Machine learning corrected quantum dynamics calculations

Abstract

Quantum scattering calculations for all but low-dimensional systems at low energies must rely on approximations. All approximations introduce errors. The impact of these errors is often difficult to assess because they depend on the Hamiltonian parameters and the particular observable under study. Here, we illustrate a general, system-and approximation-independent, approach to improve the accuracy of quantum dynamics approximations. The method is based on a Bayesian machine learning (BML) algorithm that is trained by a small number of exact results and a large number of approximate calculations, resulting in ML models that can generalize exact quantum results to different dynamical processes. Thus, a ML model trained by a combination of approximate and rigorous results for a certain inelastic transition can make accurate predictions for different transitions without rigorous calculations. This opens the possibility of improving the accuracy of approximate calculations for quantum transitions that are out of reach of exact scattering theory.

Perspective on integrating machine learning into computational chemistry and materials science

“…ML shows great promise in nonadiabatic excitedstate simulations 20,21 as documented by recent works using NNs to construct excited-state energy landscapes to perform fewest-switches surface hopping MD at longer time scales or with more comprehensive ensemble averaging than would otherwise be possible with on-the-fly dynamics. 84,254,255 Similar progress has been achieved in nonadiabatic dynamics at metal surfaces, where NNs have been used to construct excited-state landscapes 4,256 and continuous representations of the electronic friction tensor 257 used in MD with electronic friction simulations. 258,259 Even full quantum dynamics simulations have recently seen an increasing uptake of ML methodology to push beyond longstanding limitations in the dimensionality of systems that can be simulated.…”

“…275 While most approaches focus on assisting MD by providing highly-accurate interatomic potentials and force fields, they have also shown great potential in predicting dynamical properties directly and skipping the MD simulation completely or in assessing the validity of different approximations in dynamical simulations. The latter has only recently been shown by Jasinski et al 276 with a Bayesian model to estimate errors due to different approximations in quantum scattering simulations. Going forward, complex dynamical simulation methods will become more accessible to nonexpert users with the help of ML and will open avenues to tackle complex systems in solvent environments 71 or dynamics at hybrid organic-inorganic interfaces.…”

Gaussian Processes with Spectral Delta kernel for higher accurate Potential Energy surfaces for large molecules

“…The latter quantifies the similarity between a pair of points. If the kernel function can generalize a similarity metric, GPs are efficient regression algorithms that require less training data than NNs 1 , and are also capable of extrapolating functions beyond the training data regime 17,[34][35][36][37] . To achieve more robust kernel functions, once can simply combine different simple kernel functions 38,39 .…”

Rainbow scattering in rotationally inelastic collisions of HCl and H$_2$

“…Identifying the collisional parameters that control the collision outcomes has received much attention in theoretical and experimental studies. [1][2][3][4][5] The Wigner threshold law, 6 Breit-Wigner and Fano-Feshbach profiles for resonances, [7][8][9][10] and the Langevin model 11,12 are well-known examples of useful concepts to characterize the physical origin and behavior of cross sections as a function of collision energy. In the rapidly evolving field of ultracold atoms and molecules, zero-energy Feshbach resonances as functions of external magnetic and/or electric fields play a central role in the control of the collision outcome.…”

“…More recently, novel methods based on machine learning are actively being developed to interpolate cross sections and rate coefficients as functions of energy and temperature. 5,[18][19][20][21][22] Rainbow scattering, leading to characteristic parameter dependence of the scattering properties, may occur in systems with isotropic potentials and multiple partial waves. 1,2,4,[23][24][25][26][27][28] Rainbow features arise from an interplay between the shortrange repulsive and long-range attractive forces.…”