Insights From Linking Schrödinger Equation to Machine Learning

David Kim
McMaster University
Department of Chemistry and Chemical Biology

The Schrödinger equation is a difficult equation to solve, but not without its reward. It provides a fairly complete description of a chemical system, making it essential for elucidating the inner workings of reactions and material properties. Over the past century, many in theoretical chemistry and physics made efforts to find equations and approximations that are both tractable and accurate. It seems that accurate descriptions of complex systems are difficult to obtain in a reasonable amount of time without specialists that have a very good understanding of the model and/or the system. In contrast, recent advances in machine learning, particularly in neural networks, have led to the productions of models of complicated systems without too much prior knowledge. Though we may attribute the differences between these two disciplines to the fundamental differences in the problems being solved, we can show that the Schrödinger equation can be reformulated into loss functions commonly used in regression analysis. Through this link, we can reinterpret these equations within the context of theoretical physics and data science to obtain further insights that may not be obvious when viewed from inside only one discipline. In fact, we may even transfer techniques from machine learning to solve the Schrödinger equation and vice versa. In this presentation, we will explore this link between quantum mechanics and machine learning and its implications on the two disciplines.

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