state. An important inverse problem is therefore whether readily measurable macroscopic plasma quantities contain sufficient information to reconstruct the underlying kinetic state. In this work, we investigate this problem by learning a nonlinear mapping from spatially resolved macroscopic plasma observables to the corresponding spatially resolved EEDFs/IEDFs using a deep learning framework. Paired datasets comprising 2D macroscopic observables and spatially resolved EDFs are generated using 2D-3V PIC-MCC simulations. Three representative learning paradigms, a U-Net, a FNO, and a MeshGraphNet, are employed in this study to learn this inverse mapping. The predicted EDFs reproduce both bulk plasma and sheath characteristics with good agreement to the PIC-MCC reference data, with the FNO providing the best overall performance. Beyond conventional metrics, physics-based validation demonstrates that the reconstructed EDFs accurately recover the corresponding density and temperature, and rate coefficients. These results demonstrate that macroscopic plasma observables encode sufficient information to infer important kinetic properties in LTPs, providing a potential foundation for surrogate kinetic modeling and next-generation plasma diagnostics.