Estimating positive largest Lyapunov exponents from data is comparatively natural because neighboring trajectories separate, whereas stable dynamics require resolving contraction before measurement noise or finite precision erases the signal. We introduce a period-aware forecast-error contraction procedure for estimating a dominant negative Lyapunov exponent from ensembles of short scalar trajectories without using governing equations or an analytical Jacobian.
arXiv:2608. 05522v1 Announce Type: cross Abstract: Estimating positive largest Lyapunov exponents from data is comparatively natural because neighboring trajectories separate, whereas stable dynamics require resolving contraction before measurement noise or finite precision erases the signal.
The paper presents an ensemble Kalman–Bucy smoother (EnKBS) for continuous‑time data assimilation of nonlinear dynamical systems, reconstructing conditional distributions from ensemble moments without needing tangent‑linear or adjoint models. It demonstrates that EnKBS achieves exact smoothing mean and covariance in the infinite‑ensemble limit for linear‑Gaussian systems and incorporates regularization techniques like covariance localization and inflation for high‑dimensional problems. The method is applied to Bayesian inference of causal relationships in a dyadic trigger‑feedback model and to an iterative learning algorithm that uncovers the structure and hidden parameters of a reduced‑order model of midlatitude atmospheric circulation, all with small ensembles under partial observations.
arXiv:2606. 01596v1 Announce Type: cross Abstract: Learning chaotic dynamical systems from data requires more than short-term predictive accuracy: the learned model must preserve the attractor geometry and its invariant statistics.
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:2608. 16098v1 Announce Type: cross Abstract: Multivariate time-series forecasting faces a structural dilemma: sharing one temporal predictor across variables is parameter-efficient but forces heterogeneous variables through an identical history-to-future map, whereas learning an independent predictor per variable restores flexibility at a cost that grows with the product of variable count, context length, and horizon.
Vector autoregressive moving-average (VARMA) models have long been considered impractical beyond moderate dimensions: the likelihood is non-convex, the parametrization is identified only up to equivalence, and every evaluation costs a pass over the entire series. Yet their moving-average term captures with a few parameters what a pure autoregression matches only with many lags.
arXiv:2602. 12756v2 Announce Type: replace Abstract: Large Language Models (LLMs) have recently shown exceptional potential in time series forecasting (TSF), leveraging their inherent sequential reasoning capabilities to model complex temporal dynamics.
The paper compares different Ensemble Kalman methods for calibrating climate model parameters by minimizing the misfit between modeled and observed climate statistics. It conducts systematic numerical experiments on Lorenz-type models, including neural network parameterizations, to evaluate computational efficiency and accuracy of each method. The study examines how prior information and dimensionality affect the cost of these methods.
Training-free feature forecasting accelerates diffusion sampling by predicting features at skipped denoising steps. Recent work has mainly focused on designing stronger forecasters.
arXiv:2608. 01740v1 Announce Type: new Abstract: Training-free feature forecasting accelerates diffusion sampling by predicting features at skipped denoising steps.
arXiv:2608.30899v1 Announce Type: new Abstract: Most trajectory forecasting models are trained on clean annotated histories, and are often evaluated under the same idealized assumption, although prac...
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.