Multi-Time-Scale Time Encoding for CNN Prediction of Fenna–Matthews–Olson Energy-Transfer Dynamics

Machine learning simulations of open quantum dynamics often rely on recursive predictors that accumulate error. We develop nonrecursive convolutional neural networks (CNNs) that map system parameters and a redundant time encoding directly to excitation energy transfer (EET) populations in the Fenna-Matthews-Olson (FMO) complex. The encoding-modified logistic plus tanh function normalizes time and resolves fast, transitional, and quasi-steady regimes, while physics-informed labels enforce population conservation and intersite consistency. Trained only on 0-7 ps reference trajectories generated with a Lindblad model in QuTiP, the network accurately predicts 0-100 ps dynamics across a range of reorganization energies, bath rates, and temperatures. Beyond 20 ps, the absolute relative error remains below 0.05, demonstrating stable long-time extrapolation. By avoiding step-by-step recursion, the method suppresses error accumulation and generalizes across time scales. These results show that redundant time encoding enables data-efficient inference of long-time quantum dissipative dynamics in realistic pigment-protein complexes and may aid the data-driven design of light-harvesting materials.