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At least 271 records · Page 15

ZEUS: An Efficient GPU Optimization Method Integrating PSO, BFGS, and Automatic Differentiation

We introduce a novel, efficient computational method, ZEUS, for numerical optimization, and provide an open-source implementation. It has four key ingredients: (1) particle swarm optimization (PSO), (2) the use of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, (3) automatic differentiation (AD), and (4) GPUs. Our approach addresses the computational challenges inherent in high-dimensional, non-convex optimization problems. In the first phase of the algorithm, we get a potentially good set of starting points using PSO. Thereafter, we run BFGS independently in parallel from these starting points. BFGS is one of the best-performing algorithms for numerical optimization. However, it requires the gradient of the function being optimized. ZEUS integrates automatic differentiation into BFGS thus avoiding the need for the user to calculate derivatives explicitly. The use of GPUs allows ZEUS to speed up the calculations substantially. We carry out systematic studies to explore the trade-offs between the number of PSO iterations taken, starting points, and BFGS iteration depth. We show that a handful of iterations of PSO can improve global convergence when combined with BFGS. We also present performance studies using common test functions. The source code can be found at https://github.com/fnal-numerics/global-optimizer-gpu.

Soos, Dominik [Old Dominion U.]↗

Efficient online quantum circuit learning with no upfront training

Optimization is a promising candidate for studying the utility of variational quantum algorithms (VQAs). However, evaluating cost functions using quantum hardware introduces runtime overheads that limit exploration. Surrogate-based methods can reduce calls to a quantum computer, yet existing approaches require hyperparameter pre-training and have been tested only on small problems. Here, we show that surrogate-based methods can enable successful optimization at scale, without pre-training, by using radial basis function interpolation (RBF) to construct an adaptive, hyperparameter-free surrogate. Using the surrogate as an acquisition function drives hardware queries to the vicinity of the true optima. For 16-qubit random 3-regular Max-Cut instances with the Quantum Approximate Optimization Algorithm (QAOA), our method outperforms state-of-the-art approaches, without considering their upfront training costs. Furthermore, we successfully optimize QAOA circuits for 127-qubit random Ising models on an IBM processor using 10 4 −10 5 measurements. Strong empirical performance demonstrates the promise of automated surrogate-based learning for large-scale VQA applications.

97 MATHEMATICS AND COMPUTING↗

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗

Multiphysics Co-Optimization Design and Analysis of Double-Side Cooled Silicon Carbide-Based Power Module: Preprint

With the rapid growth of Electric Vehicles (EVs) and Hybrid Electric Vehicles (HEVs), much more rigorous design targets have been set for automotive power electronics, including high power density, high reliability, and low cost. Novel power module and inverter technologies based on wide bandgap (WEG) semiconductors have been developed to meet these design targets, while providing optimal power semiconductor operating temperature and promising thermomechanical performance. Compared with conventional cooling techniques which are normally applied only on one side of power module, double-side cooling approach is now believed to be the solution to enable high power density and low thermal resistance of WEG semiconductor-based power electronics. In this work, we develop a three-phase power module that is double-sided cooled using dielectric fluid jet impingement. In each phase, four silicon carbide (SiC) power semiconductors are bonded to copper busbars without electrical insulation layers. A finite element analysis (FEA) model is created for thermal and thermomechanical analysis. Based on FEA modeling results, we select particular dimensions for a parametric study to optimize thermal and mechanical performance. Using a multi-objective genetic algorithm (MOGA)-based optimization method, we have minimized the maximum junction temperature and thermal stresses within the power module. The multiphysics co-optimization approach has enabled an efficient design process of power modules with greatly reduced computational cost, as compared to conventional processes that rely on exhaustive numerical simulations and iterations.

ADVANCED PROPULSION SYSTEMS↗

Quantum Computing in Next-Generation Transportation Optimization

We explore how quantum computing (QC) can advance transportation optimization, with a focus on two high-impact areas: traffic signal control and vehicle electrification with grid integration. As transportation systems grow in complexity, classical optimization methods increasingly struggle to deliver scalable and efficient solutions, particularly for real-time, data-rich environments. This work identifies key challenges within these two domains where QC may offer advantages, particularly in handling combinatorial decision spaces and dynamic constraints. We begin by outlining the limitations of classical approaches for traffic signal control optimization and electric vehicle charging coordination, highlighting where computational limitations arise. Previous quantum formulations are presented and new formulations are proposed to demonstrate how emerging quantum algorithms, including quantum annealing and the Quantum Approximation Optimization Algorithm, could be leveraged to reformulate and address these problems. We also evaluate the suitability of current quantum hardware and discuss recent trends that indicate when QC may become a viable tool for transportation applications. While acknowledging the present limitations of QC technologies, this poster emphasizes the importance of preparing quantum-compatible models today. By reviewing and establishing formulations that align with the strengths of quantum algorithms, researchers and practitioners can better position themselves to take advantage of QC advancements as they occur. This work aims to provide a practical, forward-looking perspective on the near-term potential of quantum computing in transportation optimization.

