Multifidelity Machine Learning for Molecular Excitation Energies

Abstract

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 excitation energies. To this end, machine learning techniques can be a very useful tool, though the cost of generating highly accurate training data sets still remains a severe challenge. To overcome this hurdle, this work proposes the use of multifidelity 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 vertical excitation energies to the first excited state for three molecules of increasing size, namely, benzene, naphthalene, and anthracene. The energies are trained and tested for conformations stemming from classical molecular dynamics and density functional based tight-binding simulations. It can be shown that the multifidelity machine learning model can achieve the same accuracy as a machine learning model built only on high-cost training data while expending 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.

Optimized multifidelity machine learning for quantum chemistry

“…Various supervised and unsupervised learning approaches have seen widespread application in the field of QC. These applications include areas of material design and discovery [4][5][6][7][8][9][10][11][12] excitation energies [3,[13][14][15][16], potential energy surfaces [17][18][19][20][21][22][23], the prediction of chemical reactions [24], and molecular dynamics for the simulation of infrared spectra [25]. The usually numerically expensive QC calculations are gradually being replaced by ML models or hybrids of ML and QC resulting in a drastic reduction of the compute cost associated with chemical design and discovery.…”

“…Thus, the compute cost associated with discovery in QC is shifted from conventional QC calculations to the cost associated with generating the training data sets for these ML models. While any of the aforementioned ML methods is a promising candidate to replacing the time-consuming conventional calculations, only rather recently the cost of the training data generation for the various ML models has been investigated [16,21,50,51]. Previously, various techniques and models have been implemented to reduce this cost.…”

“…Recently, a systematic generalization of the ∆-ML method called multifidelity machine learning (MFML) [51] was applied to the excitation energies of small to medium-size molecules [16]. The MFML method exploits the existence of varying levels of accuracy of conventional QC methods, thereby resulting in a hierarchy of methods for properties such as excitation energies.…”

“…The MFML model is built by iteratively adding models built on the difference between the excitation energies calculated at the various fidelities. In MFML, the number of training samples is decreased by a factor of two for each subsequent more costly fidelity [16]. Thus, there is an inherent decrease in the number of costly training samples.…”

“…The various sub-models are combined to give the final MFML model. This combination was performed based on the sparse-grid combination technique [58][59][60][61][62] as has been discussed in [16,51].…”