arXiv:2606. 14079v1 Announce Type: new Abstract: We propose a spectral learning method for stochastic nonlinear dynamical systems represented with embedded latent transfer operators in deep feature spaces.
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. 02251v1 Announce Type: cross Abstract: Robust state estimation is central to robotic autonomy, yet classical Kalman filters struggle with frequency-dependent disturbances and model mismatch such as sensor vibrations, electromagnetic interference, and periodic noise.
arXiv:2606. 14195v1 Announce Type: new Abstract: Kalman filters based on the Embedded Latent Transfer Operators (ELTO) emerge as novel statistical tools for sequential state estimation.
arXiv:2606. 05131v1 Announce Type: new Abstract: Koopman theory turns nonlinear dynamics into a linear spectral problem.
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.
The paper introduces DOODL, a framework that learns a dictionary of spectral dynamics to represent related dynamical systems as points on a low‑dimensional manifold in operator space. By constraining operator estimation to this learned manifold, DOODL provides compact, interpretable embeddings and enables fast, accurate operator estimation from short, partially observed trajectories. Experiments on metastable Langevin dynamics and turbulent plasma simulations show that DOODL achieves one to two orders of magnitude lower errors than independent estimation methods, especially in low‑data regimes.
The paper introduces AURA, a meta‑learning framework that learns a low‑dimensional latent state‑space model for the evolution of optimal model parameters under distribution shift. Online adaptation is performed via extended Kalman filtering in this latent space, followed by reconstruction of full model parameters through a learned lifting map, enabling efficient single‑step updates. Experiments on neural wireless receivers and non‑stationary image classification show that AURA improves adaptation speed, accuracy, and computational efficiency compared to existing online learning and Bayesian filtering baselines.
arXiv:2606. 12691v1 Announce Type: cross Abstract: Auto-regressive models have emerged as powerful tools for sequential data, from language to video.
arXiv:2608. 05416v1 Announce Type: new Abstract: Can nonlinear dynamical systems be learned through a compact linear state-space representation, without directly solving a non-convex system-identification problem?
arXiv:2607. 23337v1 Announce Type: new Abstract: Neural operators provide data-driven mappings for modeling dynamical systems.
Neural operators learn mappings between function spaces, but are typically developed with dense input-output training fields and fully observed inputs at inference. Many scientific problems require instead predicting solution fields from sparse, irregular, or partial observations under uncertainty.
arXiv:2607. 17990v1 Announce Type: new Abstract: Highly nonlinear chaotic dynamical systems remain difficult to model due to fundamental trade-offs between complexity, expressivity, and data efficiency.