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Transfer Learning for Analysis of Collective and Non-Collective Thomson Scattering Spectra

T. Van Hoomissen, J. Alhuthali, A. M. Ortiz, D. A. Mariscal, R. S. Dorst, S. Eisenbach, H. Zhang, J. J. Pilgram, C. G. Constantin, L. Rovige, C. Niemann, D. B. Schaeffer

TL;DR

Five architecturally diverse deep neural networks are presented, pre-trained on synthetic TS data and adapted for experimentally measured TS data, to evaluate the efficacy of transfer learning in estimating ne and Te in both the collective and non-collective scattering regimes.

Abstract

Thomson scattering (TS) diagnostics provide reliable, minimally perturbative measurements of fundamental plasma parameters, such as electron density ($n_e$) and electron temperature ($T_e$). Deep neural networks can provide accurate estimates of $n_e$ and $T_e$ when conventional fitting algorithms may fail, such as when TS spectra are dominated by noise, or when fast analysis is required for real-time operation. Although deep neural networks typically require large training sets, transfer learning can improve model performance on a target task with limited data by leveraging pre-trained models from related source tasks, where select hidden layers are further trained using target data. We present five architecturally diverse deep neural networks, pre-trained on synthetic TS data and adapted for experimentally measured TS data, to evaluate the efficacy of transfer learning in estimating $n_e$ and $T_e$ in both the collective and non-collective scattering regimes. We evaluate errors in $n_e$ and $T_e$ estimates as a function of training set size for models trained with and without transfer learning, and we observe decreases in model error from transfer learning when the training set contains $\lessapprox$ 200 experimentally measured spectra.

Transfer Learning for Analysis of Collective and Non-Collective Thomson Scattering Spectra

TL;DR

Five architecturally diverse deep neural networks are presented, pre-trained on synthetic TS data and adapted for experimentally measured TS data, to evaluate the efficacy of transfer learning in estimating ne and Te in both the collective and non-collective scattering regimes.

Abstract

Thomson scattering (TS) diagnostics provide reliable, minimally perturbative measurements of fundamental plasma parameters, such as electron density () and electron temperature (). Deep neural networks can provide accurate estimates of and when conventional fitting algorithms may fail, such as when TS spectra are dominated by noise, or when fast analysis is required for real-time operation. Although deep neural networks typically require large training sets, transfer learning can improve model performance on a target task with limited data by leveraging pre-trained models from related source tasks, where select hidden layers are further trained using target data. We present five architecturally diverse deep neural networks, pre-trained on synthetic TS data and adapted for experimentally measured TS data, to evaluate the efficacy of transfer learning in estimating and in both the collective and non-collective scattering regimes. We evaluate errors in and estimates as a function of training set size for models trained with and without transfer learning, and we observe decreases in model error from transfer learning when the training set contains 200 experimentally measured spectra.

Paper Structure

This paper contains 15 sections, 14 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Deep Transfer Learning
  4. Thomson scattering
  5. Experimental Data
  6. Synthetic Data
  7. Methods
  8. Data Pre-Processing
  9. Model Setups
  10. Hyperparameter Tuning
  11. Transfer Learning Procedure
  12. Results
  13. Conclusions
  14. Acknowledgments
  15. Data Availability

Figures (8)

  • Figure 1: Comparison of synthetic (blue) and experimental (red) Thomson scattering spectra. The synthetic spectrum is generated with the Gaussian model using the same values for electron density ($n_e=4.1 \times 10^{15}$ cm$^{-3}$) and electron temperature ($T_e=3.83$ eV) as those derived from a Gaussian fit to the experimental spectrum. Negative values in the experimentally measured spectrum arise from background subtraction of plasma-only shots.
  • Figure 2: Distributions of synthetic (blue) and experimental (red) data across electron density and temperature. While the experimental dataset is concentrated in a narrow region, the synthetic dataset covers a broader range of $n_e$ and $T_e$ values, which helps improve model generalization. The constraint of $\alpha <3$ limits synthetic data from covering the lower-right region of the plot.
  • Figure 3: Diagram of ensemble averaging and transfer learning with the multi-layer perceptron. The outputs of each model are combined to produce average estimates for $n_e$ and $T_e$ ($\mu_{n_e}$ and $\mu_{T_e}$) along with corresponding uncertainty estimates ($\sigma_{n_e}$ and $\sigma_{T_e}$).
  • Figure 4: Model estimates versus ground truth values for electron density (top row) and electron temperature (bottom row). Columns are organized by neural network architecture. Points in the top row are shaded according to the corresponding $T_e$, while points in the bottom row are shaded according to the corresponding $n_e$. Error bars span the range of model estimates for the ensemble MLP and BNN. The dashed lines represent where model estimates would fall under perfect agreement with the ground truth values.
  • Figure 5: Example TS spectrum corrupted by stray light, revealed by the spike in intensity near the probe wavelength. Inset: MLP $n_e$ estimates (x-axis) vs. ground truth values (y-axis), with the point circled in red corresponding to the example spectrum. All models underestimate $n_e$ for this spectrum.
  • ...and 3 more figures