  Currently, machine learning (ML) methods are widely used to process the
results of physical experiments. In some cases, due to the limited amount of
experimental data, ML-models can be pre-trained on synthetic data simulated
based on the analytical theory and then fine-tuned using experimental data. A
limitation of this approach is the presence of the latent parameters of the
analytical model, which values are difficult or impossible to estimate. Setting
these parameters incorrectly may induce a dataset shift even when applied to
synthetic data. To overcome this problem, we train the ML-model on a dataset
with randomly varied latent parameters of the analythical model to force the
ML-model to concentrate on more general patterns that depend weakly on the
latent parameters. We applied this approach to the problem of tight focusing of
a laser pulse with the complex structure of the wavefront. We observed good
accuracy of reconstructing of the tilt parameters when training and testing the
ML-model on datasets generated for different values of the latent parameters.
This confirms that the ML-model was able to select relevant information without
over-fitting for specific features inherent in certain values of the latent
parameters. We believe that this approach will enrich possible applications of
ML-methods to an experimental diagnostics of laser pulses.
