## 1 Introduction and Motivation
### High-Harmonic Generation  
In order to have sufficient input data for the training of the ANN, extensive simulation of the complete HHG process has been performed using a 3D non-adiabatic model [44] while the theoretical basis implemented in the simulation code has been described in [45]. According to the physical reality, this model has three main parts: (A) solves the propagation equation of the fundamental laser pulse in the generating medium, which is a noble gas in our case; (B) quantify the response of the individual atoms to the external laser electric field; and (C) solves the propagation equation of the dipole radiation generated in step (B) within the same medium. (A) The propagation equation for the fundamental laser pulse is the Maxwell wave equation. This is solved with a self-consistent iterative method in frequency domain and using the paraxial approximation. The method is implemented in a way that the full electric field (carrier and envelope) is calculated, without using the slowly varying envelope approximation. The interaction configuration is considered to have cylindrical symmetry around the propagation direction defined as \(z\) axis, and \(r\) the radial coordinate. The pulse experiences an effective refractive index--function of time and spatial coordinates--which accounts for the linear refraction and absorption, the intensity-dependent optical Kerr effect and the dispersion due to the free electrons. In this way the modifications of the generating pulse during propagation are included: self-phase modulation, pulse lengthening, intensity clamping, possible self-guiding. The propagation part of the simulation code is partially parallelized. For detailed mathematical formulation we refer to [44]. (B) The elemental interaction of a laser pulse with an atom is treated within the strong-field approximation and the generated dipole is calculated by solving the Lewenstein integral [46]. This part of the simulation code has been also parallelized, but it is still the most demanding part of the calculation in terms of CPU time and memory use. (C) The total harmonic field results from the propagation and coherent addition of the atomic polarizations calculated in step (B). The wave equation describing the propagation of the harmonic field is similar to the wave equation for the fundamental, but the source term here is the non-linear polarization calculated in step (B). This simulation code has several advantages which make it a very useful tool in the design and interpretation of HHG experiments. When we construct one specific case all the needed input data are experimentally measurable (or can be estimated). These are information about the fundamental laser pulse like beam type, pulse energy, duration, carrier-envelope phase, chirp; geometrical arrangement like aperture, focusing, cell position and length, far-field detection configuration; interaction medium like gas type and pressure profile. One typical full calculation yields a complex set of quantities in the grid points built over the interaction domain such as: laser pulse shape before and after propagation in time and frequency representation, peak intensity and ionization fraction, harmonic spectrum in near- and far-field (spectral domain), harmonic bursts in temporal domain, spatial build-up of selected harmonic orders. The most important outcome is the harmonic power spectrum which can be directly compared to the experimentally measured spectra. In addition, the simulation results provide a detailed insight into the physics of the whole process (laser and harmonic field propagation), at sub-optical-cycle temporal resolution, while phase-matching conditions can be examined as well. The model is flexible in the sense that it can be modified according to diverse experimental conditions. It has been extended to be able to treat multiple electric fields (two-color [47; 48; 49; 50; 51; 52; 53] and three- or four-color field coming from a light-field synthesizer [22]) or multiple jets configurations.