Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observations

Modeling and reconstructing multidimensional physical dynamics from sparse and off-grid observations presents a fundamental challenge in scientific research. Recently, diffusion-based generative modeling shows promising potential for physical simulation. However, current approaches typically operate on on-grid data with preset spatiotemporal resolution, but struggle with the sparsely observed and continuous nature of real-world physical dynamics. To fill the gaps, we present SDIFT, Sequential DIffusion in Functional Tucker space, a novel framework that generates full-field evolution of physical dynamics from irregular sparse observations. SDIFT leverages the functional Tucker model as the latent space representer with proven universal approximation property, and represents observations as latent functions and Tucker core sequences. We then construct a sequential diffusion model with temporally augmented UNet in the functional Tucker space, denoising noise drawn from a Gaussian process to generate the sequence of core tensors. At the posterior sampling stage, we propose a Message-Passing Posterior Sampling mechanism, enabling conditional generation of the entire sequence guided by observations at limited time steps. We validate SDIFT on three physical systems spanning astronomical (supernova explosions, light-year scale), environmental (ocean sound speed fields, kilometer scale), and molecular (organic liquid, millimeter scale) domains, demonstrating significant improvements in both reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.

Generalized Temporal Tensor Decomposition with Rank-revealing Latent-ODE

Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by incorporating continuous timestamps in latent factors, they still struggle with general tensor data with continuous indexes not only in the temporal mode but also in other modes, such as spatial coordinates in climate data. Additionally, the problem of determining the tensor rank remains largely unexplored in temporal tensor models. To address these limitations, we propose \underline{G}eneralized temporal tensor decomposition with \underline{R}ank-r\underline{E}vealing laten\underline{T}-ODE (GRET). Our approach encodes continuous spatial indexes as learnable Fourier features and employs neural ODEs in latent space to learn the temporal trajectories of factors. To automatically reveal the rank of temporal tensors, we introduce a rank-revealing Gaussian-Gamma prior over the factor trajectories. We develop an efficient variational inference scheme with an analytical evidence lower bound, enabling sampling-free optimization. Through extensive experiments on both synthetic and real-world datasets, we demonstrate that GRET not only reveals the underlying ranks of temporal tensors but also significantly outperforms existing methods in prediction performance and robustness against noise.

Estimating Channels With Hundreds of Sub-Paths for MU-MIMO Uplink: A Structured High-Rank Tensor Approach

This letter introduces a structured high-rank tensor approach for estimating sub-6G uplink channels in multi-user multiple-input and multiple-output (MU-MIMO) systems. To tackle the difficulty of channel estimation in sub-6G bands with hundreds of sub-paths, our approach fully exploits the physical structure of channel and establishes the link between sub-6G channel model and a high-rank four-dimensional (4D) tensor Canonical Polyadic Decomposition (CPD) with three factor matrices being Vandermonde-constrained. Accordingly, a stronger uniqueness property is derived in this work. This model supports an efficient one-pass algorithm for estimating sub-path parameters, which ensures plug-in compatibility with the widely-used baseline. Our method performs much better than the state-of-the-art tensor-based techniques on the simulations adhering to the 3GPP 5G protocols.