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Bayesian optimization for inverse problems in quantum dynamics

Banff International Research Station for Mathematical Innovation and Discovery

Machine learning models are usually trained by a large number of observations (big data) to make predictions through the evaluation of complex mathematical objects. However, in many applications in science, particularly in quantum dynamics, obtaining observables is expensive so information is limited. In the present work, we consider the limit of â small dataâ . Usually, â big dataâ are for machines and â small dataâ are for humans, i.e. humans can infer physical laws given a few isolated observations, while machines require a huge array of information for accurate predictions. Here, we explore the possibility of machine learning that could build physical models based on very restricted information. In this talk, I will show how to build such models using Bayesian machine learning and how to apply such models to inverse problems aiming to infer the Hamiltonians from the dynamical observables. I will illustrate the methods by two applications: (1) the inverse problem in quantum reaction dynamics aiming to construct accurate potential energy surfaces based on reaction dynamics observables; (2) the model selection problem aiming to derive the particular lattice model Hamiltonian that gives to rise to specific quantum transport properties for particles in a phonon field.

Mathematics; Quantum theory; Statistical mechanics, structure of matter

video/mp4

Author affiliation: University of British Columbia

2020-02-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73554

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/