arXiv:2608. 14120v1 Announce Type: cross Abstract: Lagrangian modeling is vital to fluid dynamics, as it characterizes particle transport and complements the Eulerian description.
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
The paper introduces the Variational Incompressible Optimal Transport (VIOT) operator, a generative neural operator that predicts divergence‑free velocity fields for incompressible density transport. VIOT combines a stream‑function representation, a regularized transport objective, and a Fourier Neural Operator backbone to amortize the solve across new source‑target pairs and grid resolutions. Experiments on 2D and 3D benchmarks show that VIOT produces full transport trajectories in seconds, achieving roughly a $10^4 imes$ speedup over per‑instance baselines that require hours of optimization.
Variational Streaming Flow (VSF) extends the efficient Streaming Flow (SF) framework by learning a latent distribution conditioned on system dynamics, enabling probabilistic forecasting in physical time. Unlike SF’s deterministic velocity field, VSF produces multiple plausible future trajectories, improving predictive accuracy and distributional fidelity across deterministic and stochastic dynamical systems. The method supports long‑horizon rollouts over 1,000 steps, handles bifurcating dynamics, and can be integrated as a plug‑and‑play predictor into Joint‑Embedding Predictive Architecture (JEPA) world models to enhance navigation, motion planning, and manipulation tasks.
arXiv:2608. 11435v1 Announce Type: new Abstract: Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration.
arXiv:2602.23188v2 Announce Type: replace Abstract: We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while...
arXiv:2505.09063v2 Announce Type: replace Abstract: Solving time-dependent parametric partial differential equations (PDEs) with high-fidelity solvers is expensive in multi-query settings. This motiv...
arXiv:2611.05735v1 Announce Type: new Abstract: Neural operators fit their representation of functions to the task they are trained on, so every new task rebuilds a reduced space from labeled data. F...
The paper presents a lightweight retraining strategy for a parameterized Reduced Order Model (ROM) that achieves full‑model accuracy using only a fraction of the computational effort and sparse observations. The ROM architecture combines a Variational Autoencoder for dimensionality reduction with a transformer network that evolves latent states while accounting for the Reynolds number as an external control variable. By leveraging the probabilistic VAE, the method generates trajectory ensembles and uncertainty estimates, and adapts to out‑of‑sample parameters through sparse data assimilation with an ensemble Kalman filter, focusing retraining on the autoencoder to correct latent manifold distortions.
arXiv:2606. 14597v1 Announce Type: new Abstract: Transformer-based neural operators have shown remarkable performance for approximating solution operators of partial differential equations on complex geometries.
arXiv:2601.21151v3 Announce Type: replace Abstract: Machine-learning approaches to weather forecasting often employ a monolithic architecture in which distinct physical mechanisms, such as advection,...
arXiv:2606. 08657v1 Announce Type: cross Abstract: Diffusion-based visuomotor policies operating directly in raw action spaces conflate scene comprehension with trajectory generation within a single denoising process.
arXiv:2608. 09764v1 Announce Type: cross Abstract: Transformer-based neural operators have achieved substantial progress in solving Partial Differential Equations (PDEs) by projecting spatial observations into compact latent tokens and learning physical interactions in latent spaces.