Transfer learning in predicting quantum many-body dynamics: from physical observables to entanglement entropy

Deep neural networks have demonstrated remarkable efficacy in extracting meaningful representations from complex datasets. This has propelled representation learning as a compelling area of research across diverse fields. One interesting open question is how beneficial representation learning can be for quantum many-body physics, with its notouriosly high-dimensional state space. In this work, we showcase the capacity of a neural network that was trained on a subset of physical observables of a many-body system to partially acquire an implicit representation of the wave function. We illustrate this by demonstrating the effectiveness of reusing the representation learned by the neural network to enhance the learning process of another quantity derived from the quantum state. In particular, we focus on how the pre-trained neural network can enhance the learning of entanglement entropy. This is of particular interest as directly measuring the entanglement in a many-body system is very challenging, while a subset of physical observables can be easily measured in experiments. We show the pre-trained neural network learns the dynamics of entropy with fewer resources and higher precision in comparison with direct training on the entanglement entropy.