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High harmonic generation (HHG) stands as one of the most complex processes in strong-field physics, as it enables the conversion of laser light from the infrared to the extreme-ultraviolet or even the soft x-rays, enabling the synthesis and control of pulses lasting as short as tens of attoseconds. Accurately simulating this nonlinear and non-perturbative phenomena requires the coupling the dynamics of laser-driven electronic wavepackets, described by the three-dimensional time-dependent Schrödinger equation (3D-TDSE), with macroscopic Maxwell’s equations. Such calculations are extremely demanding due to the duality of microscopic and macroscopic nature of the process, thereby requiring the use of approximations. We develop a HHG method assisted by artificial intelligence that facilitates the simulation of macroscopic HHG within the framework of 3D-TDSE. This approach is particularly suited to simulate HHG driven by structured laser pulses. In particular, we demonstrate a self-interference effect in HHG driven by Hermite-Gauss beams. The theoretical and experimental agreement allows us to validate the AI-based model, and to identify a unique signature of the quantum nature of the HHG process.

High harmonic generation (HHG) is one of the richest processes in strong-field physics. It allows to up-convert laser light from the infrared domain into the extreme-ultraviolet or even soft x-rays, that can be synthesized into laser pulses as short as tens of attoseconds. The exact simulation of such highly non-linear and non-perturbative process requires to couple the laser-driven wavepacket dynamics given by the three-dimensional time-dependent Schrödinger equation (3D-TDSE) with the Maxwell equations to account for macroscopic propagation. Such calculations are extremely demanding, well beyond the state-of-the-art computational capabilities, and approximations, such as the strong field approximation, need to be used. In this work we show that the use of machine learning, in particular deep neural networks, allows to simulate macroscopic HHG within the 3D-TDSE, revealing hidden signatures in the attosecond pulse emission that are neglected in the standard approximations. Our HHG method assisted by artificial intelligence is particularly suited to simulate the generation of soft x-ray structured attosecond pulses.