Fast dynamic 1D simulation of divertor plasmas with neural PDE surrogates

Yoeri Poels (Corresponding author), Gijs Derks, Egbert Westerhof, Koen Minartz, Sven Wiesen, Vlado Menkovski

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
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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 partial differential equation (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, 2 ms of plasma dynamics can be computed in ≈ 0.63 ms of wall-clock time, several orders of magnitude faster than DIV1D.

Original languageEnglish
Article number126012
Number of pages28
JournalNuclear Fusion
Issue number12
Publication statusPublished - Dec 2023


This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200—EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them. This work made use of the Dutch national e-infrastructure with the support of the SURF Cooperative using Grant No. EINF-3557.

FundersFunder number
Surf, StichtingEINF-3557
European Commission101052200—EUROfusion


    • divertor plasma simulation
    • exhaust simulation
    • machine learning
    • neural networks
    • neural pde surrogates
    • scrape-off layer simulation
    • surrogate models


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