Bayesian Machine Learning Approach to the Quantification of Uncertainties on Ab Initio Potential Energy Surfaces

Abstract

This work introduces a novel methodology for the quantification of uncertainties associated with potential energy surfaces (PESs) computed from first-principles quantum mechanical calculations. The methodology relies on Bayesian inference and machine learning techniques to construct a stochastic PES and to express the inadequacies associated with the ab initio data points and their fit. By combining high fidelity calculations and reduced-order modeling, the resulting stochastic surface is efficiently forward propagated via quasi-classical trajectory and master equation calculations. In this way, the PES contribution to the uncertainty on predefined quantities of interest (QoIs) is explicitly determined. This study is done at both microscopic (e.g., rovibrational-specific rate coefficients) and macroscopic (e.g., thermal and chemical relaxation properties) levels. A correlation analysis is finally applied to identify the PES regions that require further refinement, based on their effects on the QoI reliability. The methodology is applied to the study of singlet (11A′) and quintet (25A′) PESs describing the interaction between O2 molecules and O atoms in their ground electronic state. The investigation of the singlet surface reveals a negligible uncertainty on the kinetic properties and relaxation times, which are found to be in excellent agreement with the ones previously published in the literature. On the other hand, the methodology demonstrated significant uncertainty on the quintet surface, due to inaccuracies in the description of the exchange barrier and the repulsive wall. When forward propagated, this uncertainty is responsible for the variability of 1 order of magnitude in the vibrational relaxation time and of factor four in the exchange reaction rate coefficient, both at 2500 K.

Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N2O and dynamics for the N + NO ↔ O + N2and N2+ O → 2N + O reactions

“…One way to probe the sensitivity of different regions of the PES on the observables can be assessed by introducing random noise/perturbation in the PES and recalculating the observables. 74 Alternatively, PES morphing-type approaches 75 can be considered which will also provide information which parts of the PES need to be further improved. This can follow similar approaches as the one highlighted for vibrational relaxation rates, namely by considering subclasses of trajectories sampling distinct regions of configuration space and determining separate observables (here relaxation rates) for each of the subclass.…”

The C(3P) + O2(3Σg−) → CO2 ↔ CO(1Σ+) + O(1D)/O(3P) reaction: thermal and vibrational relaxation rates from 15 K to 20 000 K

“…Together with suitable information from experiment the underlying PESs could be further improved from techniques such as morphing 71,72 or Bayesian inference. 73 The wave function analysis for the SA-CASSCF reference of the CO undergo a Jahn-Teller splitting caused by the splitting of the π system frontier orbitals upon bending of CO 2 . The five lowest electronic states arise then from different configuration state functions of four electrons in three frontier orbitals and rationalize the relative energy ordering of these states along the dissociation path for the bent geometry of CO 2 .…”

“…Together with suitable information from experiment the underlying PESs could be further improved from techniques such as morphing 71,72 or Bayesian inference. 73 …”

Differentiable sampling of molecular geometries with uncertainty-based adversarial attacks

“…In this context, epistemic uncertainty—the model uncertainty arising from the lack of appropriate training data—is much more relevant to ML potentials than the aleatoric uncertainty, which arises from noise in the training data. Whereas ML-based interatomic potentials are becoming increasingly popular, uncertainty quantification applied to atomistic simulations is at earlier stages 26 , 27 . ML potentials based on Gaussian processes are Bayesian in nature, and thus benefit from an intrinsic error quantification scheme, which has been applied to train ML potentials on-the-fly 9 , 28 or to accelerate nudged elastic band (NEB) calculations 29 .…”