Integrating LASSO machine learning algorithm with LLG spin dynamics

Machine learning, which is part of artificial intelligence, has become an invaluable tool to manipulate, analyze, predict, and reveal trends and associations hidden within big data. Machine learning algorithms build a mathematical model of sample data in order to make predictions or decisions, including recommending products in a search bar or discovering fundamental laws of physics. We apply the “Least Absolute Shrinkage and Selection Operator” (LASSO) method of data analysis which determines the relationship, or lack thereof, between variables, and allows for the removal of irrelevant noisy features. The LASSO module is implemented using Python’s sci-kit-learn. The method is first applied to a generic system of differential equations before showcasing its usage for a chaotic Lorenz oscillator and a 1D classical Heisenberg spin chain. For the chaotic system with synthetic Gaussian noisy data, LASSO successfully reproduces the clean Lorenz attractor solution. For the 1D spin chain, noisy data generated from unequilibrated Monte Carlo simulations were processed with LASSO. We show that the LASSO machine learning technique integrated with the LLG spin dynamics algorithm can remove irrelevant noise in spin dynamics simulations.