Journal Article10.1039/c5sc04786b
Machine learning exciton dynamics
Florian Häse,Stéphanie Valleau,Edward Pyzer-Knapp,Alán Aspuru-Guzik +3 more
Abstract: Machine learning ground state QM/MM for accelerated computation of exciton dynamics.
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Figures
Figure 3. Relative absolute deviations of predicted excited state energies from TDDFT excited state energies. Neural networks trained on one particular site (indicated by “Network”) were used to predict excited state energies of another site (indicated by “Target”). Panel A) shows the relative absolute deviation σ̄relBChl of predicted excited state energies from TDDFT excited state energies for each BChl, σ̄relBChl = ∑ i | NNBChl(ti) − TDDFTBChl (ti)|/(Nframes · 〈 TDDFTBChl 〉), in percent. Panel B) shows the deviation σmeanBChl of the mean of the predicted excited state energies from the mean of the TDDFT calculated excited state energies, σBChlmean = |〈 NNBChl〉 − 〈 TDDFTBChl 〉|/〈 TDDFTBChl 〉 in per-thousand. 
Figure 9. Average absolute deviations of predicted excited state energies from TDDFT excited state energies for neural networks with different learning rates. Neural networks were trained on 3000 Coulomb matrices randomly drawn from the 10000 frame data set. A learning rate of 10−4 resulted in the lowest prediction error. However, prediction error for other learning rates are less than 10 % larger than the minimal value. 
Figure 10. Average absolute deviations of predicted excited state energies from TDDFT calculated excited state energies for different numbers of neurons in the first and second hidden layer. Deviations are reported in eV. Neural networks were trained on 3000 Coulomb matrices randomly drawn from the 10000 frame data set. A hidden layer combination of 204 neurons in the first hidden layer and 192 neurons in the second hidden layer resulted in the smallest deviation of 31 meV. 
Figure 7. Time evolution of the exciton population for BChl 1 (red) and BChl 2 (blue) in the FMO complex calculated from excited state energy trajectories and average spectral densities using the Redfield method. The initial state is site 1 excited. Panel A) shows the exciton dynamics for neural network predicted excited state energies using the same TDDFT calculated average spectral density in all cases. Panel B) shows the exciton dynamics with both, excited state energy trajectories and harmonic average spectral densities predicted by neural networks trained with the indicated selection method. 
Figure 13. Deviation of TDDFT calculated exciton dynamics and neural network predicted exciton dynamics over time. The deviation was calculated as σiρ(t) = |ρTDDFTii (t) − ρNNii (t)|/ρTDDFTii (t) with i indicating the BChl. Panel A) shows the deviation for exciton dynamics calculated with the Redfield method and neural network predicted harmonic average spectral densities. In Panel B), the TDDFT average spectral density was used for all calculations and neural networks only predicted excited state energy trajectories. 
Figure 12. Excited state energy distributions for all eight BChls in the FMO monomer A. Excited state energies were obtained from TDDFT calculations with the PBE0 functional and the 3-21G basis set. Distributions were calculated from a total of 10000 frames spanning 40 ps with a binning of 50.
Citations
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