  Computing dynamical distributions in quantum many-body systems represents one
of the paradigmatic open problems in theoretical condensed matter physics.
Despite the existence of different techniques both in real-time and frequency
space, computational limitations often dramatically constrain the physical
regimes in which quantum many-body dynamics can be efficiently solved. Here we
show that the combination of machine learning methods and complementary
many-body tensor network techniques substantially decreases the computational
cost of quantum many-body dynamics. We demonstrate that combining kernel
polynomial techniques and real-time evolution, together with deep neural
networks, allows to compute dynamical quantities faithfully. Focusing on
many-body dynamical distributions, we show that this hybrid neural-network
many-body algorithm, trained with single-particle data only, can efficiently
extrapolate dynamics for many-body systems without prior knowledge.
Importantly, this algorithm is shown to be substantially resilient to numerical
noise, a feature of major importance when using this algorithm together with
noisy many-body methods. Ultimately, our results provide a starting point
towards neural-network powered algorithms to support a variety of quantum
many-body dynamical methods, that could potentially solve computationally
expensive many-body systems in a more efficient manner.
