Network Flow Model Research Articles

Key Structural Features of Microvascular Networks Leading to the Formation of Multiple Equilibria

We analyse mathematical models of blood flow in two simple vascular networks in order to identify structural features that lead to the formation of multiple equilibria. Our models are based on existing rules for blood rheology and haematocrit splitting. By performing bifurcation analysis on these simple network flow models, we identify a link between the changing flow direction in key vessels and the existence of multiple equilibria. We refer to these key vessels as redundant vessels, and relate the maximum number of equilibria with the number of redundant vessels. We vary geometric parameters of the two networks, such as vessel length ratios and vessel diameters, to demonstrate that equilibria are uniquely defined by the flow in the redundant vessels. Equilibria typically emerge in sets of three, each having a different flow characteristic in one of the network’s redundant vessels. For one of the three equilibria, the flow within the relevant redundant vessel will be smaller in magnitude than the other two and the redundant vessel will contain few Red Blood Cells (RBCs), if any. For the other two equilibria, the redundant vessel contains RBCs and significant flow in the two available directions. These structural features of networks provide a useful geometric property when studying the equilibria of blood flow in microvascular networks.

Stokes flows in a two-dimensional bifurcation.

The flow network model is an established approach to approximate pressure-flow relationships in a bifurcating network, and has been widely used in many contexts. Existing models typically assume unidirectional flow and exploit Poiseuille's law, and thus neglect the impact of bifurcation geometry and finite-sized objects on the flow. We determine the impact of bifurcation geometry and objects by computing Stokes flows in a two-dimensional (2D) bifurcation using the Lightning-AAA Rational Stokes algorithm, a novel mesh-free algorithm for solving 2D Stokes flow problems utilizing an applied complex analysis approach based on rational approximation of the Goursat functions. We compute the flow conductances of bifurcations with different channel widths, bifurcation angles, curved boundary geometries and fixed circular objects. We quantify the difference between the computed conductances and their Poiseuille law approximations to demonstrate the importance of incorporating detailed bifurcation geometry into existing flow network models. We parametrize the flow conductances of 2D bifurcation as functions of the dimensionless parameters of bifurcation geometry and a fixed object using a machine learning approach, which is simple to use and provides more accurate approximations than Poiseuille's law. Finally, the details of the 2D Stokes flows in bifurcations are presented.

Air Corridor Planning for Urban Drone Delivery: Complexity Analysis and Comparison via Multi-Commodity Network Flow and Graph Search

Urban drone delivery, a rapidly evolving sector, holds the potential to enhance accessibility, address last-mile delivery issues, and alleviate ground traffic congestion in cities. Effective Unmanned Aircraft System Traffic Management (UTM) is essential to scale drone delivery. A critical aspect of UTM involves planning a city-wide network with spatially-separated air corridors (air routes). Most existing works have focused on routing problems or air traffic management. Compared to these problems, the air corridor planning problem requires much higher spatial and temporal resolutions and presents computational challenges due to the scale, complexity, and density of urban airspace, along with the coupling issues of multi-path planning. Therefore, we conducted this research to understand the complexity and computational resources required to optimally solve the air corridor planning problem. In this paper, we use a minimum-cost Multi-Commodity Network Flow (MCNF) model, a mathematical model, to model the problem and demonstrate the complexity of air corridor planning through the complexity of MCNF. We then apply Gurobi’s and GLPK’s integer programming (IP) solvers to find optimal solutions. Additionally, we present two existing multi-path graph search algorithms, the Sequential Route Network Planning (SRP) algorithm and the Distributed Route Network Planning (DRP) algorithm, to address this corridor planning problem. Numerical experiments conducted at various scales and settings using IP solvers and graph search algorithms indicate that finding an optimal solution requires significant computational resources and yields only a slight improvement in optimality compared to graph search algorithms. Thus, air corridor planning is complex both theoretically and numerically, and graph search algorithms can provide a feasible solution with good enough optimality for corridor planning in real-world scenarios. Moreover, the multi-path graph search algorithms can easily incorporate side constraints that are known to be impossible to solve with polynomial algorithms, making it more practical for real-world applications. Finally, we demonstrate the application of SRP and DRP in real-world 3D urban scenarios.

