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This paper introduces low-cost High-Order Singular Value Decomposition (lcHOSVD), a tensor-based method for reconstructing high-dimensional environmental fields from sparse sensor measurements. Applied to urban flow and air-quality datasets, it achieves lower reconstruction errors and greater robustness to uneven sensor distributions compared to matrix-based approaches.
This paper introduces Separable Neural Architecture (SNA), a function class that combines neural approximation with tensor decomposition to efficiently solve parametric PDEs. The method achieves dramatic speedups (up to 150,000×) over traditional grid-based methods in engineering applications like laser powder bed fusion and material property prediction.
This paper introduces a distributional generalization of matrix completion where each entry is a probability distribution rather than a scalar, using kernel mean embeddings and Tucker rank to capture low-rank structure. The authors propose a novel estimator with non-asymptotic error bounds and demonstrate effectiveness on synthetic and real-world data.
This paper presents an online framework for modeling streaming time series as dynamic mixtures of time-delay systems, addressing regime shifts and memory constraints via a summary system tensor and tensor decomposition.