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arXiv · 2512.14416

Reducing Training Complexity in Empirical Quadrature-Based Model Reduction via Structured Compression

Björn Liljegren-Sailer
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Abstract

Model order reduction seeks to approximate large-scale dynamical systems by lower-dimensional reduced models. For linear systems, a small reduced dimension directly translates into low computational cost, ensuring online efficiency. This property does not generally hold for nonlinear systems, where an additional approximation of nonlinear terms --known as complexity reduction-- is required. To achieve online efficiency, empirical quadrature and cell-based empirical cubature are among the most effective complexity reduction techniques. However, the offline training of these methods operates on a matrix whose dimension scales with both the snapshot count and the reduced model dimension, and can become a computational bottleneck at larger scale. Existing strategies such as parallelization and randomized linear algebra reduce the cost of processing this matrix but do not reduce its dimension. In this paper, we introduce a preprocessing approach based on a specific structured compression of the training data. Crucially, our approach ensures that no operation scales concurrently with the snapshot count, the reduced model dimension, and the problem dimension. Overall, this yields roughly an order-of-magnitude reduction in offline computational cost and memory requirements, thereby enabling the application of the complexity reduction methods to larger-scale problems. Accuracy is preserved, as indicated by our error analysis and demonstrated through numerical examples.

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BibTeXRIS

Björn Liljegren-Sailer. 2026-09-16. Reducing Training Complexity in Empirical Quadrature-Based Model Reduction via Structured Compression. https://arxiv.org/abs/2512.14416

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