arXiv:2607. 14937v1 Announce Type: cross Abstract: Recent foundation models (FMs) for zero-shot reconstruction of dynamical systems (DS) achieve strong out-of-domain generalization but provide little insight into the mechanisms that underlie their forecasts.
arXiv:2602. 16864v2 Announce Type: replace-cross Abstract: Time series (TS) modeling has come a long way from early statistical, mainly linear, approaches to the current trend in TS foundation models.
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:2507. 03094v2 Announce Type: replace-cross Abstract: Many challenges in scientific imaging involve solving ill-posed inverse problems, where the goal is to recover spatio-temporal fields from indirect, noisy, and highly sparse measurements - often without access to ground truth data or reliable simulators.
The paper introduces flux‑form spatiotemporal neural operators for predicting coarse‑grained dynamics of multiscale PDEs without relying on closure models. It learns a surrogate evolution operator from filtered high‑fidelity data, using Fourier convolution for spatial mixing and a causal kernel with time‑lag attention for temporal mixing. The method incorporates a flux‑form inductive bias to maintain conservation and provides a data‑driven rule for selecting memory length, achieving stable, accurate long‑horizon rollouts on benchmark equations and turbulent flow simulations.
arXiv:2511. 08860v2 Announce Type: replace-cross Abstract: The deep learning revolution has spurred a rise in advances of using AI in sciences.
arXiv:2609.37078v1 Announce Type: new Abstract: Time series modeling increasingly demands high-quality supervision, yet target observations remain scarce - exogenous inputs are broadly available, but...
arXiv:2606. 01289v1 Announce Type: new Abstract: Zero-shot time series forecasting aims to predict future values for previously unseen series, requiring models to generalize temporal dynamics beyond the training distribution.
arXiv:2512. 21113v2 Announce Type: replace Abstract: Transformers are increasingly adopted for modeling and forecasting time-series, yet their internal mechanisms remain poorly understood from a dynamical systems perspective.
The paper introduces an in‑span adaptation technique for reduced‑order models, where the reduced subspace is continually updated using the model’s own predictions via an incremental singular‑value decomposition with a forgetting factor. This creates a trajectory‑informed spectral preconditioner that reweights and realigns the basis without changing the subspace, enabling the model to better absorb future out‑of‑span corrections. The authors demonstrate the method on a 3‑D spiral example and nonlinear PDEs such as viscous Burgers and Fisher–KPP, and relate the approach to in‑context learning in dynamical systems.
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.
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...
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.