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DOE OSTI2022

Scalable branching on dual decomposition of stochastic mixed-integer programming problems

In this work, we present a scalable branching method for the dual decomposition of stochastic mixed-integer programming. Our new branching method is based on the branching method proposed by Caroe and Schultz that creates branching disjunctions on first-stage variables only. We propose improvements to the process for creating branching disjunctions, including (1) branching on the optimal solutions of the Dantzig-Wolfe reformulation of the restricted master problem and (2) using a more comprehensive (yet simple) measure for the dispersions associated with subproblem solution infeasibility. We prove that the proposed branching process leads to an algorithm that terminates finitely, and we provide conditions under which globally optimal solutions can be identified after termination. We have implemented our new branching method, as well as the Caroe-Schultz method and a branch-and-price method, in the open-source software package DSP. Using SIPLIB test instances, we present extensive numerical results to demonstrate that the proposed branching method significantly reduces the number of node subproblems and solution times.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Extreme-scale EV charging infrastructure planning for last-mile delivery using high-performance parallel computing

Here, this paper addresses stochastic charger location and allocation problems under queue congestion for last-mile delivery using electric vehicles (EVs). The objective is to decide where to open charging stations and how many chargers of each type to install, subject to budgetary and waiting-time constraints. We formulate the problem as a mixed-integer non-linear program, where each station-charger pair is modeled as a multiserver queue with stochastic arrivals and service times to capture the notion of waiting in fleet operations. The model is extremely large, with billions of variables and constraints for a typical metropolitan area; even loading the model in solver memory is difficult, let alone solving it. To address this challenge, we develop a Lagrangian-based dual decomposition framework that decomposes the problem by station and leverages parallelization on high-performance computing systems, where the subproblems are solved by using a cutting plane method and their solutions are collected at the master level. We also develop a three-step rounding heuristic to transform the fractional subproblem solutions into feasible integral solutions. Computational experiments on data from the Chicago metropolitan area with hundreds of thousands of households and thousands of candidate stations show that our approach produces high-quality solutions in cases where existing exact methods cannot even load the model in memory. We also analyze various policy scenarios, demonstrating that combining existing depots with newly built stations under multiagency collaboration substantially reduces costs and congestion. These findings offer a scalable and efficient framework for developing sustainable large-scale EV charging networks.

Capacity allocation↗

DOE OSTI2022

Distributed Optimization Approaches with Discrete Variables in the Power Distribution Systems

Traditionally, centralized approaches have predominantly been used for the power system operation and control. With increasing penetration of small-scale distributed energy resources (DERs) in the distribution network, especially independently owned renewable resources, distributed algorithms can serve as a potential alternative for improving scalability, resiliency and addressing privacy concerns. However, the complexity of distributed algorithms significantly increases with the integration of the legacy devices, the operation of which depend on discrete control variables. This paper aims to provide a review of the distributed optimization algorithms incorporating discrete control variables for the power distribution system. While the research in this domain is still at its nascence, an extensive comparison of the approaches in the literature for applying quadratic penalty, branch and bound,ordinal optimization and proximal operator to handle discrete variables in the framework of ADMM and dual decomposition have been addressed. Future research direction in this field have been also provided.

Adan, Jannatul↗

NASA NTRS2018

PURE: Scalable Phase Unwrapping with Spatial Redundant Arcs

Phase unwrapping is a key problem in many coherent imaging systems, such as syntheticapertureradar(SAR)interferometry. Ageneralformulationforredundant integration of ﬁnite differences for phase unwrapping (Costantini et al., 2010) was shown to produce a more reliable solution by exploiting redundant differential estimates. However, this technique requires a commercial linear programming solver for large-scale problems. For a linear cost function, we propose a method based on Dual Decomposition that breaks the given problem deﬁned over a nonplanar graph into tractable sub-problems over planar subgraphs. We also propose a decomposition technique that exploits the underlying graph structure for solving thesub-problemsefﬁcientlyandguaranteesasymptoticconvergencetotheglobally optimal solution. The experimental results demonstrate that the proposed approach is comparable to the existing state-of-the-art methods in terms of the estimate with a better runtime and memory footprint.

