Physics-informed VAE for the Minimum Threat Exposure problem

Develop a variational autoencoder for the minimum threat exposure navigation problem that incorporates the Hamiltonian zero-invariance constraint as an explicit loss term, analogous to the Z-VAE used for the Zermelo minimum-time navigation problem, and that can be trained on observed trajectory datasets whose optimality parameter differs from the model so the trajectories do not exactly satisfy the governing equations.

Background

The paper introduces Z-VAE, a physics-informed VAE that enforces the Hamiltonian invariance along optimal trajectories for the Zermelo minimum-time navigation problem. When attempting to apply the same idea to the minimum threat exposure problem, the authors note that the observed training dataset (OTD) is noisy because the cost weight parameter λ differs between the model and the observed optimal trajectories, causing violations of the governing equations.

Due to this mismatch, the authors report that directly adding a Hamiltonian residual term to the VAE loss (as done in Z-VAE) was not successful for the minimum threat exposure case. They propose Split-VAE as an alternative architecture that leverages both noiseless model trajectories and noisy observed trajectories by conditioning separate components of the latent space.