What it is: A generative adversarial network (GAN) architecture for synthetic univariate time-series data, integrating Hopf bifurcation theory into the training dynamics to improve stability over long training runs.
The problem: Standard GANs are notoriously unstable to train — mode collapse and oscillating losses are common, and time-series data’s temporal dependencies make that instability worse. The result is often synthetic data that looks realistic briefly, then degrades.
Our approach: We treat the generator-discriminator training dynamic as a dynamical system and apply Hopf bifurcation analysis to identify the stability boundary between controlled convergence and oscillatory failure, structuring training to stay on the stable side of that boundary for longer.
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