FreKoo++ is a continuous spectral-dynamical framework designed for Temporal Domain Generalization (TDG). It unifies continuous Koopman modal dynamics with adaptive spectral disentanglement, mapping source-domain parameters into a latent space and modeling their evolution as a superposition of learnable continuous modes. The method handles irregular timestamps, supports arbitrary horizon extrapolation, and introduces an adaptive soft spectral weighting mechanism that isolates persistent dynamics from transient noise, achieving state‑of‑the‑art performance on discrete and continuous TDG benchmarks.
arXiv:2607. 02937v1 Announce Type: new Abstract: Reduced-order models compress high-dimensional dynamics into low-dimensional representations that can be evaluated rapidly, but they lose accuracy when online dynamics drift beyond the training data.
arXiv:2606. 01894v1 Announce Type: new Abstract: Accurate Remaining Useful Life prediction is critical for industrial predictive maintenance.
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.
arXiv:2606. 04930v1 Announce Type: cross Abstract: Real-time data analysis requires the ability to accurately and adaptively address nonlinear dynamics in a nonstationary data stream while preserving computational efficiency.
arXiv:2603. 13751v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have achieved notable success in modeling dynamical systems governed by partial differential equations (PDEs).
Neural PDE solvers provide efficient surrogates for time-dependent physical systems, but autoregressive prediction over long horizons remains challenging because local errors can induce distribution s...
arXiv:2606. 06010v1 Announce Type: new Abstract: Long-term time series forecasting benefits from inductive biases that expose recurring temporal structure.
arXiv:2606. 28486v1 Announce Type: cross Abstract: The emergence of low-dimensional structures in the spectra of neural network weight matrices is a common empirical feature of trained models, but the dynamical origin of this phenomenon during learning remains an open problem.
arXiv:2605. 15690v2 Announce Type: replace Abstract: Accurate and efficient long-term multivariate time series forecasting requires capturing recurring temporal structure while keeping inference cheap across many variables and horizons.
arXiv:2608. 07924v1 Announce Type: cross Abstract: Drifting models are a recent class of one-step generative models that evolve the model distribution during training using a predefined sample-based drift field.
arXiv:2608. 11237v1 Announce Type: new Abstract: Neural operators have shown strong potential for learning solution operators of partial differential equations (PDEs).
The paper introduces a variational framework called VAMO that incorporates latent Markov dynamics for neural PDE solvers, aiming to improve long‑horizon predictions by mitigating error accumulation. By representing physical states as latent distributions and evolving them through probabilistic transitions, the method aligns learned dynamics with a spectral geometry induced by structured Gaussian perturbations. Experiments on fluid‑dynamics benchmarks show that VAMO reduces error growth and enhances rollout stability compared to deterministic and noise‑injection baselines.