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: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.
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).
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.
arXiv:2606. 04143v1 Announce Type: cross Abstract: Accurate flood forecasting is essential for mitigating disaster risks and protecting communities.
arXiv:2407. 06312v2 Announce Type: replace-cross Abstract: Many systems resist analytical modeling, making data-driven inference of dynamics important.
arXiv:2602. 23461v2 Announce Type: replace-cross Abstract: Data assimilation (DA) for compressible flows with shocks is challenging because many classical DA methods generate spurious oscillations and nonphysical features near uncertain shocks.
arXiv:2608. 12624v1 Announce Type: new Abstract: Structure-preserving machine learning embeds physical structure directly into model architectures, yet uncertainty quantification (UQ) for such hard-constrained models remains limited because standard UQ methods may violate the encoded admissibility conditions, require architectural modifications, or impose substantial computational costs.