Thanks for the response. There is a method for imposing physical constraints on the neural network, in which a physics-based loss is added to the loss function. This term is usually a function of the output of the network.
As a simplistic example, assume the network outputs a number, which should not fall below “3”. We add a (penalty) regularization term of the form “max(3-output, 0)” that penalizes when output is below 3 and is canceled when output is above 3.
As this is essentially a constrained optimization (minimizing NN loss function subject to the physical constraint above), which is turned into a regularized unconstraint optimization (in the form of a Lagrangian function), we need to find a Lagrangian multiplier for the regularization term. This Lagrangian multiplier is what I’m wondering if is possible to learn, rather than tune (as suggested in many papers).
You can see one such a work here:
https://papers.nips.cc/paper/7942-constrained-generation-of-semantically-valid-graphs-via-regularizing-variational-autoencoders.pdf 11. (section 3 and Eq 8 in particular)
Thank you!