Machine learning modelling for turbulent Dynamos – MilaDy

Magnetohydrodynamics (MHD) studies the interactions between electrically conductive fluids and magnetic fields, which are essential for industrial applications and for understanding phenomena such as the dynamo effect (DyE). DyE involves the amplification of small magnetic seeds in turbulent fluids, such as in stars or planetary cores, which makes it rare and complex to reproduce. Only three experiments, including the one at Cadarache in France, have succeeded in obtaining DyE with liquid sodium. The DRESDYN experiment currently underway in Germany aims to reproduce DyE using a cylinder in precession.
Simulating DyE is difficult because of the non-linear coupling between the Navier-Stokes equations and the induction equation, making direct numerical simulations (DNS) very computationally expensive. Reduced models (ROMs) are valuable for simplifying these simulations, while machine learning (ML) shows potential for handling high-dimensional dynamics, although capturing rare events remains a challenge. Data assimilation (DA) with ML is becoming more accessible, thanks in particular to the TorchDA framework.
MilaDy aims to advance MHD research with two main goals: (i) Investigating magnetic field reversals and burst dynamo phenomena using data-driven methods to identify key features and develop ROMs that reproduce observed dynamics. The project investigates whether ML can improve understanding of magnetic reversals and create faster surrogate models that distinguish phases like precursor, reversal, and recovery. (ii) Optimizing the DRESDYN setup with parametric ROMs to explore conditions for DyE, such as precession-to-spin frequency ratios. ROMs offer efficient parameter exploration, potentially aiding experimentalists in managing these complex systems.