Time-Series Learning Based on Neural Ordinary Differential Equations for Nonadiabatic Molecular Dynamics Simulations

Time-series learning using purely data-driven models struggles to emulate physical dynamic systems effectively, primarily due to the lack of relevant physical constraints. Here, we introduce two time-series learning architectures based on neural ordinary differential equations (NODEs)—continuous normalizing flow (CNF) and Hamiltonian neural networks (HNN)—to model nonadiabatic molecular dynamics (NAMD). CNF incorporates the mathematical constraint of log-normalized energy gap distributions into the loss function, enhancing the model’s ability to handle monotonic changes in state populations in photophysical systems. However, CNF is less effective in cases involving significant back-hopping during nonadiabatic transitions. To address this, we employ HNN, which integrates the physical constraint of the Hamiltonian mechanism. This enables HNN to learn vector fields from observed NAMD trajectories, allowing it to accurately model nuclear propagation and coupled nonadiabatic transitions. These two architectures have provided potential solutions for ultrafast dynamics simulations. The CNF model effectively captures photophysical processes without the need for intricate parameter tuning, while the HNN model excels in simulating photochemical-induced configurational reorganization.