Replacing Chemical Intuition by Machine Learning: a Mixed Design of Experiments - Reinforcement Learning Approach to the Construction of Training Sets for Model Hamiltonians

Model Hamiltonians based on the so-called cluster expansion (CE), which consist of a linear fit of parameters corresponding to geometric patterns, provide an efficient and rigorous means to quickly evaluate the energy of diverse arrangements of adsorbate mixtures on reactive surfaces as typically relevant for heterogeneous catalysis. However, establishing the model Hamiltonian is a tedious task, requiring the construction and optimization of many geometries. Today, most of these geometries are constructed by hand, based on chemical intuition or random choices. Hence, the quality of the training set is unlikely to be optimal and its construction is not reproducible. Herein, we propose a reformulation of the construction of the training set as a strategy-based game, aiming at an efficient exploration of the relevant patterns constituting the model Hamiltonian. Based on this reformulation, we exploit a typical active learning solution for machine-learning such a strategy game: an upper confidence tree (UCT) based framework. However, in contrast to standard games, evaluating the true score is computationally expensive, as it requires a costly geometry optimization. Hence, we augment the UCT with a pre-exploration step inspired by the variance-based Design of Experiments (DoE) methods. This novel mixed UCT+DoE framework allows to automatically construct a well adapted training set, minimizing computational cost and user-intervention. As a proof of principle, we apply our UCT+DoE approach on the CO oxidation reaction on Pd(111), for which a relevant model Hamiltonian has been established previously. The results demonstrate the effectiveness of the custom built UCT and its significant benefits on a DoE-based approach.

Asymmetric butterfly velocities in 2-local Hamiltonians

The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a ``butterfly velocity", which can be measured via out-of-time-ordered correlation functions. In general, the butterfly velocity can depend asymmetrically on the direction of information propagation. In this work, we construct a family of simple 2-local Hamiltonians for understanding the asymmetric hydrodynamics of operator spreading. Our models live on a one dimensional lattice and exhibit asymmetric butterfly velocities between the left and right spatial directions. This asymmetry is transparently understood in a free (non-interacting) limit of our model Hamiltonians, where the butterfly speed can be understood in terms of quasiparticle velocities.

Forbidden transitions in nuclear weak processes relevant to neutrino detection, nucleosynthesis and evolution of stars

The distribution of the spin-dipole strengths in 16O and neutrino-induced reactions on 16O areinvestigated by shell-model calculations with new shell-model Hamiltonians. Chargedcurrent and neutral-current reactioncross sections are valuated in various particle and γ emission channels as well as the total ones at neutrinoenergies up to Eν≈ 100 MeV. Effects of multiparticle emission channels, especially the αp emission channels, on nucleosynthesis of 11B and 11C in core-collapse supernova explosions are investigated. The MSW neutrino oscillation effects oncharged-current reaction cross sections are investigated for future supernova burst. Electron capture rates for a forbidden transition 20Ne(Og.s.+) → 20F(2g.s.+) in stellar environments are evaluated by the multipole expansion method with the use of shell model Hamiltonians, and compared with those obtained by a prescription that treats the transition as an allowed GamowTeller (GT) transition. Different electron energy dependence of the transition strengths between the two methods is found to lead to sizable differences in the weak rates of the two methods.