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DOE OSTI2025

Graph decomposition techniques for solving combinatorial optimization problems with variational quantum algorithms

The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to hardware constraints. In this work, we develop an algorithm that decomposes the QAOA input problem graph into a smaller problem and solves MaxCut using QAOA on the reduced graph. The algorithm requires a subroutine that can be classical or quantum—in this work, we implement the algorithm twice on each graph. One implementation uses the classical solver Gurobi in the subroutine and the other uses QAOA. We solve these reduced problems with QAOA. On average, the reduced problems require only approximately 1/10 of the number of vertices than the original MaxCut instances. Furthermore, the average approximation ratio of the original MaxCut problems is 0.75, while the approximation ratios of the decomposed graphs are on average of 0.96 for both Gurobi and QAOA. With this decomposition, we are able to measure optimal solutions for ten 100-vertex graphs by running single-layer QAOA circuits on the Quantinuum trapped-ion quantum computer H1-1, sampling each circuit only 500 times. This approach is best suited for sparse, particularly k-regular graphs, as k-regular graphs on n vertices can be decomposed into a graph with at most $\frac{nk}{k+1}$ vertices in polynomial time. Further reductions can be obtained with a potential trade-off in computational time. In conclusion, while this paper applies the decomposition method to the MaxCut problem, it can be applied to more general classes of combinatorial optimization problems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2018

Sizing and Layout Design of an Aeroelastic Wingbox Through Nested Optimization

The goals of this work are to 1) develop an optimization algorithm that can simultaneously handle a large number of sizing variables and topological layout variables for an aeroelastic wingbox optimization problem and 2) utilize this algorithm to ascertain the benefits of curvilinear wingbox components. The algorithm used here is a nested optimization, where the outer level optimizes the rib and skin stiffener layouts with a surrogate-based optimizer, and the inner level sizes all of the components via gradient-based optimization. Two optimizations are performed: one restricted to straight rib and stiffener components only, the other allowing curved members. A moderate 1.18% structural mass reduction is obtained through the use of curvilinear members.

Stanford, Bret K.↗

DOE OSTI2021

Globally Optimizing QAOA Circuit Depth for Constrained Optimization Problems

We develop a global variable substitution method that reduces n-variable monomials in combinatorial optimization problems to equivalent instances with monomials in fewer variables. We apply this technique to 3-SAT and analyze the optimal quantum unitary circuit depth needed to solve the reduced problem using the quantum approximate optimization algorithm. For benchmark 3-SAT problems, we find that the upper bound of the unitary circuit depth is smaller when the problem is formulated as a product and uses the substitution method to decompose gates than when the problem is written in the linear formulation, which requires no decomposition.

3-SAT↗

DOE OSTI2022

An overview of the operation architectures and energy management system for multiple microgrid clusters

The emerging novel energy infrastructures, such as energy communities, smart building-based microgrids, electric vehicles enabled mobile energy storage units raise the requirements for a more interconnective and interoperable energy system. It leads to a transition from simple and isolated microgrids to relatively large-scale and complex interconnected microgrid systems named multi-microgrid clusters. In order to efficiently, optimally, and flexibly control multi-microgrid clusters, cross-disciplinary technologies such as power electronics, control theory, optimization algorithms, information and communication technologies, cyber-physical, and big-data analysis are needed. This paper introduces an overview of the relevant aspects for multi-microgrids, including the outstanding features, architectures, typical applications, existing control mechanisms, as well as the challenges.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Online multi-objective particle accelerator optimization of the AWAKE electron beam line for simultaneous emittance and orbit control

Multi-objective optimization is important for particle accelerators where various competing objectives must be satisfied routinely such as, for example, transverse emittance vs bunch length. We develop and demonstrate an online multi-time scale multi-objective optimization algorithm that performs real time feedback on particle accelerators. We demonstrate the ability to simultaneously minimize the emittance and maintain a reference trajectory of a beam in the electron beamline in CERN’s Advanced Proton Driven Plasma Wakefield Acceleration Experiment.

