Velocity field reconstruction by Machine Learning during kinematic dynamo process

Generation and reversal of the Earth’s magnetic field have remained one of the most controversial topics.  It is well known that the Earth’s magnetic field is generated by dynamo action in the liquid iron outer core. This mechanism explains how a rotating, convecting, and electrically conducting fluid sustains a magnetic field.

In this study, we investigate the kinematic dynamo action associated with the well-known ABC-flow (see Dombre et al. [1986]). We focus on the “A = B = C = 1. Its dynamo properties have been assessed in 1981 by Arnold et al. [1981]. It belongs to fast dynamo action: a flow which achieves exponential magnetic field amplification over a typical time related to the advective timescale and not the ohmic diffusive timescale (in which case it is referred to as a “slow dynamo”).

We use DNS method for solving the kinematic dynamo problem, for which a solenoidal magnetic field evolution is governed under a prescribed flow by the induction equation.

In this work, we propose a deep learning method to solve the inverse dynamo problem by estimating the velocity field from the magnetic field. We train our deep learning algorithm from the velocity field and the magnetic field values obtained from the above flow model. Once the algorithm parameters are trained, the optimized algorithm is tested for the velocity field estimation from magnetic field.