Physics-informed neural networks for quantum propagators in Wavepacket dynamics

We explore the capability of linear fully connected neural networks (FCNs) to learn and predict quantum dynamics governed by various equations of motion, including the time-dependent Schrödinger equation, quantum Liouville equation, and thermofield dynamics (TFD). Given the inherent linearity of these equations, linear FCNs naturally align with the fundamental structure of quantum propagators, making them a promising machine-learning approach for simulating quantum systems. Through numerical experiments on different model systems, including single-state and two-state anharmonic potentials, we demonstrate that linear FCNs without hidden layers achieve high accuracy while preserving population conservation. For finite-temperature dynamics, we find that learning TFD is more efficient than learning density matrix evolution due to the suppressed noise from the partial trace over the fictitious Hilbert space. However, as system dimensionality increases, the computational cost of linear FCNs becomes substantial due to scaling and sampling challenges, suggesting the necessity of more efficient network structures. Our results highlight the potential of physics-informed neural networks for quantum dynamics and point toward future developments in neural network architectures inspired by physical principles.