43 PARTICLE ACCELERATORS↗

DOE OSTI2018

Simplifying Energy Efficiency for Homeowners - Results from a California Utility's Pilot Study of a Scalable Solution to Assess Retrofit and Solar Opportunities: Preprint

For homeowners, typical choices to reduce net energy use in their homes include: upgrading their home with a tailored efficiency retrofit or investing in roof-top solar. Determining the unique combination of these options that will provide the most cost-effective solution requires analysis for each home. This analysis needs to be presented in a simple and actionable way to homeowners. The solution should also be easily scalable to thousands of homes to enable utilities to better target efficiency program options and support solar installations. Sacramento Municipal Utility District (SMUD) piloted a new tool developed by Vistar Energy called XeroHome that automates the assessment of energy efficiency and solar opportunities in existing homes. XeroHome demonstrates an approach to using building energy modeling, energy use data analytics and homeowner engagement to identify and target energy efficiency opportunities at scale. XeroHome uses automation to build an EnergyPlus model for each home, based on information from public data sources such as property assessment records, building permit records, aerial/satellite photography, and template models derived from ResStock. Utilizing cloud computing, machine learning and optimization algorithms, energy upgrade packages are ranked by cost-effectiveness for each home and presented over an interactive web-portal. This paper discusses SMUD's pilot project using XeroHome to conduct analysis for 1,500 existing homes in Sacramento, CA. Development of XeroHome's advanced analytics capabilities are discussed in the context of applicability for utility programs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2018

Simplifying Energy Efficiency for Homeowners - Results from a California Utility's Pilot Study of a Scalable Solution to Assess Retrofit and Solar Opportunities

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2018

Numerical parameter optimizations of the Ignition and Growth model for a HMX plastic bonded explosive

We present here a novel method for optimizing parameters of the Ignition and Growth (I&G) reactive flow model for high explosives. The I&G model predicts the shock initiation response of explosives subjected to dynamic loading. However, calibrating the model is a time-consuming process because it has several parameters, typically requires multiple data sets, and there are no direct correlations between parameters and data. In this study, we couple a scalable optimization algorithm to simulations of shock initiation experiments in the multi-physics code ALE3D. We develop four I&G model parameter sets for the HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane)-based explosive LX-07 [90 wt. % HMX, 10 wt. % Viton A] based on minimizing the difference between calculations and measurements at the embedded pressure gauges in 1D gun shock experiments. Our study shows that a cost function based on both shock time of arrival and pressure pulse shape demonstrates the best agreement with experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Autonomous sputter synthesis of thin film nitrides with composition controlled by Bayesian optimization of optical plasma emission

Autonomous experimentation has emerged as an efficient approach to accelerate the pace of material discovery. Although instruments for autonomous synthesis have become popular in molecular and polymer science, solution processing of hybrid materials, and nanoparticles, examples of autonomous tools for physical vapor deposition are scarce yet important for the semiconductor industry. Here, we report the design and implementation of an autonomous workflow for sputter deposition of thin films with controlled composition, leveraging a highly automated sputtering reactor custom-controlled by Python, optical emission spectroscopy (OES), and a Bayesian optimization algorithm. We modeled film composition, measured by x-ray fluorescence, as a linear function of plasma emission lines monitored during co-sputtering from elemental Zn and Ti targets in an N 2 and Ar atmosphere. A Bayesian control algorithm, informed by OES, navigates the space of sputtering power to fabricate films with user-defined compositions by minimizing the absolute error between desired and measured optical emission signals. We validated our approach by autonomously fabricating Zn x Ti 1-x N y films that deviate from the targeted cation composition by a relative ±3.5%, even for 15 nm thin films, demonstrating that the proposed approach can reliably synthesize thin films with a specific composition and minimal human interference. Moreover, the proposed method can be extended to more difficult synthesis experiments where plasma intensity lines depend non-linearly on pressure, or the elemental sticking coefficients strongly depend on the substrate temperature.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Approaching hydro-equivalent ignition in laser direct-drive via target design optimization using novel statistical modeling

Laser direct-drive offers significant advantages in terms of target simplicity, improved energy coupling, and large fuel masses over indirect drive. However, performance degradations from hydrodynamic and laser-plasma instabilities seeded and driven by the direct illumination pose limitations on the parameter space available for achieving ignition. In this paper, new design improvements are identified to forge a path forward for a hydro-equivalent ignition demonstration. The first is related to a new formulation of the statistical model (SM) used to accurately predict target performance directly from input parameters such as laser pulse shape and target specifications. This new SM formulation provides direct guidance on target dimensions and laser beam-to-target radius to achieve the highest fusion yield on the OMEGA laser. The second improvement comes from cooling the deuterium–tritium (DT) ice layer below the triple point right before shot time leading to lower DT vapor densities and higher convergence. Guided by these design improvements, a Bayesian optimization algorithm was used to design an implosion that is predicted to closely approach a Lawson triple product that hydrodynamically scales to ignition if equivalent laser–target coupling is achieved at laser energies typical of the National Ignition Facility.

