arXiv:2608. 22277v2 Announce Type: replace Abstract: Deep learning surrogates for forecasting chaotic dynamical systems suffer from catastrophic error accumulation over long-term autoregressive rollouts.
By Zhou Fang, Gianmarco Mengaldo
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
Autoregressive transformers trained on limited trajectories of nonlinear dynamical systems can extrapolate to unseen parameter regimes, reproducing period-doubling cascades, chaotic dynamics, and attractor structures with high fidelity. In the logistic map, the model captures successive period doublings up to period 128, achieving a scaling ratio within $5 imes10^{-4}$ of the Feigenbaum constant. The study also shows how control‑parameter information is processed via attention, shaping the closed‑loop dynamics during training.
By Yilun Liu, Yi Zhang, Ganyu Wu, Sikuan Yan, Mengyue Wang, Alois Knoll, Volker Tresp, Yunpu Ma
The paper investigates why latent neural surrogate solvers, which compress physical system dynamics into a lower‑dimensional space, often fail during long‑horizon autoregressive rollouts. It demonstrates that training the latent representation only for reconstruction leads to instability, and proposes a set of training interventions—Koopman operator learning, Hamming noise injection, and multi‑step rollout fine‑tuning—that align the latent space with long‑horizon forecasting. These interventions reduce long‑rollout error by about 40 % and achieve accuracy comparable to full‑resolution models while using far fewer floating‑point operations and GPU memory, enabling stable extrapolation in mesoscale crystal‑plasticity simulations of high‑cycle fatigue.
By Andreas E. Robertson, Ashley T. Lenau, John D. Shimanek, Benjamin A. Jasperson, Vivek Oommen, David L. Damm, Krishna Garikipati, Remi Dingreville
The paper introduces a mechanism‑aware conditioning framework that uses a nudged coarse ensemble to capture local instability geometry in chaotic systems. By injecting ensemble covariance statistics via a small FiLM module, the authors enhance rare‑event emulation in both a low‑dimensional chaotic benchmark and a quasi‑geostrophic flow model, achieving significant improvements in exceedance‑frequency and tail‑density errors with limited data. The approach demonstrates that local instability information can be leveraged as a practical conditioning signal for data‑efficient emulation of extreme events.
By Isabella S. Thiel, Juan Bello-Rivas, Yannis G. Kevrekidis, Themistoklis P. Sapsis
The paper introduces Chameleon, a channel‑dependent state space model for multivariate time series forecasting that allows data‑dependent, fine‑grained interactions across variables while maintaining linear scaling with the number of variables. By integrating selective state space models with a Kalman filter and adapting GatedDeltaNet as the backbone, Chameleon improves generalization and achieves lower MSE and MAE on strongly dependent ODE and PEMS datasets compared to both channel‑independent and prior channel‑dependent methods. Across 28 benchmark settings, it outperforms baselines in the majority of cases and demonstrates competitive training‑time and memory efficiency on Traffic and ETT datasets.
By Yu-Cheng Wu, Fan-Keng Sun, Li-Chun Lu, Duane S. Boning