液压网络不可压缩流动的数据驱动计算框架
A Data-Driven Computational Framework for Incompressible Flow in Hydraulic Networks
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中文总结 AI 辅助
本文提出一种绕过本构模型的数据驱动液压网络不可压缩流动计算框架，评估三种算法，验证了确定性退火法的优势及框架在复杂网络上的可扩展性与实用性。
中文摘要 AI 辅助
求解液压网络的经典方法依赖于本构方程假设，该假设描述了沿边的压力梯度与通量之间的关系。本文提出一种数据驱动框架，绕过这些本构模型，直接在图拓扑上构建不可压缩流动问题。通过将离散测量数据点分配给网络边，该问题被转化为关于节点压力、边状态和数据分配的混合整数二次优化问题，可同时适应层流（凸）和湍流（非凸）状态。为求解该问题，评估了三种算法：GPU加速的蛮力法、交替方向法（ADM）和确定性退火法（DA）。蛮力法可为小型网络验证全局最优解，为迭代求解器建立良好基准。研究表明，ADM对其初始化高度敏感，需要忠实的替代模型以避免局部最小值；相比之下，DA通过无监督聚类消除了这种依赖性，通过将数据分配从质心退火到严格的最近邻投影，无需先验流形重构即可始终达到全局最优。此外，数值实验显示，DA对噪声数据具有鲁棒性，除最粗糙和噪声最大的数据集外，在所有数据集上均保持热力学可容性，且在蛮力法难以处理、ADM性能下降的更大网络上仍保持收敛速率。最后，该框架在复杂配置上得到成功验证，包括混合组件网络和具有非牛顿Carreau-Yasuda模型的958边动静脉床，证明了其可扩展性和实际适用性。
英文摘要
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.
