Charting electronic-state manifolds across molecules with multi-state learning and gap-driven dynamics via efficient and robust active learning.

We present a robust protocol for affordable learning of electronic states to accelerate photophysical and photochemical molecular simulations. The protocol solves several issues precluding the widespread use of machine learning (ML) in excited-state simulations. We introduce a novel physics-informed multi-state ML model that can learn an arbitrary number of excited states across molecules, with accuracy better or similar to the accuracy of learning ground-state energies, where information on excited-state energies improves the quality of ground-state predictions. We also present gap-driven dynamics for accelerated sampling of the small-gap regions, which proves crucial for stable surface-hopping dynamics. Together, multi-state learning and gap-driven dynamics enable efficient active learning, furnishing robust models for surface-hopping simulations and helping to uncover long-time-scale oscillations in -azobenzene photoisomerization. Our active-learning protocol includes sampling based on physics-informed uncertainty quantification, ensuring the quality of each adiabatic surface, low error in energy gaps, and precise calculation of the hopping probability.