SPARDA: Sparsity-constrained dimensional analysis via convex relaxation for parameter reduction in high-dimensional engineering systems

Abstract

Effective analysis of high-dimensional systems with intricate variable interactions is crucial for accurate modeling and engineering applications. Previous methods using sparsity techniques or dimensional analysis separately often face limitations when handling complex, large-scale systems. This study introduces a sparsity-constrained dimensional analysis framework that integrates the classical Buckingham Pi theorem with sparse optimization techniques, enabling precise nondimensionalization. The framework, formulated as a convex optimization problem, addresses computational challenges associated with sparsity in high-dimensional spaces. Rigorously tested across various datasets, including the Fanning friction factor for rough pipe flow, an international standards-based dataset of physical quantities and units, and experimental data from flow boiling studies, this method successfully identified critical dimensionless groups that encapsulate core system dynamics. This approach not only offers a more compact and interpretable representation than conventional methods but also retains more characteristics of function variability. It proves particularly effective in systems governed by high-dimensional interactions, demonstrating a lower failure rate and mean relative error compared to an algorithm for comparison. The methodology is applicable to the modeling and analysis of complex engineering physical systems such as nuclear power, wind tunnel design, and marine engineering, as well as in designing scaled verification experiments.