Data Driven Machine Learning Discovery of Fundamental Physical Laws

Abstract

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, whether simply filtering emails and recommending products in a search bar or discovering the fundamental laws governing highly sensitive chaotic systems. In this research investigation we apply the "Least Absolute Shrinkage and Selection Operator" (LASSO) method of data analysis that determines the relationship, or lack thereof, between variables, allowing for the removal of irrelevant features. The method is first applied to a generic system of differential equations, to demonstrate its applicability, before showcasing its application within the context of a chaotic Lorenz oscillator system. The generic coupled system is solved using the LASSO module available in Python's sci-kit-learn. A similar computational approach for the chaotic system with synthetic Gaussian noisy data successfully reproduces the original Lorenz attractor solution.