Best way to Normalize the Input of a PINN

[cpe.sk]

Hello,

I’m trying to reproduce the results of this paper: Physics-informed neural networks for transcranial ultrasound wave propagation - ScienceDirect

The metrics used are multi-scale (e.g. milliseconds (ms) and kiloHertz (kHz)). The setup of the problem requires the normalization of the input to PINNs to obtain accurate results.

Does Modulus have a specific feature that can be used to deal with multi-scale problems? If so, what do you recommend?
If not, then what is the best approach to have the input normalized before training and prediction?

Please share any suggestions to work around this.

[ngeneva]

Hi @cpe.sk

I have not read this paper but Modulus does have multiple Fourier networks which have been seen to learning multi-scale physics better than standard fully-connected. Using these could help. Regarding normalization, typically the best approach is to non-dimensionalize the system if possible then make further adjustments. Theres quite a few “tricks” you can try for difficult problems you could consider in our documentation.