Balancing Wigner sampling and geometry interpolation for deep neural networks learning photochemical reactions

Abstract

Machine learning photodynamics simulations are revolutionary tools to resolve elusive photochemical reaction mechanisms with time-dependent high-fidelity structure information. Besides the recent advances in neural networks (NNs) potentials, it still lacks a general rule for designing training data for learning photochemical reaction mechanisms with Wigner sampling and geometry interpolation. We present an in-depth investigation of the relationship between the accuracy of the multiple layer NNs and the combinations of training data based on the Wigner sampling and geometry interpolation using model photochemical reactions of the [3]-ladderdiene systems. The NNs trained with Wigner sampling data show underfitting, where the NN errors increase with the structural complexity and diversity. The NNs trained with composite Wigner sampling and geometry interpolation data show one magnitude reduced errors, suggesting an essential role of geometry interpolation in facilitating NNs learning the potential energy surfaces. However, increasing the interpolation steps results in overfitting if the Wigner sampled configuration space is narrowed. Correlating the mean absolute errors (MAE) of the NN predicted energies for the sampled and out-of-sample structures shows an optimal combination ratio of 100:10 between the Wigner sampling structures and geometry interpolation steps for 1000 training data, where the MAE of the sampled structures achieve chemical accuracy while the MAE of the out-of-sample structures is minimized. The NNs trained with the optimally combined data can detect the out-of-sample structures in adaptive sampling with a positive correlation between the maximum standard deviation and MAE of the predicted energies. Collectively, our findings suggest a general rule for designing the training data for ML photodynamics.