Optimizing Water Level Regulation in the Great Lakes: An Integrated Approach Using Genetic Algorithms and Network Flow Models for Sustainable Resource Management

The Great Lakes, as a vital freshwater resource, are significantly influenced by climate change and anthropogenic activities, leading to acute water level fluctuations with profound impacts on various sectors including agriculture, industry, and ecology. This study addresses the need for scientifically sound water level regulation by developing an integrated approach that employs a genetic algorithm and a network flow model. The model is designed to balance the interests of multiple stakeholders and optimize water levels across different periods, thereby ensuring the sustainable use of water resources and ecological balance. Through comprehensive data collection and processing, the study constructs a robust prediction model that accounts for economic activities and ecological protection. The application of genetic algorithms enhances the efficiency and accuracy of the model, providing a practical tool for decision-makers in water resource management. The findings underscore the model's reliability and its potential to support policy-making for sustainable water resource management in the Great Lakes region.

Ride-pooling Electric Autonomous Mobility-on-Demand: Joint optimization of operations and fleet and infrastructure design

This paper presents a modeling and design optimization framework for an Electric Autonomous Mobility-on-Demand system that allows for ride-pooling, i.e., multiple users can be transported at the same time towards a similar direction to decrease vehicle hours traveled by the fleet at the cost of additional waiting time and delays caused by detours. In particular, we first devise a multi-layer time-invariant network flow model that jointly captures the position and state of charge of the vehicles. Second, we frame the time-optimal operational problem of the fleet, including charging and ride-pooling decisions as a mixed-integer linear program, whereby we jointly optimize the placement of the charging infrastructure. Finally, we perform a case-study using Manhattan taxi-data. Our results indicate that jointly optimizing the charging infrastructure placement allows to decrease overall energy consumption of the fleet and vehicle hours traveled by approximately 1% compared to a heuristic placement. Most significantly, ride-pooling can decrease such costs considerably more, and up to 45%. Finally, we investigate the impact of the vehicle choice on the energy consumption of the fleet, comparing a lightweight two-seater with a heavier four-seater, whereby our results show that the former and latter designs are most convenient for low- and high-demand areas, respectively.

Code and Data Repository for A New Multicommodity Network Flow Model and Branch and Cut for Optimal Quantum Boolean Circuit Synthesis

This directory contains the entire set of result files that are reported in our paper.

A New Multicommodity Network Flow Model and Branch and Cut for Optimal Quantum Boolean Circuit Synthesis

This study introduces a new optimization model and a branch-and-cut approach for synthesizing optimal quantum circuits for reversible Boolean functions, which are pivotal components in quantum algorithms. Although heuristic algorithms have been extensively explored for quantum circuit synthesis, research on exact counterparts remains relatively limited. However, the need to design quantum circuits with guaranteed optimality is increasing, especially for improving computational fidelity on noisy intermediate-scale quantum devices. This study presents mathematical optimization as a viable option for optimal synthesis, with the potential to accommodate practical considerations arising in fast-evolving quantum technologies. We set a demonstrative problem to implement reversible Boolean functions using high-level gates known as multiple control Toffoli gates while minimizing a technology-based proxy called quantum cost—the number of low-level gates used to realize each high-level gate. To address this problem, we propose a discrete optimization model based on a multicommodity network and discuss potential future variations at an abstract level to incorporate technical considerations. A customized branch and cut is then developed upon different aspects of our model, including polyhedron integrality, surrogate constraints, and variable prioritization. Our experiments demonstrate the robustness of the proposed approach in finding cost-optimal circuits for all benchmark instances within a two-hour time frame. Furthermore, we present interesting intuitions from these experiments and compare our computational results with relevant studies, highlighting newly discovered circuits with the lowest quantum costs reported in this paper. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Quantum Computing. Funding: This research was supported by the Ministry of Science and Information and Communication Technology, South Korea [Grants 2017R1E1A1A0307098814 and 2020R1A4A307986411]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0562 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0562 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Junction conditions for one-dimensional network hemodynamic model for total cavopulmonary connection using physically informed deep learning technique

