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Md Taufique Hussain (Wake Forest University)5/19/26, 3:45 PMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
In the era of big data, effectively compressing large datasets while performing complex mathematical operations is crucial. Tensor-based decomposition methods have shown superior compression capabilities with minimal loss of accuracy compared to traditional matrix methods. Under the $\star_M$ tensor framework, tensors can be decomposed in a matrix-mimetic way, including using the $\star_M$...
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Fan Tian5/19/26, 4:10 PMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
Tensor decomposition is widely used for analyzing multi-way data in various applications that often involve continuously generated data. Efficient methods to process and extract meaningful patterns dynamically are hence essential for these applications. In this talk, we consider the problem of computing the streaming tensor BM-decompositions (BMD). An incremental algorithm, OnlineBMD, is...
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Vishwas Rao5/19/26, 4:35 PMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
We propose using the starM tensor product framework for constructing Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM) reduced order models. By exploiting the inherent multidimensional relationship structure of snapshot data, the approach enables efficient computation of the reduced bases. Operating directly on tensor representations reduces storage and...
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Prof. Joe Kileel (University of Texas, Austin)5/19/26, 5:00 PMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
In this talk, I will present a new method for maintaining low-rank CP decompositions of tensorial data streams. Numerical results indicate that the approach has acceptable computational costs at scale, while significantly improving accuracy and adaptivity to changes in the data stream compared to existing methods. Convergence theory will be provided, in addition to demonstrations on real...
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Dr Rick Archibald (Oak Ridge National Laboratory)5/20/26, 11:00 AMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
The exponential growth of scientific data from simulations and experiments demands efficient compression techniques for storage and processing. This talk introduces a novel streaming weak-SINDy algorithm designed for real-time compression of streaming scientific data. Leveraging the underlying structure of physical systems, the algorithm constructs memory-efficient feature matrices and target...
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Prof. Leo Rebholz (Clemson University)5/20/26, 11:25 AMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
We extend a low rank tensor ROM recently developed by Olshanskii et al by enhancing it with continuous data assimilation (CDA). We show how CDA is easily incorporated into the ROM, and analytically show that it provides for theoretical long time error estimates. Numerical tests illustrate the theory and show it is an effective tool for simulating incompressible flow over a wide range of...
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Prof. Omar Ghattas (University of Texas, Austin)5/20/26, 11:50 AMRecent Advances in Tensor Decompositions for Model and Data ReductionMinisymposium Talk
We introduce Tucker tensor train Taylor series (T4S) surrogate models for high dimensional mappings that depend implicitly on the solution of a partial differential equation. Traditionally, Taylor series are intractable here because the derivative tensors are enormous, and are only accessible through multilinear actions. We overcome these challenges by approximating each derivative tensor with...
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