The paper introduces neural network nudging, a data‑driven method for learning observation‑driven control terms in nonlinear state‑space models. It builds on Kazantzis–Kravaris–Luenberger observer theory to prove the existence of such terms and demonstrates the approach on three chaotic benchmarks: Lorenz 96, Kuramoto–Sivashinsky, and Kolmogorov flow.
arXiv:2501. 11655v3 Announce Type: replace-cross Abstract: This paper proposes a novel learning approach for designing Kazantzis-Kravaris or nonlinear Luenberger (KKL) observers for autonomous nonlinear systems.
arXiv:2604.07169v3 Announce Type: replace-cross Abstract: Bayesian filtering and smoothing are central to data assimilation in nonlinear dynamical systems. Recent advances in deep generative models p...
arXiv:2608. 05416v1 Announce Type: new Abstract: Can nonlinear dynamical systems be learned through a compact linear state-space representation, without directly solving a non-convex system-identification problem?
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. 04471v1 Announce Type: cross Abstract: Time series in real-world applications are often generated by nonlinear dynamical systems, making accurate forecasting challenging.
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: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:2410.23667v2 Announce Type: replace Abstract: Neural differential equations offer a powerful approach for learning dynamical systems from data. However, they do not inherently respect known con...
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:2608.22112v1 Announce Type: cross Abstract: We present a machine learning framework for identifying sparse, interpretable models of dynamical systems directly from time-series data. Our approac...
arXiv:2512. 18928v4 Announce Type: replace Abstract: This work introduces a novel nonlinear optimal filtering method, termed the Ensemble Schr{\"o}dinger Bridge nonlinear filter.
arXiv:2507. 09652v2 Announce Type: replace-cross Abstract: Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data.