Multi-Fidelity Machine Learning for Excited State Energies of Molecules
Vivin Vinod Sayan Maity Peter Zaspel Ulrich Kleinekathöfer
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.