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Neural-Network solver of ideal MHD equilibria

Created by
  • Haebom

Author

Timo Thun, Andrea Merlo, Rory Conlin, Dario Panici, Daniel B ockenhoff

Outline

This paper presents a novel method for computing 3D magnetohydrodynamic (MHD) equilibrium states using artificial neural networks. Compared with conventional solvers, we parameterize the Fourier modes as artificial neural networks and minimize the global nonlinear force residual in real space using a first-order optimization technique. As a result, we achieve the same level of residual minimum as that computed by conventional codes at a competitive computational cost, and at the expense of increased computational cost, we obtain a lower residual minimum via neural networks, suggesting a new lower bound on the force residual. With a minimal complexity of neural networks, we expect significant improvements not only in solving single equilibrium states but also in computing neural network models valid for continuous equilibrium distributions.

Takeaways, Limitations

Takeaways:
A novel method for calculating 3D MHD equilibrium states using artificial neural networks is presented.
Achieving similar levels of accuracy at competitive computational cost compared to existing methods.
A new lower bound is presented by achieving a lower power residual.
Presenting the computational feasibility of valid neural network models for continuous equilibrium state distributions.
Limitations:
Lack of detailed description of the specific structure and parameters of the neural network presented in the paper.
Further validation of generalizability to different MHD equilibrium states is needed.
Further analysis of __T5088_____'s performance improvement due to increased computational cost is needed.
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