Lanka, Ravi↗

NASA NTRS1996

A New Coarsening Operator for the Optimal Preconditioning of the Dual and Primal Domain Decomposition Methods: Application to Problems with Severe Coefficient Jumps

We present an optimal preconditioning algorithm that is equally applicable to the dual (FETI) and primal (Balancing) Schur complement domain decomposition methods, and which successfully addresses the problems of subdomain heterogeneities including the effects of large jumps of coefficients. The proposed preconditioner is derived from energy principles and embeds a new coarsening operator that propagates the error globally and accelerates convergence. The resulting iterative solver is illustrated with the solution of highly heterogeneous elasticity problems.

Farhat, Charbel↗

DOE OSTI2023

Physics guided machine learning for multi-material decomposition of tissues from dual-energy CT scans of simulated breast models with calcifications

We introduce a physics guided data-driven method for image-based multi-material decomposition for dual-energy computed tomography (CT) scans. The method is demonstrated for CT scans of virtual human phantoms containing more than two types of tissues. The method is a physics-driven supervised learning technique. We take advantage of the mass attenuation coefficient of dense materials compared to that of muscle tissues to perform a preliminary extraction of the dense material from the images using unsupervised methods. We then perform supervised deep learning on the images processed by the extracted dense material to obtain the final multi-material tissue map. The method is demonstrated on simulated breast models with calcifications as the dense material placed amongst the muscle tissues. The physics-guided machine learning method accurately decomposes the various tissues from input images, achieving a normalized root-mean-squared error of 2.75%.

Gopalakrishnan Meena, Murali↗

NASA NTRS1987

A three-dimensional dual potential procedure with applications to wind tunnel inlets and interacting boundary layers

A dual potential decomposition of the velocity field into a scalar and a vector potential function is extended to three dimensions and used in the finite-difference simulation of steady three-dimensional inviscid rotational flows and viscous flow. The finite-difference procedure was used to simulate the flow through the 80 by 120 ft wind tunnel at NASA Ames Research Center. Rotational flow produced by the stagnation pressure drop across vanes and screens which are located at the entrance of the inlet is modeled using actuator disk theory. Results are presented for two different inlet vane and screen configurations. The numerical predictions are in good agreement with experimental data. The dual potential procedure was also applied to calculate the viscous flow along two and three dimensional troughs. Viscous effects are simulated by injecting vorticity which is computed from a boundary layer algorithm. For attached flow over a three dimensional trough, the present calculations are in good agreement with other numerical predictions. For separated flow, it is shown from a two dimensional analysis that the boundary layer approximation provides an accurate measure of the vorticity in regions close to the wall; whereas further away from the wall, caution has to be exercised in using the boundary-layer equations to supply vorticity to the dual potential formulation.

Rao, K. V.↗

DOE OSTI2021

A Privacy-Preserving Distributed Control of Optimal Power Flow

Here, we consider a distributed optimal power flow formulated as an optimization problem that maximizes a nondifferentiable concave function. Solving such a problem by the existing distributed algorithms can lead to data privacy issues because the solution information exchanged within the algorithms can be utilized by an adversary to infer the data. To preserve data privacy, in this paper we propose a differentially private projected subgradient (DP-PS) algorithm that includes a solution encryption step. We show that a sequence generated by DP-PS converges in expectation, in probability, and with probability 1. Moreover, we show that the rate of convergence in expectation is affected by a target privacy level of DP-PS chosen by the user. We conduct numerical experiments that demonstrate the convergence and data privacy preservation of DP-PS.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

The Average Spectrum Norm and Near-Optimal Tensor Completion

We propose the average spectrum norm to study the minimum number of measurements required to approximate a multidimensional array (i.e., sample complexity) via low-rank tensor recovery. Our focus is on the tensor completion problem, where the aim is to estimate a multiway array using a subset of tensor entries corrupted by noise. Our average spectrum norm-based analysis provides near-optimal sample complexities, exhibiting dependence on the ambient dimensions and rank that do not suffer from exponential scaling as the order increases.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1987

A three-dimensional dual potential procedure for inlets and indraft wind tunnels

Rao, K. V.↗

NASA NTRS1985

The numerical simulation of steady transonic rotational flow using a dual potential formulation

A finite-difference method is presented that simulates steady transonic rotational flow of an inviscid fluid by representing the velocity field as the sum of scalar and vector potentials. This dual potential velocity decomposition extends the validity of the scalar (full) velocity potential to include vorticity. The inclusion of a vector potential also permits an alternate treatment of lift that does not require a circulation wake cut. This is accomplished by specifying the vector potential as a constant on the airfoil surface in order to satisfy a Kutta condition. The governing equations are solved as iteratively decoupled scalar equations using approximate factorization techniques, and the overall efficiency approaches that of the full potential equation. The governing equations are able to convect entropy and vorticity throughout the flow field and are equivalent to the Euler equations in continuous flow domains, however at shocks the Rankine-Hugoniot entropy jump must be supplied. An entropy correction method is presented and verified with transonic airfoil solutions of the Euler equations.

