Inquiry on Incorporating Physical Structural Constraints in the Learning Framework

[heyang49]

Hi,

I wanted to take a moment to express my appreciation for the excellent work done on the automatic learning framework. It is truly impressive and has been very beneficial for my projects.

In my current explorations, I’ve been considering how we can enhance the framework by integrating additional forms of prior knowledge, particularly concerning the physical structural constraints on the state variables. Specifically, I am interested in the following equation:

$$ \frac{d,}{dt}x(t) = f(W(t)x(t)) - g(A(t)x(t)), $$

where ( x(t) ) represents the state variables, and ( W(t) ) and ( A(t) ) are matrices that model the interactions within the system.

Would it be possible to incorporate these physical constraints into the model to achieve physical regularization? I look forward to your insights on this matter .

Thank you!

Best regards,