System–bath modeling in vibrational spectroscopy via molecular dynamics: A machine learning framework for hierarchical equations of motion (HEOM)

Molecular vibrations in solutions, especially OH stretching and bending in water, drive ultrafast energy relaxation and dephasing in chemical and biological systems. We present a machine learning approach for constructing system-bath models of intramolecular vibrations in solution, compatible with quantum simulations via the hierarchical equations of motion (HEOM). Using classical molecular dynamics trajectories generated with a force field specifically developed for intramolecular modes, the model captures anharmonic mode coupling and non-Markovian dissipation through spectral distribution functions (SDFs). These results enable a fully quantum mechanical description of ultrafast energy relaxation and vibrational dephasing processes in the presence of quantum heat baths within the HEOM framework. The trained model yields physically interpretable parameters, validated against infrared spectra. Notably, we demonstrate that synergistically integrating a Brownian oscillator (BO) SDF and a Drude SDF-representing intermolecular and intramolecular vibrational relaxation, respectively-substantially improves learning efficiency for nuclear trajectories. However, the linear absorption spectrum calculated by this model is accurately reproduced in the Drude-only SDF case, as incorporating intermolecular vibrational effects solely within the BO SDF leads to their overestimation. Possible remedies to this issue are also discussed.