# Probabilistic and Geometry Aware Neural Surrogate of Scrape Off Layer Plasma Simulations

arXiv: https://arxiv.org/abs/2609.28116 · HTML: https://mlsanity.com/paper/2609.28116/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Fast Dynamic 1D Simulation of Divertor Plasmas with Neural PDE Surrogates](https://mlsanity.com/paper/2305.18944/) (2023)

## Abstract (arXiv)

Fast surrogates for tokamak boundary-plasma simulation are typically deterministic regressors mapping a global operating point to a flattened vector of cell values. Near the divertor detachment transition the steady state is not reliably single-valued. A point estimate must average over qualitatively different plasma states, and it arrives with no statement of confidence. Moreover, the flattened vector representation discards the geometric structure of the SOLPS-ITER mesh. This work addresses both problems. We unroll the curvilinear mesh into three fixed-size image tensors whose layout preserves cell adjacency and inverts exactly, letting a convolutional network act on the geometry without loss of information. A conditional flow matching model, well suited to highly sensitive systems, is then trained on this representation. The result is an efficient, scalable surrogate that captures multiple plausible outcomes even at sensitive operating points. Along a gas-puff scan, the predictive distribution splits into a hot and a cold mode across an early regime transition. A further check on synthetic data with an injected bifurcation of known size confirms the model recovers both branches rather than their average.