Chaderjian, N. M.↗

DOE OSTI2021

Catalytic Site Requirements for N2O Decomposition on Cu-, Co-, and Fe-SSZ-13 Zeolites

N2O decomposition is investigated on Cu, Co and Fe-exchanged SSZ-13 zeolite catalysts at relatively low metal loadings. The catalysts are synthesized by solution ion exchange, and subjected to X-ray diffraction (XRD), temperature-programed-reduction by H2 (H2-TPR), temperature-programed-reaction of N2O (N2O-TPR) coupled with in-situ transmission FTIR, and finally steady-state flow reaction tests. At low N2O pressures (< 0.05 kPa), all catalysts display pseudo first-order kinetics. From Arrhenius analysis, Cu and Fe-SSZ-13 display very different apparent activation energies but similar pre-exponential factors, suggesting their similar reaction mechanisms. N2O decomposition follows a dual-site mechanism, occurring on dimeric M-O-M sites in these catalysts, and O2 is formed by the combination of two O ad-atoms from two vicinal metal sites. Under low N2O pressure (0.05 kPa) and first-order kinetic regime, the reaction is limited by N-O cleavage on bare metal active sites. In comparison to Cu-SSZ-13, the much higher N2O decomposition rate over Fe-SSZ-13 is attributed to the much lower activation barriers for the N-O cleavage step. N2O decomposition occurs on isolated Co2+ ions in Co-SSZ-13. The rate-limiting step is N-O cleavage on an O-occupied Co site in the low-pressure first order kinetic regime. This single-site mechanism leads to much higher pre-exponential factors as compared to the dual-site mechanism. This beneficial factor for reaction rate enhancement, however, is compromised by the much higher activation barriers over this catalyst.

Lin, Fan↗

NASA NTRS1976

Hydrogen production by water decomposition using a combined electrolytic-thermochemical cycle

A proposed dual-purpose power plant generating nuclear power to provide energy for driving a water decomposition system is described. The entire system, dubbed Sulfur Cycle Water Decomposition System, works on sulfur compounds (sulfuric acid feedstock, sulfur oxides) in a hybrid electrolytic-thermochemical cycle; performance superior to either all-electrolysis systems or presently known all-thermochemical systems is claimed. The 3345 MW(th) graphite-moderated helium-cooled reactor (VHTR - Very High Temperature Reactor) generates both high-temperature heat and electric power for the process; the gas stream at core exit is heated to 1850 F. Reactor operation is described and reactor innards are illustrated. A cost assessment for on-stream performance in the 1990's is optimistic.

Farbman, G. H.↗

DOE OSTI2026

A hybrid Penman-Monteith and machine learning model for simulating evapotranspiration and its components

Integrating physical processes with machine learning has advanced evapotranspiration (ET) simulation, yet most hybrid models fail to partition total ET into its components: soil evaporation (E) and vegetation transpiration (T). This study introduces Residual Neural Network–Penman–Monteith (RNN-PM), a novel hybrid dual-source ET model designed to overcome this limitation. The model synergizes the physically-based Penman–Monteith framework with three specialized residual neural networks trained to estimate key conductance parameters (canopy conductance, soil surface conductance, and aerodynamic conductance). Furthermore this explicit parameterization allows for the direct partitioning of total ET. Validation at National Ecological Observatory Network (NEON) flux sites using high-frequency partitioned E and T shows that RNN-PM reliably reproduces ET and the transpiration fraction (T/ET). For ET, the model achieves an average Kling–Gupta efficiency (KGE) of 0.89 and a root-mean-square error (RMSE) of 0.55 mm/day; for T/ET, the KGE is 0.87 with an RMSE of 0.06. Furthermore, RNN-PM demonstrates robust generalization, accurately simulating ET and its components well beyond the initial training dataset, even under extreme climatic conditions. This study extended the analysis by comparing the RNN-PM model with seven established dual-source ET models. The results indicate that RNN-PM outperforms both conventional machine learning models and purely physical process-based models in simulating ET components in most cases. Among the purely physical process-based dual-source models, those based on surface temperature decomposition showed improved performance as the leaf area index (LAI) decreased when evaluated against high-frequency ET component datasets. In contrast, the performance of conductance-based dual-source models declined with decreasing LAI. Although purely machine learning-based models can produce relatively accurate simulations of ET components, they often exhibit limited generalization capability, an issue that the RNN-PM model effectively overcomes. Ultimately, the RNN-PM model represents a significant advance in simulating ET components, offering a novel and scalable approach for improving the representation of land–atmosphere interactions in Earth system models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Enhancing carbon nanotube production from carbon dioxide and ethane using bimetallic catalysts