33 ADVANCED PROPULSION SYSTEMS↗

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control. We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians. Additionally, we present an efficient, grid-free numerical solver based on our representation formulas, which is shown to scale linearly with the state dimension, and thus, to overcome the curse of dimensionality. Using existing optimization methods and the min-plus technique, we extend our numerical solvers to address more general classes of convex and nonconvex initial costs. We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit (CPU) and a field-programmable gate array (FPGA). In several cases, our FPGA implementation obtains over a 10 times speedup compared to the CPU, which demonstrates the promising performance boosts FPGAs can achieve. Furthermore, our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

97 MATHEMATICS AND COMPUTING↗

A unified funnel restoration SQP algorithm

We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of basic algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss Army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with a sequential quadratic programming (SQP) algorithm that maintains an acceptable upper bound on the constraint violation, called a funnel, that is monotonically decreased to control the feasibility of the iterates. Infeasible quadratic subproblems are handled by a feasibility restoration strategy. Globalization is controlled by a line search or a trust-region method. We prove global convergence of the trust-region funnel SQP method, building on known results from filter methods. We implement the algorithm in Uno, and we provide extensive test results for the trust-region line-search funnel SQP on small CUTEst instances.

Kiessling, David [Katholieke Univ. Leuven, Heverle↗

Nearly optimal state preparation for quantum simulations of lattice gauge theories

Here, we present several improvements to the recently developed ground-state preparation algorithm based on the quantum eigenvalue transformation for unitary matrices (QETU), apply this algorithm to a lattice formulation of U(1) gauge theory in (2+1) dimensions, as well as propose an alternative application of QETU, a highly efficient preparation of Gaussian distributions. The QETU technique was originally proposed as an algorithm for nearly optimal ground-state preparation and ground-state energy estimation on early fault-tolerant devices. It uses the time-evolution input model, which can potentially overcome the large overall prefactor in the asymptotic gate cost arising in similar algorithms based on the Hamiltonian input model. We present modifications to the original QETU algorithm that significantly reduce the cost for the cases of both exact and Trotterized implementation of the time evolution circuit. We use QETU to prepare the ground state of a U(1) lattice gauge theory in two spatial dimensions, explore the dependence of computational resources on the desired precision and system parameters, and discuss the applicability of our results to general lattice gauge theories. We also demonstrate how the QETU technique can be utilized for preparing Gaussian distributions and wave packets in a way which outperforms existing algorithms for as little as n q ≳ 2–5 qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Reduced-order modeling on a near-term quantum computer

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems of equations as well as systems of linear ordinary differential equations (ODEs) and partial differential equations (PDEs). Reducedorder modeling (ROM) algorithms for studying fluid dynamics have shown success in identifying linear operators that can describe flowfields, where dynamic mode decomposition (DMD) is a particularly useful method in which a linear operator is identified from data. In this work, DMD is reformulated as an optimization problem to propagate the state of the linearized dynamical system on a quantum computer. This reformulation was chosen as a means of facilitating implementation on a near-term quantum computer. Quadratic unconstrained binary optimization (QUBO), a technique for optimizing quadratic polynomials in binary variables, allows for quantum annealing algorithms to be applied. A quantum circuit model (quantum approximation optimization algorithm, QAOA) is utilized to obtain predictions of the state trajectories. Results are shown for the quantum-ROM predictions for flow over a 2D cylinder at Re = 220 and flow over a NACA0009 airfoil at Re = 500 and α = 15°. The quantum-ROM predictions are found to depend on the number of bits utilized for a fixed point representation and the truncation level of the DMD model. Comparisons with DMD predictions from a classical computer algorithm are made, as well as an analysis of the computational complexity and prospects for future, more fault-tolerant quantum computers.

97 MATHEMATICS AND COMPUTING↗

Streamlining Ocean Dynamics Modeling with Fourier Neural Operators: A Multiobjective Hyperparameter and Architecture Optimization Approach

Training an effective deep learning model to learn ocean processes involves careful choices of various hyperparameters. We leverage DeepHyper’s advanced search algorithms for multiobjective optimization, streamlining the development of neural networks tailored for ocean modeling. The focus is on optimizing Fourier neural operators (FNOs), a data-driven model capable of simulating complex ocean behaviors. Selecting the correct model and tuning the hyperparameters are challenging tasks, requiring much effort to ensure model accuracy. DeepHyper allows efficient exploration of hyperparameters associated with data preprocessing, FNO architecture-related hyperparameters, and various model training strategies. We aim to obtain an optimal set of hyperparameters leading to the most performant model. Moreover, on top of the commonly used mean squared error for model training, we propose adopting the negative anomaly correlation coefficient as the additional loss term to improve model performance and investigate the potential trade-off between the two terms. The numerical experiments show that the optimal set of hyperparameters enhanced model performance in single timestepping forecasting and greatly exceeded the baseline configuration in the autoregressive rollout for long-horizon forecasting up to 30 days. Utilizing DeepHyper, we demonstrate an approach to enhance the use of FNO in ocean dynamics forecasting, offering a scalable solution with improved precision.

