arXiv:2610.06798v2 Announce Type: replace-cross
Abstract: Machine-learning emulators of chaotic and stochastic systems are usually validated on forecast skill and long-run statistics. Neither certifi...
By Jo\~ao B\"oger, Simon Driscoll, Niccol\`o Zagli, Valerio Lucarini, Francisco Camara Pereira
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
Neural surrogates for forecasting physical fields from sparse, noisy sensors typically use a spatial window and a temporal history of past snapshots. This study compares the trade‑off between window size and history length against the Bayes‑optimal error, showing that for fields with local dynamics the optimal forecast relies mainly on distant sensors via spatial correlation. Experiments on Burgers flow and the chaotic Kuramoto‑Sivashinsky equation reveal that the benefit of additional snapshots depends on lead time and system stability, leading to design rules that size the window in correlation lengths and split input budgets between window and history based on forecast horizon.
By Ruige Kong
arXiv:2606. 09929v1 Announce Type: cross Abstract: Physical reservoir computing harnesses nonlinear mechanical dynamics but, by convention, freezes the substrate and trains only a linear readout, presuming the substrate is not usefully trainable.
By Caleb Munigety
The paper introduces a world model that learns to predict the evolution of physical systems while respecting key physical principles. By hard‑coding a general structure—generating dynamics from the gradient of a learned energy via a fixed reversible operator and imposing constraints on energy, dissipation, and interventions—the model achieves second‑law compatible dissipation, accurate responses to parameter changes, long‑term stability, and robustness to disturbances. Experiments on an electromagnetic cavity, a particle‑in‑cell grid, and shallow‑water fluid demonstrate that the model can recover accurate constitutive functions, distinguish conserving from dissipating regimes, and transfer learned physics to unseen conditions, outperforming unconstrained models.
By Yufeng Wang, Parivesh Priye, Lu Wei, Haibin Ling
arXiv:2606. 11251v1 Announce Type: new Abstract: Many multivariate dynamical systems are observed only through trajectories, leaving the mechanisms governing their joint dynamics hidden.
By Xingji Cui