Accurate non-adiabatic molecular dynamics (NAMD) simulations play a vital role across various research domains in photophysics and photochemistry. These simulations delve into the exploration of light-induced reactions, considering light as one of the most prevalent energy sources on Earth. They facilitate the exploration of diverse phenomena, including but not limited to, 1-3 vision, or radiation damage. All these processes involve molecular reactions occurring after excitation to higher electronic states. By studying the subsequent nuclear dynamics, it is possible to uncover the intricate relationships between molecular structure and photochemical properties, paving the way towards the design of new photoactive molecules, including photocatalysts, photosensitive drugs, or photovoltaic materials. Despite the importance of these NAMD simulations, the prohibitive costs associated with accurate quantum chemistry calculations for photodynamics have limited the scope of excited-state simulations. These restrictions apply specifically to full quantum dynamics or semi-classical dynamics simulations, confining them to short time scales (usually several picoseconds) and small systems (typically a few dozen atoms). Typical semi-classical photodynamics simulations usually cover only a range of several picoseconds for a few dozen of atoms. With the advent of machine learning (ML) in theoretical chemistry, analytic representations of potential energy surfaces (PESs) and related properties have been developed. These approaches accelerate the simulations by decoupling the computational costs of electronic structure calculations from the dynamics simulations. While ground-state PES fitting has been pursued for over two decades and has enabled the simulation of molecular dy-namics of systems with many thousands to millions of atoms with ab initio accuracy, the application of ML approaches to excited-state processes has appeared much later, with most developments occurring mainly in this century. As a consequence, there is significant methodological work to be done in accurately and meaningfully fitting the numerous excited-state PESs and associated properties. Equivariant ML models have recently emerged for groundstate properties and have achieved notable success in fitting thereof. These models have demonstrated improved accuracy and efficiency compared to traditional ML models by successfully capturing the underlying symmetries of molecules and exploiting them to achieve accurate predictions even with limited training data. However, to the best of our knowledge, only one study has applied equivariant ML to describing excited state properties. Gómez-Bombarelli and co-workers developed a diabatic artificial neural network using the equivariant PaiNN 30 model, achieving a six-fold speedup in photodynamics simulations for azobenzene derivatives. Although their model demonstrated robustness and transferability within the chemical space of azobenzenes, it was not compared to the performance of invariant approaches, such as PyRAI 2 MD and SchNarc . The latter is based on SchNet, the invariant precursor to PaiNN used in the aforementioned study 31. This omission makes it unclear whether equivariant models have an advantage over invariant models for excited states.