arXiv:2606. 05618v1 Announce Type: cross Abstract: Extreme events -- such as earthquakes and coronal mass ejections -- are common in many chaotic dynamical systems, yet are difficult to characterize and predict due to the subtle instability mechanisms that drive them.
arXiv:2505. 23863v3 Announce Type: replace-cross Abstract: Understanding chaotic dynamics is a fundamental problem across scientific disciplines, including climate science, neuroscience, and fluid dynamics, yet direct experimentation and intervention in such systems are often infeasible.
arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.
arXiv:2608. 22277v2 Announce Type: replace Abstract: Deep learning surrogates for forecasting chaotic dynamical systems suffer from catastrophic error accumulation over long-term autoregressive rollouts.
arXiv:2308. 08794v4 Announce Type: replace Abstract: Tipping points are abrupt, drastic, and often irreversible changes in the evolution of non-stationary and chaotic dynamical systems.
The paper presents a probabilistic deep learning emulator—a ResNet‑inspired Conditional Variational Autoencoder—for the stochastic Holton–Mass model of stratospheric variability, which exhibits rare transitions between strong and weak polar vortex regimes. The emulator accurately reproduces short‑term dynamics, steady‑state distributions, regime persistence, rare transition rates, the committor function, and expected lead times. Analysis of the 32‑dimensional latent space via PCA reveals an unsupervised separation into four physically interpretable clusters that correspond to the two vortex regimes and their stable or transition‑prone states.
arXiv:2608. 22277v3 Announce Type: replace Abstract: Deep learning surrogates have become powerful tools for simulating and forecasting complex dynamical systems, yet their utility remains limited by catastrophic error accumulation during long-term autoregressive rollouts.
arXiv:2511. 06609v4 Announce Type: replace Abstract: The accurate forecasting of complex, high-dimensional dynamical systems from observational data is a fundamental task across numerous scientific and engineering disciplines.
arXiv:2512. 19804v2 Announce Type: replace Abstract: Reduced-order models (ROMs) can represent spatiotemporal processes in significantly fewer dimensions and can often be solved many orders of magnitude faster than their governing partial differential equations (PDEs).
The paper introduces a mechanism‑aware conditioning framework that uses a nudged coarse ensemble to capture local instability geometry in chaotic systems. By injecting ensemble covariance statistics via a small FiLM module, the authors enhance rare‑event emulation in both a low‑dimensional chaotic benchmark and a quasi‑geostrophic flow model, achieving significant improvements in exceedance‑frequency and tail‑density errors with limited data. The approach demonstrates that local instability information can be leveraged as a practical conditioning signal for data‑efficient emulation of extreme events.
arXiv:2608. 14716v1 Announce Type: cross Abstract: Abrupt transitions in complex systems are often preceded by early warning signals.
arXiv:2602. 13847v5 Announce Type: replace-cross Abstract: A central challenge across science and engineering is to build data-driven reduced-order models of turbulent dynamical systems that reproduce stationary statistics, predict responses to external perturbations, and remain practical for real-world applications.
arXiv:2608. 16084v1 Announce Type: new Abstract: Neural autoregressive models have rapidly emerged as powerful emulators of high-dimensional chaotic systems, yet their long-term instability and error growth remain poorly understood, leading to ad-hoc solutions.