Deuterium↗

DOE OSTI2022

Hybrid quantum-classical algorithms for approximate graph coloring

We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX- k -CUT, the problem of finding an approximate k -vertex coloring of a graph. We compare this proposal to the best known classical and hybrid classical-quantum algorithms. First, we show that the standard (non-recursive) QAOA fails to solve this optimization problem for most regular bipartite graphs at any constant level p : the approximation ratio achieved by QAOA is hardly better than assigning colors to vertices at random. Second, we construct an efficient classical simulation algorithm which simulates level- 1 QAOA and level- 1 RQAOA for arbitrary graphs. In particular, these hybrid algorithms give rise to efficient classical algorithms, and no benefit arising from the use of quantum mechanics is to be expected. Nevertheless, they provide a suitable testbed for assessing the potential benefit of hybrid algorithm: We use the simulation algorithm to perform large-scale simulation of level- 1 QAOA and RQAOA with up to 300 qutrits applied to ensembles of randomly generated 3 -colorable constant-degree graphs. We find that level- 1 RQAOA is surprisingly competitive: for the ensembles considered, its approximation ratios are often higher than those achieved by the best known generic classical algorithm based on rounding an SDP relaxation. This suggests the intriguing possibility that higher-level RQAOA may be a potentially useful algorithm for NISQ devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1972

An algorithm for control system design via parameter optimization

An algorithm for design via parameter optimization has been developed for linear-time-invariant control systems based on the model reference adaptive control concept. A cost functional is defined to evaluate the system response relative to nominal, which involves in general the error between the system and nominal response, its derivatives and the control signals. A program for the practical implementation of this algorithm has been developed, with the computational scheme for the evaluation of the performance index based on Lyapunov's theorem for stability of linear invariant systems.

Sinha, P. K.↗

DOE OSTI2022

Multi-scale and multi-physics analysis, design optimization, and experimental validation of heat exchangers utilizing high performance, non-round tubes

Air-to-refrigerant heat exchangers (HXs) are fundamental components in HVAC&R systems, and considerable research has been dedicated designing continually smaller, lighter, and more efficient HX designs. In recent years, researchers have leveraged advancements in Computational Fluid Dynamics (CFD), Finite Element Analysis (FEA), and optimization algorithms to consider primary tube shape and topology optimization to design highly compact, high performance HXs for a multitude of applications. In this research, we present a computationally efficient, comprehensive, multi-scale, and multi-physics analysis and optimization method for air-to-refrigerant HXs featuring automated CFD and FEA simulations and approximation-assisted optimization. This methodology was utilized to design HXs with shape-optimized, non-round tubes which outperform current state-of-the-art tube-fin HXs without compromising structural integrity. The optimal HXs were shown to deliver similar thermal performance to the baseline HXs while also achieving more than 20% reductions in airside pressure drop and core envelope volume and more than 30% reduction in internal volume. Comprehensive experimental validation of the optimization methodology was conducted through the testing of two prototypes in a standardized wind tunnel facility under multiple operating conditions. For prototype #1 under dry evaporator conditions, the predicted heat load agreed within ± 10% of measured values and the predicted airside pressure drop agreed within ± 30%, while for dehumidifying conditions, the predicted sensible and latent heat loads agreed within ± 10% and ± 20% of the measured values, respectively. For prototype #2, the predicted condenser heat load agreed within ± 3.0% of measured values, and the predicted airside pressure drop agreed within ± 27%. The acceptable agreement between simulation and experimental results for the present application highlights the flexibility of the novel optimization methodology to design next generation HXs with improved performance and reduced volume, weight, and environmental impact.

42 ENGINEERING↗

DOE OSTI2025

Bayesian Optimized Deep Ensemble for Uncertainty Quantification of Deep Neural Networks: a System Safety Case Study on Sodium Fast Reactor Thermal Stratification Modeling

Deep neural networks (DNNs) are increasingly important to scientific computing and engineering system simulations. Accurate uncertainty quantification (UQ) for DNNs is critical in safety-sensitive engineering domains. Traditional Deep Ensemble (DE) methods, while easy to implement, frequently suffer from poorly calibrated uncertainty estimates and limited predictive accuracy due to reliance on fixed architectures with varied weight initializations. To address these issues, we introduce a workflow that combines Bayesian Optimization (BO) and DE. The workflow is modular, scalable, and integrates parallel BO initialized with Sobol sequences to individually optimize the hyperparameters of each ensemble member. This method enhances ensemble diversity, improves predictive accuracy, and provides reliable uncertainty estimates. We evaluate the proposed BODE approach in a sodium fast reactor thermal stratification modeling case study, where we used a densely connected convolutional neural network to predict turbulent viscosity during the reactor transient with consideration of data noise. We benchmark its performance against several optimization approaches, including baseline deep ensemble, evolutionary algorithm-optimized ensemble, ensemble formed via random search combined with greedy selection, and a BO ensemble using random initialization. Here, our results demonstrate superior performance of the developed BODE approach. In noise-free scenarios, BODE notably reduces incorrect aleatoric uncertainty and significantly enhances predictive accuracy. Under conditions of 5% and 10% Gaussian noise, BODE adaptively quantifies uncertainty proportional to data noise, achieving up to an 80% reduction in root mean square error compared to baseline methods and producing well-calibrated prediction intervals.