Abstract This paper presents a novel methodology utilizing physics-informed neural network (PINN) as a junction condition for a 1D network model of blood flow in total cavopulmonary connection generated by the Fontan procedure. The technique integrates a 3D mesh generation process based on the parameterization of the junction geometry, along with a sophisticated physically regularized neural network architecture. Synthetic datasets are produced using 3D steady Stokes simulations within fixed boundaries. We use a physically informed feedforward neural network that utilizes a physically regularized loss function, which incorporates the principle of mass conservation. Our PINN achieves a tolerance of 6% on the test set. We develop a 1D-PINN multiscale model based on a previously developed method for multiscale 1D–3D simulations. Comparison with 1D–3D Stokes based model and 3D Navier–Stokes based model verifies the 1D-PINN model. In the first and second comparison, the maximum deviations of the averaged pressures and flows do not exceed 1.48% and 12.26%, respectively.

A Microscopic On-Ramp Model Based on Macroscopic Network Flows

While macroscopic traffic flow models adopt a fluid dynamic description of traffic, microscopic traffic flow models describe the dynamics of individual vehicles. Capturing macroscopic traffic phenomena accurately remains a challenge for microscopic models, especially in complex road sections. Based on a macroscopic network flow model calibrated to real traffic data and new rules for the acceleration and merging behavior on the on-ramp, we propose a microscopic model for on-ramps. To evaluate the performance of the new flow-based model, we conduct traffic simulations assessing speeds, accelerations, lane change positions, and risky behavior. Our results show that, although the proposed model exhibits some limitations, its performance is superior to the Intelligent Driver Model in the evaluated aspects. While the Intelligent Driver Model simulations are almost free of conflicts, the proposed model evokes a realistic amount and severity of conflicts and therefore can be considered for safety analysis.

A qualitative analysis of the artificial neural network model and numerical solution for the nanofluid flow through an exponentially stretched surface

This article aims to analyze the two-dimensional (2D) nanofluid (Ag/C2H6O2) flow past an exponentially stretched sheet. The magnetic field impact, heat source/sink, and convection in the thermal profile are taken into account. The complexity of the problem is reduced by introducing a dimensionless group of functions. The reduced model is transformed into a system of first-order ordinary differential equations (ODEs). This system is further analyzed with the artificial neural network (ANN), which is trained using the Levenberg–Marquardt algorithm. The whole dataset is sub divided into three parts: training (70%), validation (15%), and testing (15%). The impact of nonlinear heat source/sink parameter, magnetic parameter, volume fraction of nanoparticles, and Prandtl number is displayed through graphs. The heat source, volume fraction, and the Prandtl number cause an increase in the thermal profile with its larger values. The magnetic parameter causes a decline in both the thermal and momentum boundary layers with its higher values. The analysis shows that the thermal energy profile is enhanced with the larger values of the volume fraction of silver nanoparticles and heat source. For each case study, the residual error (RE), regression line, and validation of the results are presented. The performance of the proposed methodology is numerically tabulated for the nanoparticle volume fraction shown in Table 3, where the minimum absolute error (AE) is 5.3373e−11 at ϕ=0.05. Based on this, we recommend ϕ=0.05 for better performance. The AEs for the ANN and bvp4c are computed for the state variables in Tables for the magnetic parameter M=5,10, and 15. These tables show the overall performance of the ANN and further validate the present study. We have also validated the results of the ANN through the mean squared error graphically, where the accuracy of the proposed methodology is proven.

Methodology to Characterize Row Manifolds for High Power Direct to Chip Liquid Cooling Data Centers

Abstract Demand is growing for the dense and high-performing IT computing capacity to support artificial intelligence, deep learning, machine learning, autonomous cars, the Internet of things, etc. This led to an unprecedented growth in transistor density for high-end CPUs and GPUs, creating thermal design power (TDP) of even more than 700 watts for some of the NVIDIA existing GPUs. Cooling these high TDP chips with air cooling comes with a cost of the higher form factor of servers and noise produced by server fans close to the permissible limit. Direct-to-chip cold plate-based liquid cooling is highly efficient and becoming more reliable as the advancement in technology is taking place. Several components are used in the liquid-cooled data centers for the deployment of cold plate based direct to chip liquid cooling like cooling loops, rack manifolds, CDUs, row manifolds, quick disconnects, flow control valves, etc. Row manifolds used in liquid cooling are used to distribute secondary coolant to the rack manifolds. Characterizing these row manifolds to understand the pressure drops and flow distribution for better data center design and energy efficiency is important. In this paper, the methodology is developed to characterize the row manifolds. Water-based coolant Propylene glycol 25% was used as the coolant for the experiments and experiments were conducted at 21 °C coolant supply temperature. Two, six-port row manifolds' P-Q curves were generated, and the value of supply pressure and the flow rate were measured at each port. The results obtained from the experiments were validated by a technique called Flow Network Modeling (FNM). FNM technique uses the overall flow and thermal characteristics to represent the behavior of individual components.

