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Using Deep Learning to Design High Aspect Ratio Fusion Devices

P. Curvo, D. R. Ferreira, R. Jorge

TL;DR

The paper confronts the inverse design challenge for stellarators in a high-dimensional, non-axisymmetric parameter space. It leverages a second-order near-axis expansion to reduce design degrees of freedom and employs Mixture Density Networks to model multimodal input distributions conditioned on target confinement properties, enabling sampling of multiple viable designs. An iterative data-augmentation workflow substantially improves the representation of good and viable stellarators, enabling reliable generation of configurations with desired axis length, iota, elongation, and confinement metrics while highlighting challenges for some second-order outputs. This physics-informed probabilistic approach accelerates discovery of high-performance stellarator configurations and suggests avenues for integrating near-axis methods with differentiable layers and full MHD optimization.

Abstract

The design of fusion devices is typically based on computationally expensive simulations. This can be alleviated using high aspect ratio models that employ a reduced number of free parameters, especially in the case of stellarator optimization where non-axisymmetric magnetic fields with a large parameter space are optimized to satisfy certain performance criteria. However, optimization is still required to find configurations with properties such as low elongation, high rotational transform, finite plasma beta, and good fast particle confinement. In this work, we train a machine learning model to construct configurations with favorable confinement properties by finding a solution to the inverse design problem, that is, obtaining a set of model input parameters for given desired properties. Since the solution of the inverse problem is non-unique, a probabilistic approach, based on mixture density networks, is used. It is shown that optimized configurations can be generated reliably using this method.

Using Deep Learning to Design High Aspect Ratio Fusion Devices

TL;DR

The paper confronts the inverse design challenge for stellarators in a high-dimensional, non-axisymmetric parameter space. It leverages a second-order near-axis expansion to reduce design degrees of freedom and employs Mixture Density Networks to model multimodal input distributions conditioned on target confinement properties, enabling sampling of multiple viable designs. An iterative data-augmentation workflow substantially improves the representation of good and viable stellarators, enabling reliable generation of configurations with desired axis length, iota, elongation, and confinement metrics while highlighting challenges for some second-order outputs. This physics-informed probabilistic approach accelerates discovery of high-performance stellarator configurations and suggests avenues for integrating near-axis methods with differentiable layers and full MHD optimization.

Abstract

The design of fusion devices is typically based on computationally expensive simulations. This can be alleviated using high aspect ratio models that employ a reduced number of free parameters, especially in the case of stellarator optimization where non-axisymmetric magnetic fields with a large parameter space are optimized to satisfy certain performance criteria. However, optimization is still required to find configurations with properties such as low elongation, high rotational transform, finite plasma beta, and good fast particle confinement. In this work, we train a machine learning model to construct configurations with favorable confinement properties by finding a solution to the inverse design problem, that is, obtaining a set of model input parameters for given desired properties. Since the solution of the inverse problem is non-unique, a probabilistic approach, based on mixture density networks, is used. It is shown that optimized configurations can be generated reliably using this method.
Paper Structure (7 sections, 12 equations, 7 figures, 9 tables)

This paper contains 7 sections, 12 equations, 7 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Physical Model
  3. Mixture Models and Density Networks
  4. Mixture Density Networks
  5. Data Generation and Training
  6. Model Performance
  7. Conclusions

Figures (7)

  • Figure 1: Plasma boundary of a quasisymmetric stellarator with three field periods, $n_{\text{fp}}=3$. The colors represent the magnetic field strength at the boundary and a magnetic field line is shown in black.
  • Figure 2: Example of mixture models with two components, each represented by a Gaussian distribution, illustrating how a mixture model forms from two distributions and the influence of mixture weights on data distribution modeling.
  • Figure 3: (left) Sketch of the neural network architecture used in this work to estimate the parameters of a mixture model. (right) Architecture of the Mixed Density Network as an inverse model for the near-axis method.
  • Figure 4: Loss (left) and validation loss (right) curves during training for the different models. The initial learning rate, $1 \times 10^{-3}$, was decreased with a scheduler in epochs 10, 20, 30, 40, 50 with a $\gamma = 0.5$.
  • Figure 5: (left) Distribution of the $R_{c1}$ variable during the iterative process. (right) Distribution of the $R_{c1}$ variable for the good stellarators and the viable stellarators.
  • ...and 2 more figures