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Panqi Chen

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NeurIPS Conference 2025 Conference Paper

Functional Complexity-adaptive Temporal Tensor Decomposition

Panqi Chen
Lei Cheng
Jianlong Li
Weichang Li
Weiqing Liu
Jiang Bian
Shikai Fang

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. Moreover, the challenge of self-adapting model complexity is largely unexplored in functional temporal tensor models, with existing methods being inapplicable in this setting. To address these limitations, we propose functional Complexity-Adaptive Temporal Tensor dEcomposition (Catte). 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 enable automatic adaptation of model complexity, we introduce a sparsity-inducing 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 Catte not only reveals the underlying ranks of functional temporal tensors but also significantly outperforms existing methods in prediction performance and robustness against noise.

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NeurIPS Conference 2025 Conference Paper

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

Panqi Chen
Yifan Sun
Lei Cheng
Yang Yang
Weichang Li
Yang Liu
Weiqing Liu
Jiang Bian

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 sparse 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.

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