Does the second-order moment of the GRU output have real physical meaning？

[Sjtu-hyg]

Hello author, I would like to ask whether you have examined the quantities output by the GRU, such as:

out_Q, self.h_Q = self.GRU_Q(in_Q, self.h_Q)
out_Sigma, self.h_Sigma = self.GRU_Sigma(in_Sigma, self.h_Sigma)

Do these outputs have real physical meaning? Can they be directly used?
I compared the results with those from the EKF (Extended Kalman Filter) and found that, numerically, they do not seem to exhibit fully similar/consistent trends.

Thank you!

[XiaoyongNI]

Hello,

Thanks for your question. You're right to notice that the GRU outputs like out_Q and out_Sigma don't necessarily align with the true physical Q and Σ matrices. Our current training approach doesn't guarantee this direct physical correspondence: the GRUs learn representations that maximize the performance, but they aren't explicitly constrained to match physical meanings.

However, this is a very interesting direction for future research.

Best,
Xiaoyong