arXiv:2601. 22328v2 Announce Type: replace Abstract: Real-world scientific systems are rarely observed through complete, regularly sampled state trajectories.
arXiv:2606. 00988v1 Announce Type: new Abstract: Symbolic regression (SR) offers a route to scientific discovery by converting observations into interpretable governing equations.
arXiv:2607. 06287v1 Announce Type: cross Abstract: We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator from input-output pairs and an online kernel reconstruction operator recovers the output function from predicted observations.
We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator from input-output pairs and an online kernel reconstruction operator recovers the output function from predicted observations. Our main theoretical contribution is an explicit budget allocation condition relating the number $N$ of training pairs, the number $n$ of input observations, and the output resolution $m$.
arXiv:2607. 09801v1 Announce Type: new Abstract: Governing equations provide compact descriptions of physical systems, yet the variables in which they are simple are often hidden in high-dimensional measurements.
arXiv:2607. 16251v1 Announce Type: new Abstract: Spatio-Temporal Foundation Models (STFMs) aim to learn generalizable representations of complex dynamical systems across space and time.
arXiv:2604. 24662v2 Announce Type: replace-cross Abstract: Identifying the dynamical state variables of a system from high-dimensional observations is a central problem across physical sciences.
arXiv:2606. 01894v1 Announce Type: new Abstract: Accurate Remaining Useful Life prediction is critical for industrial predictive maintenance.
arXiv:2605. 19805v2 Announce Type: replace-cross Abstract: Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift.
arXiv:2607. 23337v1 Announce Type: new Abstract: Neural operators provide data-driven mappings for modeling dynamical systems.
arXiv:2505. 07068v2 Announce Type: replace-cross Abstract: In this paper, we investigate the data-driven identification of asymmetric interaction kernels in the Motsch-Tadmor model based on observed trajectory data.
arXiv:2607. 04738v1 Announce Type: cross Abstract: Reconstructing population dynamics is a central problem in the physical and data sciences.
arXiv:2602. 04643v2 Announce Type: replace Abstract: Time-series anomaly prediction aims to forecast future system failures before they fully emerge, making latent predictive models such as JEPA a promising framework for capturing precursor dynamics.