Accelerated spin dynamics using deep learning corrections

Abstract

theoretical models capture very precisely the behaviour of magnetic materials at the microscopic level. This makes computer simulations of magnetic materials, such as spin dynamics simulations, accurately mimic experimental results. New approaches to efficient spin dynamics simulations are limited by integration time step barrier to solving the equations-of-motions of many-body problems. Using a short time step leads to an accurate but inefficient simulation regime whereas using a large time step leads to accumulation of numerical errors that render the whole simulation useless. In this paper, we use a Deep Learning method to compute the numerical errors of each large time step and use these computed errors to make corrections to achieve higher accuracy in our spin dynamics. We validate our method on the 3D Ferromagnetic Heisenberg cubic lattice over a range of temperatures. Here we show that the Deep Learning method can accelerate the simulation speed by 10 times while maintaining simulation accuracy and overcome the limitations of requiring small time steps in spin dynamic simulations. Magnetic materials have a wide range of industrial applications such as in Nd-Fe-B-type permanent magnets used for motors in hybrid cars 1,2 , magnetoresistive random access memory (MRAM) based on the storage of data in stable magnetic states 3 , ultrafast spins dynamics in magnetic nanostructures 4,5 , heat assisted magnetic recording and ferromagnetic resonance methods for increasing the storage density of hard disk drives 6,7 , exchange bias related to magnetic recording 8 , and magnetocaloric materials for refrigeration technologies 1. Understanding the underlying physics of magnetic material enables us to develop much better applications. In particular, the study of the properties of these magnetic materials is performed experimentally by using neutron scattering 9. Magnetic properties of materials are also studied theoretically using computational methods. Spin dynamics simulations 10 are powerful tools for understanding fundamental properties of magnetic materials that can be verified by experimental methods. In spin dynamics simulations, classical equations of motion of spin systems are solved numerically using well known integrators such as leapfrog, Verlet, predictor-corrector, and Runge-Kutta methods 11-13. The accuracy of these simulations depends on a time integration step size. If a large time step is used, the accumulated truncation error becomes larger. Conversely, using a short time step is very computationally demanding. So, it is important to find a trade off between speed and accuracy. Symplectic methods 14,15 are among the most useful time integrators for spin dynamics simulations. The numerical solutions of symplectic methods have properties of the time reversibility and the energy conservation. For example, high order Suzuki-Trotter decomposition method, one of the symplectic methods, allows for larger time step with limited error in its computation. In this paper, we seek to enhance the time integration st...

Physics-constrained machine learning for electrodynamics without gauge ambiguity based on Fourier transformed Maxwell's equations

“…Machine learning (ML) methods have demonstrated to be useful in non-invasive measurements and diagnostics of charged beams 34 . They have also been found to speed up lattice quantum Monte Carlo simulations 35 , the design and simulation of fin field-effect transistors 36 , the simulation of spin dynamical systems 37 and finding the optimal ramp up for the production of Bose-Einstein Condensates 38 .…”

Physics-constrained machine learning for electrodynamics without gauge ambiguity based on Fourier transformed Maxwell’s equations

“…Machine learning (ML) methods have demonstrated to be useful in non-invasive measurements and diagnostics of charged beams 34 and in the simulations of magnetic fields through physics-informed neural networks 35 . They have also been found to speed up lattice quantum Monte Carlo simulations 36 , the design and simulation of fin field‑effect transistors 37 , the simulation of spin dynamical systems 38 and finding the optimal ramp up for the production of Bose–Einstein condensates 39 .…”