Guideline for variable scaling in modulus


I don’t understand how to decide the scale of variables(time, length, mass, etc.) for normalization in training various type of modulus models.

If you know some kind of guideline for such a scaling, I would like you to let me know.


Hi @yokoi.toshiaki

We have some information on variable scaling in our user-guide with some external links. We also have some automated utils to help with scaling/non-dimensionalization which can be seen in the cylinder example.

There’s also a few posts on this forum discussing this topic such as:

Hi @ngeneva

Thank you for your reply.

I have tried sevral approaches in the unsteady CFD problem with low Re num. based on that document so far.
However I can’t find a good scaling condition in which NN convergence is achieved.

Therefore I have a question.

In the most of your CFD samples, nu is ~0.01 and they work well.
How did you find such a good conditions?



Mostly experience and empirical testing. Think about this like normalizing data for traditional DL models, there are a lot of ways to do this with varying results (as commented here).

Regarding the viscosity, its also key that a system is selected that’s not too complex in terms of the underlying dynamics. That’s why for many of the flow problems are at lower Reynolds number or have a turbulence models to help with the smaller scales.

Sadly, there isn’t one sure-fire solution for all problems, rather a lot of techniques that can be used to improve convergence in certain instances. Check out the user guide with a list of ideas to test. For example, integral continuity planes can really help with flow problems as used in many of our examples including annular ring.