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Stable BCE-loss training and mode-collapse mitigation for physics-informed GANs (Z-GANs)

Determine generator–discriminator hyperparameters, loss formulations, and training procedures that achieve stable convergence and avoid mode collapse when training physics-informed GANs with Binary Cross-Entropy loss on optimal trajectory datasets for the Zermelo minimum-time navigation problem.

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Background

The paper studies S-GAN and two physics-informed GAN variants (Z-GAN1 and Z-GAN2) for the Zermelo navigation problem, where the generator loss includes terms enforcing Hamiltonian invariance and, in Z-GAN2, the costate–control relation. During training, the authors found Binary Cross-Entropy (BCE) loss unstable and switched to Mean Squared Error (MSE) loss.

They report that with BCE loss they could not find hyperparameters that yield convergence and observed persistent mode collapse, which they were unable to resolve. This instability motivated transitioning to VAE-based architectures in subsequent experiments.

References

We were unable to find model hyperparameters for convergence of the BCE loss, and therefore we used the MSE loss. For the Z-GANs, using the BCE loss instead of MSE caused mode collapse that we could not resolve.

— Case Studies of Generative Machine Learning Models for Dynamical Systems (2508.04459 - Bapat et al., 6 Aug 2025) in Section 4.1 (S-GAN and Z-GAN Implementation), Other Characteristics