Thank you all for your replies!
Yes, my question arose exactly from Python - my colleague works on the ANN-based eikonal equation solver implemented with Tensorflow - and I wanted to play with this problem using WL.
A particular thanks to Sam's reply: interesting approach to the problem!
Not sure if this is useful to you guys: Teaching neural networks to solve partial differential equations https://community.wolfram.com/groups/-/m/t/1379466
I have tried for a couple hours, but I have not found any solution.
You could export the model and use mxnet python to do the training. Perhaps, you could still use the Python integration to send the equations from Wolfram language to Python.