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.
By Adnan Harun Dogan, Berken Utku Demirel, Christian Holz
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.
By Naichang Ke, Pongpisit Thanasutives, Yoshinobu Kawahara
arXiv:2606. 05131v1 Announce Type: new Abstract: Koopman theory turns nonlinear dynamics into a linear spectral problem.
By Kelan Gray, Finlay Brown, Nicolas Boull\'e, Matthew J. Colbrook
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.
By Junyi Liao, Johann Guilleminot, Vahid Tarokh
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.
By Thibaut Germain, Sami Chemlal, R\'emi Flamary, Vladimir R. Kostic, Karim Lounici