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 the electronic-state manifold to accelerate photophysical and photochemical molecular simulations. The protocol solves several pertinent 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 with established ML potentials. We also present gap-driven dynamics for meticulous accelerated sampling of the small-gap regions: which proves crucial for stable surface-hopping dynamics. Put together, multi-state learning and gap-driven dynamics enable efficient active learning furnishing robust models for surface-hopping simulations. 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. The thresholds for uncertainty quantification are automatically chosen based on statistical and physical considerations. The protocol will be made available with the next release of the open-source MLatom as described at https://github.com/dralgroup/al-namd