Physics-regularized neural network of the ideal-MHD solution operator in Wendelstein 7-X configurations
arXiv:2211.09743 · doi:10.1088/1741-4326/acc852
Abstract
The computational cost of constructing 3D magnetohydrodynamic (MHD) equilibria is one of the limiting factors in stellarator research and design. Although data-driven approaches have been proposed to provide fast 3D MHD equilibria, the accuracy with which equilibrium properties are reconstructed is unknown. In this work, we describe an artificial neural network (NN) that quickly approximates the ideal-MHD solution operator in Wendelstein 7-X (W7-X) configurations. This model fulfils equilibrium symmetries by construction. The MHD force residual regularizes the solution of the NN to satisfy the ideal-MHD equations. The model predicts the equilibrium solution with high accuracy, and it faithfully reconstructs global equilibrium quantities and proxy functions used in stellarator optimization. We also optimize W7-X magnetic configurations, where desiderable configurations can be found in terms of fast particle confinement. This work demonstrates with which accuracy NN models can approximate the 3D ideal-MHD solution operator and reconstruct equilibrium properties of interest, and it suggests how they might be used to optimize stellarator magnetic configurations.
arXiv comment47 pages, 28 figures, published in Nuclear Fusion
References in corpus (16)
- Adam: A Method for Stochastic Optimization
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Array Programming with NumPy
- Decoupled Weight Decay Regularization
- DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
- Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
- The Power of Depth for Feedforward Neural Networks
- Magnetic fields with precise quasisymmetry for plasma confinement
- An adjoint method for gradient-based optimization of stellarator coil shapes
- A New Optimized Quasihelically SymmetricStellarator
- Symplectic integration with non-canonical quadrature for guiding-center orbits in magnetic confinement devices
- Energetic particle transport in optimized stellarators
- Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization
- Proof of concept of a fast surrogate model of the VMEC code via neural networks in Wendelstein 7-X scenarios
- Gradient-based optimization of 3D MHD equilibria
- The DESC Stellarator Code Suite Part I: Quick and accurate equilibria computations