is it possible to use statistical learning to get results on thermodynamics, heat transfer, and fluid dynamics, ... etc,, some phenomenons are still complicated and without experiments, there is no way to get their results.
Of course,
See for example this open book on: "Statistical Mechanics and Thermodynamics"
http://cgarrod.org/Book/index.html
and also,
https://www-physics.ucsd.edu/students/courses/spring2010/physics210a/LECTURES/210_COURSE.pdf
With best luck.
What problems did you have in mind?
I may be wrong, but my opinion is that statistical learning cannot help in these fields. Statistical learning can be useful to make predictions where we have a lot of data and no theory. Making predictions without theory is not really part of the philosophy of the fields that you mention. Even where there is a lot of data, e.g. turbulence research, we still want a theory to interpret the data, not just a machine-derived prediction.
in some experiments, differents modes can be observed, such as heat conduction, convection, boiling, and fluid flow, all of them at the same time,,, the results of the experiments won't be gotten without doing it,
In these cases, careful use of dimensional analysis can simplify the problem greatly. For instance for the drop time of a dripping tap. Inertia, surface tension and viscosity can all be important. Calculating the relevant dimensionless gorups shows which of the competing forces are actually important under a given set of conditions.
I can imagine that you are right and that Principal Component Analysis could be applied to some big data sets to find the effective number of variables.
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