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EuroPED-NN: Uncertainty aware surrogate model

A. Panera Alvarez, A. Ho, A. Jarvinen, S. Saarelma, S. Wiesen, JET Contributors, the AUG team

Abstract

This work successfully generates an uncertainty-aware surrogate model of the EuroPED plasma pedestal model using the Bayesian neural network with noise contrastive prior (BNN-NCP) technique. This model is trained using data from the JET-ILW pedestal database and subsequent model evaluations, conforming to EuroPED-NN. The BNN-NCP technique has been proven to be a suitable method for generating uncertainty-aware surrogate models. It matches the output results of a regular neural network while providing confidence estimates for predictions as uncertainties. Additionally, it highlights out-of-distribution (OOD) regions using surrogate model uncertainties. This provides critical insights into model robustness and reliability. EuroPED-NN has been physically validated, first, analyzing electron density $n_e\!\left(ψ_{\text{pol}}=0.94\right)$ with respect to increasing plasma current, $I_p$, and second, validating the $Δ-β_{p,ped}$ relation associated with the EuroPED model. This affirms the robustness of the underlying physics learned by the surrogate model. On top of that, the method was used to develop a EuroPED-like model fed with experimental data, i.e. an uncertainty aware experimental model, which is functional in JET database. Both models have been also tested in $\sim 50$ AUG shots.

EuroPED-NN: Uncertainty aware surrogate model

Abstract

This work successfully generates an uncertainty-aware surrogate model of the EuroPED plasma pedestal model using the Bayesian neural network with noise contrastive prior (BNN-NCP) technique. This model is trained using data from the JET-ILW pedestal database and subsequent model evaluations, conforming to EuroPED-NN. The BNN-NCP technique has been proven to be a suitable method for generating uncertainty-aware surrogate models. It matches the output results of a regular neural network while providing confidence estimates for predictions as uncertainties. Additionally, it highlights out-of-distribution (OOD) regions using surrogate model uncertainties. This provides critical insights into model robustness and reliability. EuroPED-NN has been physically validated, first, analyzing electron density with respect to increasing plasma current, , and second, validating the relation associated with the EuroPED model. This affirms the robustness of the underlying physics learned by the surrogate model. On top of that, the method was used to develop a EuroPED-like model fed with experimental data, i.e. an uncertainty aware experimental model, which is functional in JET database. Both models have been also tested in AUG shots.
Paper Structure (19 sections, 6 equations, 31 figures, 1 table)

This paper contains 19 sections, 6 equations, 31 figures, 1 table.

Table of Contents

  1. Introduction
  2. Development of EuroPED-NN
  3. Model description, inputs and outputs
  4. BNN-NCP Technique
  5. Neural network architecture and loss function
  6. Zero-Dimensional Pedestal Database
  7. Hyperparameters for epistemic and aleatoric uncertainty
  8. Verification and Characterization of EuroPED-NN
  9. Performance
  10. Independent physical analysis
  11. $I_p$ scan
  12. $\Delta-\beta_{p,ped}$ relation
  13. Contextualization in data-driven pedestal models
  14. Extrapolation of EuroPED-NN to AUG data
  15. Extension of the methodology to experimental data and extrapolation to AUG experimental data.
  16. ...and 4 more sections

Figures (31)

  • Figure 1: Main network scheme
  • Figure 2: Output layer scheme
  • Figure 4: Input data histograms for EuroPED-NN from the dataset used in this study, obtained from aJETExperimentalPedestalDatabase-Frassinetti. $\mu$ stands for the parameter defined in equation \ref{['eq:mu']}, $B_t$ for toroidal magnetic field, $\epsilon$ for inverse aspect ratio, $\kappa$ for elongation parameter, $\delta$ for triangularity, $P_{tot}$ for injected auxiliary heating power, $n_{e,sep}$ for separatrix electron density and $Z_{eff,h}$ for line-integrated effective charge.
  • Figure 5: $\Delta$
  • Figure 6: $n_{e,ped}$
  • ...and 26 more figures