I am new to this field and to StackExchage, so I guess I'll start by saying hello!

I am building a deep neural network to model a physical system which takes a set of inputs based on real-world measurements and predicts a single continuous value, another real-world parameter. It's a pretty straightforward regression problem.

While I am a bit limited in the amount of data I can collect and train the model on, I do have a lot of a priori knowledge about the system's physical constraints that could provide some useful "guardrails" which I'd like to build into the architecture of the model, and some googling has helped me with many of those.

Some are a little more confounding:

For a certain value of one of the n elements of X, say x_n, the result in an undefined value for y regardless of the values of x_0 through x_n-1.

Similarly, for a certain value of another element, let's say x_0, any combination of the remaining elements of input vector X result in a y equal to zero.

Outside of a model architecture approach, I've thought that maybe I could use data augmentation and randomize part of X while keeping the relevant elements of X and y constant, but that would end up making my data set like 90% augmentation, and 10% real data. Is that a good approach?

  • $\begingroup$ maybe lagrangian neural networks will be of interest (especially as they are designed to conserve certain known properties of a physical system) $\endgroup$
    – Nikos M.
    Jan 28 at 18:35

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