Eigenanalysis Framework Reveals Stability Origins in Neural Emulators of Chaotic Dynamics

A recent preprint on arXiv (2608.16084) presents an eigenanalysis framework aimed at elucidating error growth in neural autoregressive models that serve as emulators for high-dimensional chaotic systems. This new submission tackles the long-term instability and error growth issues, which have previously been addressed through makeshift solutions. By examining the Jacobian of the learned one-step update map concerning the state, the researchers reveal that the spectral radius governs inference-time error growth and model stability. They observe that direct-step architectures, which predict the next state based on the previous one, typically have unstable eigenvalues with magnitudes greater than one, leading to rapid divergence. Conversely, integration-constrained models, which estimate the time derivative and use a higher-order integrator, confine their eigenspectrum to the unit circle, resulting in neutral stability and consistent linear error growth. This theoretical perspective not only clarifies the empirical effectiveness of integration-constrained methods but also serves as a diagnostic tool for assessing and creating stable neural emulators for chaotic dynamics. These insights could enhance the reliability of machine learning simulations in areas like weather forecasting, climate modeling, and other intricate physical systems.