Bayesian optimization↗

DOE OSTI2020

Generation of thermofield double states and critical ground states with a quantum computer

Significance Our experiment prepares two types of nontrivial quantum states on a trapped ion quantum computer: the thermofield double state of the transverse-field Ising model at arbitrary temperature and the quantum critical state of the zero-temperature model. We use techniques motivated by the quantum approximate optimization algorithm, and we implement a hybrid quantum–classical optimization loop to prepare the quantum critical state. Our results pave the way for exploring strongly correlated models at finite temperature and teleportation protocols inspired by black hole physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Natural evolutionary strategies for variational quantum computation

Abstract Natural evolutionary strategies (NES) are a family of gradient-free black-box optimization algorithms. This study illustrates their use for the optimization of randomly initialized parameterized quantum circuits (PQCs) in the region of vanishing gradients. We show that using the NES gradient estimator the exponential decrease in variance can be alleviated. We implement two specific approaches, the exponential and separable NES, for parameter optimization of PQCs and compare them against standard gradient descent. We apply them to two different problems of ground state energy estimation using variational quantum eigensolver and state preparation with circuits of varying depth and length. We also introduce batch optimization for circuits with larger depth to extend the use of ES to a larger number of parameters. We achieve accuracy comparable to state-of-the-art optimization techniques in all the above cases with a lower number of circuit evaluations. Our empirical results indicate that one can use NES as a hybrid tool in tandem with other gradient-based methods for optimization of deep quantum circuits in regions with vanishing gradients.

Anand, Abhinav (ORCID:0000000280812310)↗

DOE OSTI2015

SU-E-T-42: A Method to Determine the Optimal Proton Scanned Beam Angle to Ensure Robust Treatment Planning

Purpose: The ability of pencil beam scanning (PBS) to deliver highly conformal dose distributions may be affected by patient- and physics-related uncertainties. In clinical practice, selection of proton beam angles is determined qualitatively. This study investigates whether an optimal proton PBS beam angle could be quantitatively determined to ensure robust planning for pelvic targets. Methods: PBS beam angles were optimized based on two independent criteria; shortest and most homogeneous path from the patient surface to the distal edge of the target. The beam angle optimization criteria for gantry angles between 90°-270° were quantified in 10° increments for each ray, calculated as the straight line distance from the surface of the skin to the CTV’s distal edge. The goal was to minimize the path length of a proton PBS beam from the patient surface to the distal edge of the CTV, relative to the entry point, while minimizing HU inhomogeneity along the ray. HU homogeneity (i.e. HU variation) was quantitatively defined as the standard deviation of the average intra-ray HU intensity distribution of the rays comprising a single beam. This method was validated relative to inter-fraction changes on ten consecutive, locally advanced, rectal cancer patients, who underwent an average 4 verification CTs. The displacement of the 95–98% isodose lines was determined from forward calculated dose distributions on verification CTs. Results: The posterior beam (180°) had the average shortest path length, 132.7±17.2mm, and the most homogenous path, 31.9±4.3HU. The 95–98% isodose lines from all plans verified our path length to within 2.3±1.2% and HU homogeneity to within 1.2±0.5%. Conclusion: The proposed optimization algorithm determined the posterior beam dose distribution as the most robust relative to inter-fraction variation for large pelvic targets treated with PBS and was validated via verification CT for our patient cohort. Future work will focus on further algorithm development.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2017

Adjoint-based optimization of mechanical performance in polycrystalline materials and structures through texture control

The texture of a polycrystalline material refers to the preferred orientation of the grains within the material. In metallic materials, texture can significantly affect the mechanical properties such as elastic moduli, yield stress, strain hardening, and fracture toughness. Recent advances in additive manufacturing of metallic materials offer the possibility in the not too distant future of controlling the spatial variation of texture. In this work, we investigate the advantages, in terms of mechanical performance, of allowing the texture to vary spatially. We use an adjoint-based gradient optimization algorithm within a finite element solver (COMSOL) to optimize several engineering quantities of interest in a simple structure (hole in a plate) and loading (uniaxial tension) condition. As a first step to general texture optimization, we consider the idealized case of a pure fiber texture in which the homogenized properties are transversely isotropic. In this special case, the only spatially varying design variables are the three Euler angles that prescribe the orientation of the homogenized material at each point within the structure. This work paves a new way to design metallic materials for tunable mechanical properties at the microstructure level.

36 MATERIALS SCIENCE↗