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A machine learning framework for developing quasilinear saturation rules of turbulent transport from linear gyrokinetic data

Preeti Sar, Sebastian De Pascuale, Harry Dudding, Gary Staebler

Abstract

A new neural network model for a quasilinear saturation rule has been developed to map linear gyrokinetic data to nonlinear saturated potential magnitudes to predict the total energy and particle fluxes. The training dataset is taken from the high resolution simulation database generated from nonlinear gyrokinetic turbulence simulations with the CGYRO code for developing the SAT3 model. This new model, named SAT3-NN, overall is able to capture the 1D saturated potential magnitudes of the dataset more accurately than SAT3, as depicted by lower percentage errors in the peak locations and peak values of the 1D saturated potentials. The resulting fluxes also had smaller deviations from the nonlinear CGYRO data as compared to previous saturation models such as SAT0 - SAT2. Consistent with SAT3, SAT3-NN is able to recreate the anti-gyroBohm scaling of fluxes seen for the TEM-dominated cases considered.

A machine learning framework for developing quasilinear saturation rules of turbulent transport from linear gyrokinetic data

Abstract

A new neural network model for a quasilinear saturation rule has been developed to map linear gyrokinetic data to nonlinear saturated potential magnitudes to predict the total energy and particle fluxes. The training dataset is taken from the high resolution simulation database generated from nonlinear gyrokinetic turbulence simulations with the CGYRO code for developing the SAT3 model. This new model, named SAT3-NN, overall is able to capture the 1D saturated potential magnitudes of the dataset more accurately than SAT3, as depicted by lower percentage errors in the peak locations and peak values of the 1D saturated potentials. The resulting fluxes also had smaller deviations from the nonlinear CGYRO data as compared to previous saturation models such as SAT0 - SAT2. Consistent with SAT3, SAT3-NN is able to recreate the anti-gyroBohm scaling of fluxes seen for the TEM-dominated cases considered.

Paper Structure

This paper contains 13 sections, 5 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Turbulent Fluxes and Simulation Database
  3. Machine Learning Methodology
  4. Architecture
  5. Normalization of inputs and outputs
  6. Calculation of Delta ky
  7. Loss function
  8. Training the model
  9. Results
  10. 1D Saturated Potentials
  11. Fluxes
  12. Model accuracy with parameters left out during training
  13. Conclusion

Figures (8)

  • Figure 1: Diagram of the neural network architecture
  • Figure 2: 1D saturated potentials for NL CGYRO (solid red), SAT3 (black dashed) and SAT3-NN (solid cyan) against binormal wavenumber $k_y$.
  • Figure 3: Summary plots comparing the peak values and peak location of the 1D saturated potentials for SAT3 and SAT3-NN model. The two modes are shown in red (ITG) and blue (TEM). The isotopes markers are triangle (Hydrogen), square (Deuterium) and circle (Tritium). Black dashed lines in (a) and (b) show a band of $\pm \Delta k_y$.
  • Figure 4: Quasilinear Approximation Function for NL CGYRO (solid red for ITG and solid blue for TEM), SAT3 (black dashed) and SAT3-NN (cyan). The mean of the maximum QLA value of each case is shown with 2 standard deviations (green)
  • Figure 5: Comparison of fluxes obtained from the SAT3 model and the SAT3-NN model plotted against NL CGYRO data. The two modes are shown in red (ITG) and blue (TEM). The isotopes markers are triangle (Hydrogen), square (Deuterium) and circle (Tritium).
  • ...and 3 more figures