Machine Learning the Long-Time Dynamics of Spin Ice*

Over ten orders of magnitude separate the microscopic processes and macroscopic equilibration time for spin ices such as Dy₂Ti₂O₇. Understanding the slow, stochastic, dynamics of these systems is a problem on which machine learning may be able to lend some new insight. To this end, we have generated datasets consisting of kinetic Monte Carlo simulations of both two-dimensional artificial spin ice and three-dimensional pyrochlore spin ice.

In the interest of increasing the scale of simulations, we've implemented a convolutional neural network which contains no dense layers. This means that the model is agnostic to input-size and thus highly scalable. The kernel size of our model is also minimal, only permitting nearest-neighbor interaction, yet the model reproduces the principle dynamics quite well. This suggests that, to some extent, the rules governing the dynamics of spin ice are primarily local and that the scalability of the 'ice rules' may be a viable route to solving the spin ice problem. This also demonstrates that a deterministic neural network is capable of learning the stochastic time-series of a complex physical system, a general problem.