Converting CO 2 into carbon nanotubes (CNTs) offers a promising way for CO 2 utilization and sequestration, potentially mitigating environmental impacts from anthropogenic emissions. This study reports that bimetallic CoFe catalysts can increase CNT production from the reaction of CO 2 and C 2 H 6 by an order of magnitude compared to their monometallic counterparts. The active sites and CNT morphologies are composition-dependent: Co-rich catalysts (Co/Fe ratio ≥ 5) form stable face-centered cubic (fcc) CoFe alloys, producing cylindrical CNTs; Fe-containing catalysts (Co/Fe ≤ 2) favor body-centered cubic (bcc) CoFe alloy upon reduction, which transforms into carbides, resulting in bamboo-like CNTs. Experimental evidence and DFT calculations reveal that adjacent Fe and Co atoms modulate CO and C x H y adsorption, regulating CNT production pathways through the CO Boudouard reaction and C 2 H 6 decomposition. In conclusion, these results highlight the dual benefits of bimetallic catalysts in enhancing CNT yield and controlling CNT morphology through adjustment of catalyst compositions.

58 GEOSCIENCES↗

NASA NTRS1976

Study of removal of ammonia from urine vapor by dual catalyst

The feasibility of ammonia removal from urine vapor by a low temperature dual-catalyst system was investigated. The process is based on the initial catalytic oxidation of ammonia present in urine vapor to nitrogen and nitrous oxide, followed by a catalytic decomposition of the nitrous oxide formed into its elements. The most active catalysts for the oxidation of ammonia and for the decomposition of N2O, identified in screening tests, were then combined into dual catalyst systems and tested to establish their overall efficiencies for the removal of ammonia from artificial gas mixtures. Dual catalyst systems capable of ammonia removal from the artificial gas mixtures were then tested with the actual urine vapor produced by boiling untreated urine. A suitable dual catalyst bed arrangement was found that achieved the removal of ammonia and organic carbon, and recovered water of good quality from urine vapor.

Budininkas, P.↗

DOE OSTI2024

Geometric representations of braid and Yang–Baxter gates

Brick-wall circuits composed of the Yang–Baxter gates are integrable. It becomes an important tool to study the quantum many-body system out of equilibrium. To put the Yang–Baxter gate on quantum computers, it has to be decomposed into the native gates of quantum computers. It is favorable to apply the least number of native two-qubit gates to construct the Yang–Baxter gate. We study the geometric representations of all X-type braid gates and their corresponding Yang–Baxter gates via the Yang–Baxterization. We find that the braid and Yang–Baxter gates can only exist on certain edges and faces of the two-qubit tetrahedron. We identify the parameters by which the braid and Yang–Baxter gates are the Clifford gate, the matchgate, and the dual-unitary gate. The geometric representations provide the optimal decompositions of the braid and Yang–Baxter gates in terms of other two-qubit gates. We also find that the entangling powers of the Yang–Baxter gates are determined by the spectral parameters. Our results provide the necessary conditions to construct the braid and Yang–Baxter gates on quantum computers.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Dynamic model and cooperative control of a serially linked manipulator system

The use of a redundant manipulator to execute multiple tasks specified at different points on the manipulator is demonstrated. This is accomplished by decomposing a redundant arm at an intermediate arm location called the 'elbow' into two nonredundant local arms referred as the 'basearm' and the 'forearm'. This decomposition transforms a redundant arm into a serially linked dual-arm system, where the cooperation between the basearm and the forearm is carried out through the task distribution and the elbow control. The kinematics of a decomposed redundant manipulator are discussed, and a Cartesian space dynamic model and dynamic equation of a decomposed redundant manipulator are presented. The capability of generating Cartesian force, the local efficiency of generating Cartesian acceleration, and dynamic task distribution are discussed.

Lee, Sukhan↗