Shear-induced permeability evolution of natural fractures in granite: Implications for stimulation of EGS reservoirs

Permeability evolution of natural fractures during shearing is one of the critical issues in enhanced geothermal system (EGS). In this study, we conducted a series of numerical simulations of shear-flow tests under different normal stresses to investigate the permeability evolution and shear behavior of natural fractures during shearing. All numerical simulations in this study are executed based on a coupled hydro-mechanical pore network model (PNM) for fluid flow within the discrete element method (DEM). The numerical model uses a 33 mm × 25 mm fracture surface profile extracted from X-ray computed tomography scanning data of joints in a rock core retrieved from a 4.2-km-deep well at the Pohang EGS site. The results demonstrate a positive correlation between fracture permeability and shear displacement when the normal stress is relatively high. The central aspect of permeability evolution lies in the variation of local aperture distribution along the pathway: an increase in the variance of fracture aperture distribution leads to an increase in fracture permeability. Permeability evolution of fractures is significantly affected by normal stress, fracture roughness, and relative flow direction. Larger fracture roughness facilitates the formation of high-permeability pathways. Higher local normal stress often corresponds to lower local permeability. Moreover, high normal stress amplifies the effect of fracture roughness on permeability evolution. These findings enhance our comprehensive understanding of hydraulic-mechanical coupling effects during EGS stimulation.

Linear optimal power flow model for modern distribution systems: Management of normally closed loop grids and on-load tap changers

Modern distribution systems face new challenges due to the rise of small-scale renewable energy resources and the electrification of energy demand. Additionally, the complexity of network management increases with the exchange of flexibility services between distribution and higher voltage levels. The system operator's role involves optimizing the planning and operation of the distribution network. In current scenarios, this includes managing flexibility resources (such as generators, demand response, and on-load tap changers) and implementing new operating strategies (such as closed-loop topologies and dynamic reconfiguration). This paper proposes a reformulation of one of the most used linear approximations of the Optimal Power Flow model for distribution networks. The novelty of this reformulation lies in integrating equations to handle tap-changing transformers with closed-loop/meshed network operation, while preserving the original linear formulation and computational tractability.

Floria: fast and accurate strain haplotyping in metagenomes.

Shotgun metagenomics allows for direct analysis of microbial community genetics, but scalable computational methods for the recovery of bacterial strain genomes from microbiomes remains a key challenge. We introduce Floria, a novel method designed for rapid and accurate recovery of strain haplotypes from short and long-read metagenome sequencing data, based on minimum error correction (MEC) read clustering and a strain-preserving network flow model. Floria can function as a standalone haplotyping method, outputting alleles and reads that co-occur on the same strain, as well as an end-to-end read-to-assembly pipeline (Floria-PL) for strain-level assembly. Benchmarking evaluations on synthetic metagenomes show that Floria is > 3× faster and recovers 21% more strain content than base-level assembly methods (Strainberry) while being over an order of magnitude faster when only phasing is required. Applying Floria to a set of 109 deeply sequenced nanopore metagenomes took <20 min on average per sample and identified several species that have consistent strain heterogeneity. Applying Floria's short-read haplotyping to a longitudinal gut metagenomics dataset revealed a dynamic multi-strain Anaerostipes hadrus community with frequent strain loss and emergence events over 636 days. With Floria, accurate haplotyping of metagenomic datasets takes mere minutes on standard workstations, paving the way for extensive strain-level metagenomic analyses. Floria is available at https://github.com/bluenote-1577/floria, and the Floria-PL pipeline is available at https://github.com/jsgounot/Floria_analysis_workflow along with code for reproducing the benchmarks.

