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.
By Chang Liu, Bohao Zhao, Jingtao Ding, Huandong Wang, Yong Li
arXiv:2507. 03631v4 Announce Type: replace Abstract: Extracting interpretable mathematical models from complex dynamical systems is difficult, especially for chaotic dynamics observed with noisy experimental data.
By Anthony G. Chesebro, David Hofmann, Vaibhav Dixit, Earl K. Miller, Richard H. Granger, Alan Edelman, Christopher V. Rackauckas, Lilianne R. Mujica-Parodi, Helmut H. Strey
The paper introduces a data‑adaptive nonlinear vector autoregression (NVAR) model that replaces fixed polynomial or random feature maps with a shallow, trainable multilayer perceptron (MLP). By jointly training the MLP and a linear readout via gradient‑based optimization, the model learns data‑driven nonlinearities while maintaining a simple readout structure, improving scalability in high‑dimensional settings. Experiments on several chaotic systems, both noise‑free and synthetically noisy, show that this adaptive NVAR outperforms standard NVAR, a leaky echo state network (ESN), and a hybrid ESN in predictive accuracy, demonstrating robust forecasting under noisy conditions.
By Sherkhon Azimov, Susana Lopez-Moreno, Eric Dolores-Cuenca, Sieun Lee, Jae-Il Kwon, Sangil Kim
The paper investigates using reservoir computing, specifically an echo state network, to predict nonlinear dynamics in a jumping quarter‑car model. By training on limited time‑series data, the network can reconstruct bifurcation diagrams, phase‑space attractors, and time trajectories across both periodic and chaotic regimes, reproducing the period‑doubling route to chaos. These findings show that reservoir computing can serve as a data‑driven predictor for nonlinear, non‑smooth vehicle dynamics.
By Masahisa Watanabe, Shiva Dixit, Nirmal Punetha, Swati Chauhan, Manish Dev Shirimali
Echo State Networks (ESNs) offer an efficient framework for temporal prediction, but their randomly initialized reservoirs are often over-parameterized and dynamically redundant. Existing pruning methods largely rely on static connectivity or activation statistics, which may overlook neurons that shape input-driven state transitions.
arXiv:2608. 04593v1 Announce Type: cross Abstract: Echo State Networks (ESNs) offer an efficient framework for temporal prediction, but their randomly initialized reservoirs are often over-parameterized and dynamically redundant.
By Sudip Laudari, Puspa Raj Adhikari