2018/11/21 by Rodrigo A. Vargas–Hernández, Vargas-Hernández, Rodrigo A., Roman V. Krems +1
Computer Science · Materials Science · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Machine Learning in Materials Science #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.1901.00854
openalex publication_date 2018/11/21 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28
For applications in chemistry and physics, machine learning (ML) is generally\nused to solve one of three problems: interpolation, classification or\nclustering. These problems use information about physical systems in a certain\nrange of parameters or variables in order to make predictions at unknown values\nof these variables within the same range. The present work illustrates the\napplication of ML to prediction of physical properties outside the range of the\ntraining parameters. We define `physical extrapolation' to refer to accurate\npredictions y(\x^\∗) of a given physical property at a point\n\x^\∗ = [ x^\∗1, ..., x^\∗ cal D ] in the cal\nD-dimensional space, if, at least, one of the variables x^\∗i \∈ [\nx^\∗1, ..., x^\∗ cal D ] is it outside of the range covering\nthe training data. We show that Gaussian processes (GPs) can be used to build\nML models capable of physical extrapolation of quantum properties of complex\nsystems across quantum phase transitions. The approach is based on training GP\nmodels of variable complexity by the evolution of the physical functions. We\nshow that, as the complexity of the models increases, they become capable of\npredicting new transitions. We also show that, where the evolution of the\nphysical functions is analytic and relatively simple, GP models with simple\nkernels already yield accurate generalization results, allowing for accurate\npredictions of quantum properties in a different quantum phase. For more\ncomplex problems, it is necessary to build models with complex kernels. The\ncomplexity of the kernels is increased using the Bayesian Information Criterion\n(BIC). We illustrate the importance of the BIC by comparing the results with\nrandom kernels of various complexity and illustrate a method to obtain\nmeaningful extrapolation results without direct validation in the extrapolated\nregion.\n