A dual-porosity flow-net model for simulating water-flooding in low-permeability fractured reservoirs

The physics-based data-driven flow-network models with high computational efficiency have received great attention as the promising surrogate models for reservoir numerical simulation. However, the existing flow-network models developed for water-flooding reservoirs fail to consider different seepage characteristics of matrix and fractures and cannot be straightly applied to simulate the water-flooding process in low-permeability fractured reservoirs. In this study, we combine the flow-network model with the dual-porosity model to propose a new physics-based data-driven surrogate model, namely the Dual-Porosity Flow-Network Model (Flow-Net-DP), which can consider the non-Darcy flow in tight matrix and the stress-sensitive effects and preferential flow characteristic in fractures. Specifically, we refer to the dual-porosity model and use two channels to represent the connections between wells: one indicates the fracture system, the other represents the matrix system, and the fluid exchange between these two systems is considered by using a transfer function. Besides, each channel is discretized into one-dimensional grids, and a fully implicit scheme with Newton iteration is used to calculate pressure and saturation. Moreover, we establish an automated history matching method by using the Ensemble Smoother with Multiple Data Assimilation (ESMDA) algorithm to calibrate model parameters of Flow-Net-DP, and develop a production optimization method by using the Differential Evolution (DE) algorithm. Finally, the numerical simulation, history matching, and production optimization are conducted on different numerical examples to validate the capability of Flow-Net-DP. The results indicate that the Flow-Net-DP can provide a better description of water flooding process in low-permeability fractured reservoirs compared with the existing flow-network model, especially the rapid water breakthrough caused by the preferential flow characteristic in fractures. Furthermore, both history matching and production optimization based on the Flow-Net-DP yield satisfactory outcomes. For instance, when the optimization results are similar to the full-order simulation model, the optimization speed of Flow-Net-DP is increased by more than five times.

Data-driven analysis of optimal repositioning policy in bike sharing systems

In this study, we analyze the impact of optimal repositioning policy on the efficiency of bike sharing systems under several performance measures. We first develop a multi-period network flow model to find the optimal repositioning decisions which consist of the origin, destination, and the time of the repositioning that maximize the total profit of a sharing system. We further extend this model to consider demand uncertainty under a stochastic setting. The proposed model is then implemented on the real-world bike-sharing data of New York City, Toronto, and Vancouver. After finding the optimal repositioning policies, we analyze the effect of repositioning on the profit, fulfilled demand, number of required vehicles, and utilization rates of the vehicles. Through computational experiments, we show that repositioning significantly increases the efficiency of a sharing system under these performance measures. In particular, our analyses show that 32% more profit can be obtained and up to 41% more demand can be satisfied with repositioning. Moreover, it is possible to reduce the required fleet size by up to 61% and increase the average utilization rate of the vehicles by up to 21% by employing repositioning.

Influence of inertial and centrifugal forces on rate and flow patterns in natural fracture networks

Fluid production from fractured rock masses readily induces fracture flow velocities of meters per second. Yet, most discrete fracture flow models treat flow as laminar creeping flow or account for inertia effects only by single-fracture constitutive relationships.This numeric simulation study investigates water flow patterns and spatial velocity variations in a natural fracture network with mm-wide open fractures, studying the transition from laminar creeping to turbulent flow. After verification with a fracture intersection model, a Reynolds-time-averaged Navier Stokes solver serves to analyse flow regimes and velocity distribution. Our results show that for fracture flow velocities greater than ∼1-cm/s, fluid inertia begins to markedly alter flow patterns and the overall velocity distribution in the network. The pressure-gradient-flow relationship therefore becomes non-linear long before the flow in straight fractures enters the weak inertia regime. This prominence of inertia effects highlights the need to improve fracture network flow models.

