arXiv:2606. 09917v1 Announce Type: new Abstract: Multivariate time series forecasting requires capturing the continuously evolving correlation structure among interacting variables.
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:2603. 12676v3 Announce Type: replace Abstract: Generalizing neural surrogate models across different PDE parameters remains difficult because changes in PDE coefficients often make learning harder and optimization less stable.
arXiv:2603. 02220v2 Announce Type: replace-cross Abstract: Time series forecasting remains a challenging problem due to the intricate entanglement of intra-period fluctuations and inter-period trends.
arXiv:2606. 07385v1 Announce Type: cross Abstract: Detecting transient chaos from scalar observations without governing equations represents a fundamental challenge in nonlinear dynamics.
arXiv:2603.13587v2 Announce Type: replace-cross Abstract: State-space models (SSMs) are effective architectures for sequential modeling, but a rigorous theoretical understanding of their training dyn...
arXiv:2605. 27286v2 Announce Type: replace-cross Abstract: Time series foundation models (TSFMs) are transforming the forecasting paradigm through large-scale cross-domain pretraining.
arXiv:2608.29579v1 Announce Type: new Abstract: Chaotic time series forecasting is a challenging task due to its sensitivity to initial conditions and long-term unpredictability. Traditional methods...
The paper proposes a continuous‑time generative framework that models time‑dependent data as evolution on a learned data manifold. By using pretrained score‑based models as geometric priors, it learns a vector field that drives data along score‑induced interpolation paths, enabling generation at arbitrary timestamps and temporal super‑resolution. The method includes a regression‑based training objective, a stability‑promoting term interpreted as denoising score matching, and a probabilistic extension for future trajectory distributions, demonstrated on natural video, PDE‑based fields, and molecular dynamics.
WorldTS is a new forecasting framework that models latent dynamics conditioned on multimodal covariates to improve time‑series prediction. It uses a two‑stage training process: first learning latent state dynamics from historical data and covariates, then training a decoder to map predicted latent states back to future observations. Experiments on 21 real‑world datasets demonstrate the effectiveness of this approach.
CoRe is a model‑agnostic learning objective for direct multivariate time‑series forecasting that replaces pointwise errors with two output‑space constraints: a frequency coherence loss aligning predicted and target spectra, and a low‑rank relational graph loss matching pairwise differences in a PCA subspace. The objective introduces no trainable parameters and can be applied to existing forecasting backbones by changing only the loss. Experiments on standard benchmarks show that CoRe improves strong baselines, compares favorably with recent forecasting objectives, and remains effective across different backbones, datasets, and hyperparameter settings.
arXiv:2606. 30461v1 Announce Type: new Abstract: State space models (SSMs) have emerged as efficient linear-time alternatives to attention for long-sequence modeling.
The paper introduces a Nested Inductive Bias framework that uses a two‑stage diffeomorphic composition to pull back non‑Euclidean target geometries onto symmetric positive definite (SPD) manifolds. This approach allows the construction of curvature‑aligned Riemannian classifiers that respect both matrix constraints and the intrinsic relational geometry of data. Empirical results on kinematic, signal processing, and synthetic benchmarks show that class separability degrades when metric curvature does not match the data distribution, and the authors also propose the Rational Conformal Metric (RCM) for robust vectorized architectures.