Year: 2026
Type: preprint
Abstract: The classical procedure for solving hydraulic networks relies on the assumption of constitutive equations, which state the relationship between the pressure gradient and fluxes along an edge. In this paper, we propose a data-driven framework that bypasses these constitutive models, formulating the incompressible flow problem directly on the graph topology. By assigning discrete measured data points to network edges, the problem is cast as a mixed-integer quadratic optimization over nodal pressures, edgewise states, and data assignments, accommodating both laminar (convex) and turbulent (non-convex) regimes. To solve this, we evaluate three algorithms: a GPU-accelerated Brute Force method, the Alternating Direction Method (ADM), and Deterministic Annealing (DA). The Brute Force method certifies global optima for small networks, establishing a good baseline for the iterative solvers. We demonstrate that ADM is highly sensitive to its initialization, requiring a faithful surrogate model to avoid local minima. In contrast, DA eliminates this dependence through unsupervised clustering. By annealing the data assignment from the centroid to strict nearest-neighbor projections, DA consistently reaches the global optimum without prior manifold reconstruction. Furthermore, numerical experiments reveal that DA is robust to noisy data, remains thermodynamically admissible on all but the coarsest and noisiest datasets, and sustains its convergence rate on larger networks where Brute Force is intractable and ADM degrades. Finally, the framework is successfully validated on complex configurations, including mixed-component networks and a $958$-edge arteriovenous bed featuring a non-Newtonian Carreau--Yasuda model, demonstrating its scalability and practical applicability.
Source: arXiv (Cornell University)
Subfield: Civil and Structural Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funders: Indiana Corn Marketing Council, Fundação de Amparo à Pesquisa do Estado de São Paulo, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Centro de Ciências Matemáticas Aplicadas à Indústria, Division of Mathematical Sciences
Awards: G2486662831, CeMEAI - Center for Mathematical Sciences Applied to Industry, G2762345005, Data Science for Smart Industry (CDII), G2823776494, G390121578, Finite Element Data Driven Computational approaches for Complex Materials and Microfluidics, G5388466848, G5752159476, G6191138830, G6669552033, G997809267
OpenAlex ID: W7204185037
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