## 4 Conclusions  
In this work, we presented preliminary results for the prediction of the harmonic yield in different HHG configurations. The results have been obtained with the combination of a complete 3D simulation model and an artificial neural network model. The main result of this work is that we succeeded to build a complex computational tool which is able to predict the expected outcome of a HHG experiment covering conditions when several experimental parameters are varied in a given range. Since this is a usual situation in most attosecond science laboratories, we consider our achievement being a useful and very practical numerical instrument. We need to perform a sufficient number of full 3D simulations designed such as to cover (if possible uniformly) the whole explored parameter space. The next step is to introduce these results as input into the ANN, train it, validate and test. A correctly trained ANN is capable to predict the expected outcome of a possible HHG experiment to be performed with parameter combinations that were not implemented in the 3D simulations. In general terms: the 3D model for HHG combined with the ANN model provide a smooth scan of the parameter space along any variable parameter, and can indicate combinations of possible experimental circumstances which are favorable for the targeted outcome. Figure 6: Results of the complete 3D simulation performed with the following values of the parameters: \(E=9\) mJ; \(p=5.31\) mbar; \(z_{i}=-25\) cm. (**a**) Radially integrated power spectrum calculated at every 4 cm of medium length. (**b**) (_r,z_) map of the driving pulse’s intensity spatial evolution. (**c**) (_r,z_) map of how the H25 builds up during propagation. Other parameters are specified in the main text at the beginning of Section 3. Figure 7: Harmonic yield as function of the optical density of the medium. We represent the logarithm of both quantities, the units are arbitrary. Slope = 2 indicates the quadratic growth of the harmonic yield with the optical density. In particular: within the present study we targeted to obtain enhanced harmonic yield in the 20-40 eV spectral domain. The variable experimental parameters were: input laser pulse energy \(E=[0.77;11.6]\) mJ; argon pressure \(p=[0.1;20]\) mbar; cell entrance position relative to the nominal focus \(z_{i}=[-50;50]\) cm, medium length \(L_{med}=[0;20]\) cm, while we kept unchanged the pulse duration, wavelength, focal length, beam size, gas type. The main message of the obtained results is that a correctly trained ANN fed with reliable input data originating from the full 3D calculations is capable to predict the outcome of a HHG experiment in the unexplored parts of the multi-dimensional parameter space. In this particular case study we only demonstrated the capabilities of the prediction method which uses the results of full 3D simulations as input and the harmonic yield as output. However, other physical quantities of interest can be defined and predicted if the ANN is modified accordingly. We can define for example a spectral domain where we search for the existence of isolated attosecond pulse; if it has satellites, then we can predict the contrast relative to the main pulse; we can look for the configuration which provides highest brightness for a specified harmonic order, i.e., high yield combined with low divergence. ANN as a numerical instrument for prediction can use as input data either data originating from complex simulations (like in our case), or real experimental data (if available), or even a combination of experimental and simulation results. Obviously in the latter case one has to check for the agreement between them, and to perform a calibration of the simulated against the experimental data. We foresee that this prediction method can be extended to become an easy to use optimization tool, which would mean an essential progress in the way to solve the problem of low conversion efficiency in HHG. Conceptualization, V.T. ; Software, V.T. (3D model), M.V.C. (ANN model); Validation, K.K. and A.M.M.G.