Neural networks and kernel ridge regression for excited states dynamics of CH$_2$NH$_2^+$: From single-state to multi-state representations and multi-property machine learning models

TL;DR

This paper develops and compares machine learning models, including neural networks and kernel ridge regression, for predicting excited-state properties and dynamics of CH$_2$NH$_2^+$, enabling efficient simulations of photo-induced reactions.

Contribution

It introduces a novel state encoding strategy for kernel ridge regression and neural networks, improving multi-state and multi-property predictions for excited-state dynamics.

Findings

State encoding enhances multi-state property prediction accuracy.

Machine learning models successfully simulate excited-state dynamics.

Kernel ridge regression with explicit state encoding performs comparably to neural networks.

Abstract

Excited-state dynamics simulations are a powerful tool to investigate photo-induced reactions of molecules and materials and provide complementary information to experiments. Since the applicability of these simulation techniques is limited by the costs of the underlying electronic structure calculations, we develop and assess different machine learning models for this task. The machine learning models are trained on {\emph ab initio} calculations for excited electronic states, using the methylenimmonium cation (CH$_2$NH$_2^+$) as a model system. For the prediction of excited-state properties, multiple outputs are desirable, which is straightforward with neural networks but less explored with kernel ridge regression. We overcome this challenge for kernel ridge regression in the case of energy predictions by encoding the electronic states explicitly in the inputs, in addition to the molecular representation. We adopt this strategy also for our neural networks for comparison. Such a state encoding enables not only kernel ridge regression with multiple outputs but leads also to more accurate machine learning models for state-specific properties. An important goal for excited-state machine learning models is their use in dynamics simulations, which needs not only state-specific information but also couplings, i.e., properties involving pairs of states. Accordingly, we investigate the performance of different models for such coupling elements. Furthermore, we explore how combining all properties in a single neural network affects the accuracy. As an ultimate test for our machine learning models, we carry out excited-state dynamics simulations based on the predicted energies, forces and couplings and, thus, show the scopes and possibilities of machine learning for the treatment of electronically excited states.