Active Inference and Artificial Spin Ice: Control Processes and State Selection

Theory and simulations are used to demonstrate implementation of a variational Bayes algorithm called "active inference" in interacting arrays of nanomagnetic elements. The algorithm requires stochastic elements, and a simplified model based on a magnetic artificial spin ice geometry is used to illustrate how nanomagnets can generate the required random dynamics. Examples of tracking and PID control are demonstrated and shown to be consistent with the original stochastic differential equation formulation of active inference. Interestingly, nonlinear response in the form of spikes and spike trains not predicted by the original theory can appear in the nanomagnet system for certain temperature regimes. A theoretical approach using a mean-field approximation for spin systems is proposed, which describes the transition to nonlinear response. Finally, the possibility to create simple magnetic arrays using realistic models is shown with micromagnetic simulations of a simple 17 element array of nanomagnets that include magnetic anisotropies, and exchange and dipolar interactions. Possible applications are simulated to illustrate how nanomagnetic arrays can be used as the stochastic element for feedback control of processes, investigation and control of magnetic state evolution, and as a method to optimize pulsed field magnetic switching protocols.