An optimization framework for efficient and sustainable logistics operations via transportation mode optimization and shipment consolidation: A case study for GE Gas Power

General Electric (GE) Gas Power, a leading manufacturer of gas and steam turbines, manufactures and installs these turbines in power generation plants worldwide. They source components for these turbines from suppliers globally and transport these components to manufacturing and assembly locations in the United States using various modes of transportation, including ocean, air, and ground. These transportation options have different lead times and costs. The challenge lies in identifying the most cost-effective solution that meets the assembly requirements, given the high volume of shipments and the complexity of the intermodal freight network. To address this challenge, a customized, multi-period (dynamic), multi-commodity network flow model and a novel heuristic approach with a rolling time horizon are developed. This model incorporates consolidation and storage options at intermediate nodes, allowing the business to optimize its shipments. This research addresses a unique real-world logistics problem and offers an optimization model together with an efficient solution approach for industry. Computational experiments indicate that the heuristic approach proposed can yield results closely aligned with those produced by state-of-the art commercial solvers. Furthermore, the experiments show the criticality of full container load shipments in achieving substantial cost-saving in global shipments.

Network analysis of comorbid aggressive behavior and testosterone among bipolar disorder patients: a cross-sectional study

Testosterone has complex effects on psychological traits and behavior; it is associated with social dominance and competition and is a potential human sex pheromone. This study aimed to investigate the associations between testosterone levels, aggressive behavior, and manic symptoms using a network analysis among bipolar disorder (BD) patients in psychiatric emergency departments (PED). Data from January 2021 and March 2022 BD patients in PED were analyzed. Manic symptoms were assessed using the Young Mania Rating Scale (YMRS). Aggression was assessed with subscale of the PANSS scale (PANSS-AG). The undirected network structures of testosterone levels, aggressive behavior, and manic symptoms were estimated, and centrality and bridge centrality indices were examined. Network stability was examined using the case-dropping procedure. The Network Comparison Test (NCT) was conducted to evaluate whether network characteristics differed by gender. We recruited a total of 898 BD patients, with the mean YMRS score as 13.30 ± 9.58. The prevalence of level II aggression was 35.6% (95%CI = 32.5%–38.7%), level III aggression was 29.5% (95%CI = 26.3%–32.6%), and level VI aggression was 7.0% (95%CI = 5.4%–8.8%). The male participants had a mean testosterone level of 391.71 (Standard Deviation (SD):223.39) compared to 36.90 (SD:30.50) for female participants in the whole sample. Through network analysis, “Increased motor activity-energy” emerged as the central symptom, with the highest centrality expected influence, followed by “Emotional Instability” and “Disruptive/aggression behavior”. Notably, “Emotional Instability” appeared to be the bridge symptom linking manic symptoms to aggressive behavior. Within the flow network model, “Speech rate and amount” exhibited the strongest positive correlation with testosterone levels, followed closely by “Disruptive/aggression behavior”. The constructed network model demonstrated robust stability, with gender showing no significant impact on the structure. In this study, “Increased motor activity-energy” stood out as the most influential symptom, and “Speech rate and amount” acted as the main bridge symptom linking testosterone levels, aggressive behavior, and manic symptoms. Targeting the central and bridge symptoms may improve the outcomes of aggression interventions implemented among BD patients in psychiatric emergency care.

The single picker routing problem with scattered storage: modeling and evaluation of routing and storage policies

Despite ongoing automation efforts, most warehouses are still manually operated using a person-to-parts collection strategy. This process of collecting items of customer orders from different storage locations accounts for the majority of the operating costs of the warehouse. Hence, optimizing picker routes is an important instrument to reduce labor costs. We examine the scattered-storage variant of the single picker routing problem in a one-block parallel-aisle warehouse. With scattered storage, an article can be stored at several storage locations within the warehouse, whereas with classic storage, each article has a unique storage location. We use our recently published network-flow model with covering constraints that is based on an extension of the state space of the dynamic-programming formulation by Ratliff and Rosenthal. With modifications in the state graph, this model serves for both exact and all established heuristic routing methods for picker routing. The latter include traversal, return, largest gap, midpoint, and composite. We show that these routing policies can also be implemented through adaptations in the state space. Extensive computational studies highlight a comparison of the different routing and storage policies (in particular class-based storage policies) in the scattered storage context. Analyses demonstrate which combinations of policies are advantageous for the given warehouse layout. For class-based storage policies, we emphasize how the scattering of articles of different classes should be performed: scattering of C-articles is advantageous with reductions of up to 25%. In contrast, when articles are uniformly distributed, A-articles should be scattered.