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Fast Regression of the Tritium Breeding Ratio in Fusion Reactors

Petr Mánek, Graham Van Goffrier, Vignesh Gopakumar, Nikolaos Nikolaou, Jonathan Shimwell, Ingo Waldmann

TL;DR

The paper addresses the computational bottleneck of evaluating the Tritium Breeding Ratio (TBR) in fusion reactor design by developing fast surrogate estimates of a Monte Carlo neutronics model (Paramak/OpenMC). It systematically compares nine surrogate families under decoupled and adaptive training regimes, introducing Quality-Adaptive Surrogate Sampling (QASS) to selectively augment training data. The results show that deep neural networks can achieve near-perfect regression accuracy with astonishing speedups (e.g., $R^2=0.998$ and a mean prediction time of about $1.12~\text{μs}$, yielding ~$6.92\times 10^6$ relative speedup), while tree-based ensembles remain competitive, especially on smaller training sets. The work demonstrates that substantial computational gains are achievable for rapid reactor-parameter exploration, with open-source tooling and a demonstrated adaptive sampling pathway enabling broader deployment of fast TBR surrogates.

Abstract

The tritium breeding ratio (TBR) is an essential quantity for the design of modern and next-generation D-T fueled nuclear fusion reactors. Representing the ratio between tritium fuel generated in breeding blankets and fuel consumed during reactor runtime, the TBR depends on reactor geometry and material properties in a complex manner. In this work, we explored the training of surrogate models to produce a cheap but high-quality approximation for a Monte Carlo TBR model in use at the UK Atomic Energy Authority. We investigated possibilities for dimensional reduction of its feature space, reviewed 9 families of surrogate models for potential applicability, and performed hyperparameter optimisation. Here we present the performance and scaling properties of these models, the fastest of which, an artificial neural network, demonstrated $R^2=0.985$ and a mean prediction time of $0.898\ μ\mathrm{s}$, representing a relative speedup of $8\cdot 10^6$ with respect to the expensive MC model. We further present a novel adaptive sampling algorithm, Quality-Adaptive Surrogate Sampling, capable of interfacing with any of the individually studied surrogates. Our preliminary testing on a toy TBR theory has demonstrated the efficacy of this algorithm for accelerating the surrogate modelling process.

Fast Regression of the Tritium Breeding Ratio in Fusion Reactors

TL;DR

The paper addresses the computational bottleneck of evaluating the Tritium Breeding Ratio (TBR) in fusion reactor design by developing fast surrogate estimates of a Monte Carlo neutronics model (Paramak/OpenMC). It systematically compares nine surrogate families under decoupled and adaptive training regimes, introducing Quality-Adaptive Surrogate Sampling (QASS) to selectively augment training data. The results show that deep neural networks can achieve near-perfect regression accuracy with astonishing speedups (e.g., and a mean prediction time of about , yielding ~ relative speedup), while tree-based ensembles remain competitive, especially on smaller training sets. The work demonstrates that substantial computational gains are achievable for rapid reactor-parameter exploration, with open-source tooling and a demonstrated adaptive sampling pathway enabling broader deployment of fast TBR surrogates.

Abstract

The tritium breeding ratio (TBR) is an essential quantity for the design of modern and next-generation D-T fueled nuclear fusion reactors. Representing the ratio between tritium fuel generated in breeding blankets and fuel consumed during reactor runtime, the TBR depends on reactor geometry and material properties in a complex manner. In this work, we explored the training of surrogate models to produce a cheap but high-quality approximation for a Monte Carlo TBR model in use at the UK Atomic Energy Authority. We investigated possibilities for dimensional reduction of its feature space, reviewed 9 families of surrogate models for potential applicability, and performed hyperparameter optimisation. Here we present the performance and scaling properties of these models, the fastest of which, an artificial neural network, demonstrated and a mean prediction time of , representing a relative speedup of with respect to the expensive MC model. We further present a novel adaptive sampling algorithm, Quality-Adaptive Surrogate Sampling, capable of interfacing with any of the individually studied surrogates. Our preliminary testing on a toy TBR theory has demonstrated the efficacy of this algorithm for accelerating the surrogate modelling process.

Paper Structure

This paper contains 14 sections, 2 equations, 8 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Problem Description
  3. Methodology
  4. Decoupled Approach
  5. Adaptive Approach
  6. Results
  7. Decoupled Approach
  8. Hyperparameter Tuning
  9. Scaling Benchmark
  10. Model Comparison
  11. Adaptive Approach
  12. Conclusion
  13. Acknowledgements
  14. References

Figures (8)

  • Figure 1: Diagram of the simple sphere geometry (not to scale) where the blanket is , the first wall is and the neutron point source is . Blanket and first wall thickness, as well as their material and structural properties, are adjustable parameters of the simulation that are later optimized (see tbl:params for complete parameter listing).
  • Figure 2: Schematic of QASS algorithm
  • Figure 3: Experiment 1 results. 20 best surrogates per each considered family, plotted in terms of $\overline{t}_{\text{pred.}}$ and $R^2$ with 3 selected slices out of 4 (defined in tbl:slices).
  • Figure 4: Experiment 2 results, plotted analogously to fig:exp1-time-vs-reg.
  • Figure 5: Experiment 3 results, displayed as a function of $N_0$. From top to bottom, $R^2$, $\overline{t}_{\text{trn.}}$, $\overline{t}_{\text{pred.}}$.
  • ...and 3 more figures