If "non-probability sampling" means stratified sampling with an adequated startification across all resonably relebant perts that make up the population (and the sampling within each stratum is still random): yes. Otherwise: there are likely journals that would publish such studies (based on non-probability sampling), but imho they should not.

You may use genetic algorithms by adopting deep learning for the case of deep learning. See for example : https://towardsdatascience.com/evolving-deep-neural-networks-ceb8d135d74d.

In your case if your are using panel or longitudinal data, you may visit kaggle website : https://www.kaggle.com/questions-and-answers/35072

See also https://towardsdatascience.com/understanding-panel-data-regression-c24cd6c5151e

Probability sampling assumes that all members of your target population have an equal non-zero chance of being selected for your study. If you're trying to do a survey then that's not going to happen. If it's a true probability sample, then you'd need access to a list of all smartphone users from which you took a random sample, or a stratified random sample to be sure of capturing pre-defined groups.

Whether it is made clear or not in their reports, almost all social research is done with non-probability sampling.

Some researchers, including many who should know better, think that a random sample is approaching every nth person as they exit the campus library, or a shopping centre. That's not random. It's a convenience sample. You're approaching people at a time and place that is convenient to you. Only those people who are in the area have any chance of being selected, and those who are selected may be very different from those who do not attend that venue or at that time. It's no different for a sample recruited via an online advertisement, or social media.

The important question is, "does it matter?"

For a study investigating, say, "attitudes towards price of apps" or "level of concern about location-tracking software", then you need to decide whether people recruited through the usual methods (social media, a company that provides panel participants, or mall-intercepts) are likely to respond differently from most others in the population. Probably not. I acknowledge that political polling in the last UK elections were very wrong, partly because of their sampling frames. But in most cases, these samples are perfectly okay.

In my opinion, in many situation we have to research based on non-probability sampling. Especially in accountant, economics and social sciences, ...

Actually, it doesn't a big problem.