Neuroevolutionary optimization for magnetic ground state

Stable magnetic states, including particle-like topologically protected magnetic textures like skyrmions and hopfions, have recently attracted a lot of attention due to their potential applications in spintronics. In order to identify such textures, we have developed a hybrid neuroevolutionary algorithm based on a shallow neural network to find stable magnetic states in the Heisenberg spin model. Our algorithm uses both meta-heuristic global search and local optimization by combining a genetic tunneling (GT) with the stochastic gradient descent (SGD) method. It has no need of prior knowledge (i.e., an initial guess). Its capability to escape from the local minimum of the potential energy surface (PES) relies on treating the topologically protected magnetic patterns as chromosomes and performing genetic tunneling. The algorithm then finds the optimal spin configuration of the ground state of the magnetic Hamiltonian. We show that our algorithm achieves substantial improvements in robustness and effectiveness compared to traditional approaches like heat-bath simulated annealing. These features make our algorithm a promising tool for solving global optimization problems in magnetic systems.