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.
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.
By Zhang Jiang (University of Wisconsin-Madison), Marios Andreou (University of Wisconsin-Madison), Sebastian Reich (University of Potsdam), Nan Chen (University of Wisconsin-Madison)
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.
By Shinhoo Kang, Hai V. Nguyen, Tan Bui-Thanh
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.
By Miguel Liu-Schiaffini, Clare E. Singer, Nikola Kovachki, Sze Chai Leung, Hyunji Jane Bae, Kamyar Azizzadenesheli, Anima Anandkumar
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.
By Rebecca Gjini, Matthias Morzfeld, Oliver R. A. Dunbar, Tapio Schneider
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.
By Xiachong Lin, Du Yin, Hao Xue, Wen Hu, Imran Razzak, Arian Prabowo, Matthew Amos, Flora D. Salim