# Fast Dynamic 1D Simulation of Divertor Plasmas with Neural PDE Surrogates

arXiv: https://arxiv.org/abs/2305.18944 · HTML: https://mlsanity.com/paper/2305.18944/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 92 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [Neural Conservation Laws: A Divergence-Free Perspective](https://mlsanity.com/paper/2210.01741/) (2022)
- [Geometric Clifford Algebra Networks](https://mlsanity.com/paper/2302.06594/) (2023)
- [Attention Beats Concatenation for Conditioning Neural Fields](https://mlsanity.com/paper/2209.10684/) (2022)
- [Deep Learning Models for Global Coordinate Transformations that Linearize PDEs](https://mlsanity.com/paper/1911.02710/) (2019)
- [Hybrid deep learning architecture for general disruption prediction across tokamaks](https://mlsanity.com/paper/2007.01401/) (2020)

## Built on by (most cited first, 9 of 9)

- [Plasma Surrogate Modelling using Fourier Neural Operators](https://mlsanity.com/paper/2311.05967/) (2023)
- [Calibrated Physics-Informed Uncertainty Quantification](https://mlsanity.com/paper/2502.04406/) (2025)
- [Accelerating Simulation of Two-Phase Flows with Neural PDE Surrogates](https://mlsanity.com/paper/2405.17260/) (2024)
- [Robust Confinement State Classification with Uncertainty Quantification through Ensembled Data-Driven Methods](https://mlsanity.com/paper/2502.17397/) (2025)
- [Plasma State Monitoring and Disruption Characterization using Multimodal VAEs](https://mlsanity.com/paper/2504.17710/) (2025)
- [Autoregressive long-horizon prediction of plasma edge dynamics](https://mlsanity.com/paper/2512.23884/) (2025)
- [A novel Fourier neural operator framework for classification of multi-sized images: Application to three dimensional digital porous media](https://mlsanity.com/paper/2402.11568/) (2024)
- [Efficient Probabilistic Modeling of Crystallization at Mesoscopic Scale](https://mlsanity.com/paper/2405.16608/) (2024)
- [Probabilistic and Geometry Aware Neural Surrogate of Scrape Off Layer Plasma Simulations](https://mlsanity.com/paper/2609.28116/) (2026)

## Abstract (arXiv)

Managing divertor plasmas is crucial for operating reactor scale tokamak devices due to heat and particle flux constraints on the divertor target. Simulation is an important tool to understand and control these plasmas, however, for real-time applications or exhaustive parameter scans only simple approximations are currently fast enough. We address this lack of fast simulators using neural PDE surrogates, data-driven neural network-based surrogate models trained using solutions generated with a classical numerical method. The surrogate approximates a time-stepping operator that evolves the full spatial solution of a reference physics-based model over time. We use DIV1D, a 1D dynamic model of the divertor plasma, as reference model to generate data. DIV1D's domain covers a 1D heat flux tube from the X-point (upstream) to the target. We simulate a realistic TCV divertor plasma with dynamics induced by upstream density ramps and provide an exploratory outlook towards fast transients. State-of-the-art neural PDE surrogates are evaluated in a common framework and extended for properties of the DIV1D data. We evaluate (1) the speed-accuracy trade-off; (2) recreating non-linear behavior; (3) data efficiency; and (4) parameter inter- and extrapolation. Once trained, neural PDE surrogates can faithfully approximate DIV1D's divertor plasma dynamics at sub real-time computation speeds: In the proposed configuration, 2ms of plasma dynamics can be computed in ≈0.63ms of wall-clock time, several orders of magnitude faster than DIV1D.