Ulrich Kleinekathöfer

Matthias Holzenkamp, Dongyu Lyu, Ulrich Kleinekathöfer et al.

Uncertainty estimations for machine learning interatomic potentials (MLIPs) are crucial for quantifying model error and identifying informative training samples in active learning strategies. In this study, we evaluate uncertainty estimations of Gaussian process regression (GPR)-based MLIPs, including the predictive GPR standard deviation and ensemble-based uncertainties. We do this in terms of calibration and in terms of impact on model performance in an active learning scheme. We consider GPR models with Coulomb and Smooth Overlap of Atomic Positions (SOAP) representations as inputs to predict potential energy surfaces and excitation energies of molecules. Regarding calibration, we find that ensemble-based uncertainty estimations show already poor global calibration (e.g., averaged over the whole test set). In contrast, the GPR standard deviation shows good global calibration, but when grouping predictions by their uncertainty, we observe a systematical bias for predictions with high uncertainty. Although an increasing uncertainty correlates with an increasing bias, the bias is not captured quantitatively by the uncertainty. Therefore, the GPR standard deviation can be useful to identify predictions with a high bias and error but, without further knowledge, should not be interpreted as a quantitative measure for a potential error range. Selecting the samples with the highest GPR standard deviation from a fixed configuration space leads to a model that overemphasizes the borders of the configuration space represented in the fixed dataset. This may result in worse performance in more densely sampled areas but better generalization for extrapolation tasks.

Vivin Vinod, Sayan Maity, Peter Zaspel et al.

The accurate but fast calculation of molecular excited states is still a very challenging topic. For many applications, detailed knowledge of the energy funnel in larger molecular aggregates is of key importance requiring highly accurate excited state energies. To this end, machine learning techniques can be an extremely useful tool though the cost of generating highly accurate training datasets still remains a severe challenge. To overcome this hurdle, this work proposes the use of multi-fidelity machine learning where very little training data from high accuracies is combined with cheaper and less accurate data to achieve the accuracy of the costlier level. In the present study, the approach is employed to predict the first excited state energies for three molecules of increasing size, namely, benzene, naphthalene, and anthracene. The energies are trained and tested for conformations stemming from classical molecular dynamics simulations and from real-time density functional tight-binding calculations. It can be shown that the multi-fidelity machine learning model can achieve the same accuracy as a machine learning model built only on high cost training data while having a much lower computational effort to generate the data. The numerical gain observed in these benchmark test calculations was over a factor of 30 but certainly can be much higher for high accuracy data.