97 MATHEMATICS AND COMPUTING↗

SITCOMTN-154: Initial studies of photometric redshifts with LSSTComCam from DP1

This technote holds reports based on the first analyses of the Data Preview 1 (DP1) data by the Science Unit for photometric redshifts. Although photometric redshifts are not an official DP1 data product, the "Photo-z Science Unit" generated photo-z estimates for every galaxy in DP1 using the available multi-band imaging on a best-effort basis. This work included developing training and test datasets by matching DP1 data to high-quality reference redshifts obtained with spectroscopy, Grism data, and multi-band photometry. The Science Unit used the RAIL software package to make photometric redshift estimates using eight different algorithms, developed simple scientific performance metrics, used those metrics to explore how the performance of the algorithms varied with configuration changes, derived more optimized configurations of the algorithms and tested the performance of those configurations. This work, the resulting data products and expected data distribution mechanism are all described there.

79 ASTRONOMY AND ASTROPHYSICS↗

Lyapunov controlled counterdiabatic quantum optimization

We introduce a quantum algorithm that integrates counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to address combinatorial optimization problems. This approach offers versatility, allowing implementation as either a digital-analog or purely digital algorithm based on selected control strategies. By examining spin-glass Hamiltonians, we illustrate how the algorithm can explore alternative paths to enhance solution outcomes compared to conventional CD techniques. This method reduces dependence on extensive higher-order CD terms and on classical optimization techniques, making it more suitable for existing quantum computing platforms. The combination of digital compression via CD protocols and the adaptable nature of QLC methods positions this approach as a promising candidate for near-term quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Toward digital design at the exascale: An overview of project ICECap

High performance computing has entered the Exascale Age. Capable of performing over 1018 floating point operations per second, exascale computers, such as El Capitan, the National Nuclear Security Administration's first, have the potential to revolutionize the detailed in-depth study of highly complex science and engineering systems. However, in addition to these kind of whole machine “hero” simulations, exascale systems could also enable new paradigms in digital design by making petascale hero runs routine. Currently, untenable problems in complex system design, optimization, model exploration, and scientific discovery could all become possible. Motivated by the challenge of uncovering the next generation of robust high-yield inertial confinement fusion (ICF) designs, project ICECap (Inertial Confinement on El Capitan) attempts to integrate multiple advances in machine learning (ML), scientific workflows, high performance computing, GPU-acceleration, and numerical optimization to prototype such a future. Built on a general framework, ICECap is exploring how these technologies could broadly accelerate scientific discovery on El Capitan. In addition to our requirements, system-level design, and challenges, we describe some of the key technologies in ICECap, including ML replacements for multiphysics packages, tools for human-machine teaming, and algorithms for multifidelity design optimization under uncertainty. As a test of our prototype pre-El Capitan system, we advance the state-of-the art for ICF hohlraum design by demonstrating the optimization of a 17-parameter National Ignition Facility experiment and show that our ML-assisted workflow makes design choices that are consistent with physics intuition, but in an automated, efficient, and mathematically rigorous fashion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Trajectory Shaper: A Solution for Disrupted Cooperative Adaptive Cruise Control

Cooperative adaptive cruise control (CACC) can effectively reduce energy consumption, alleviate traffic congestion, and enhance safety. However, communication-related constraints and uncooperative vehicle users can disrupt CACC during real-world operations, significantly undermining the putative benefits of CACC. To alleviate the negative impacts of disrupted CACC, this study develops the trajectory shaper (TS) methods as backup solutions for two scenarios: (i) communication between vehicles is infeasible, and vehicles execute adaptive cruise control (ACC) using local sensor measurements; (ii) follower vehicles reject forming a cooperative platoon and execute their local distributed controllers using the information attained via communication. When communication is infeasible, a distributed TS is devised on each vehicle to modify the sensor measurements, enabling safe and efficient ACC operations. When communication is available but uncooperative agents are involved, the lead vehicle of the platoon executes a centralized TS to modify the information shared with uncooperative agents, achieving optimal platoon-level performance. The centralized and distributed TSs are implemented based on the model predictive control algorithms to yield optimal modifications on input information. Robustness is also factored to tackle model uncertainties during TS operations to ensure safety and efficiency. Numerical experiments validate the control performance of the proposed TSs.

Zhou, Anye [ORNL] (ORCID:0000000301455579)↗