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Results for “Mathematical optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

VAN-DAMME: GPU-accelerated and symmetry-assisted quantum optimal control of multi-qubit systems

We present an open-source software package, VAN-DAMME (Versatile Approaches to Numerically Design, Accelerate, and Manipulate Magnetic Excitations), for massively-parallelized quantum optimal control (QOC) calculations of multi-qubit systems. To enable large QOC calculations, the VAN-DAMME software package utilizes symmetry-based techniques with custom GPU-enhanced algorithms. This combined approach allows for the simultaneous computation of hundreds of matrix exponential propagators that efficiently leverage the intra-GPU parallelism found in high-performance GPUs. In addition, to maximize the computational efficiency of the VAN-DAMME code, we carried out several extensive tests on data layout, computational complexity, memory requirements, and performance. These extensive analyses allowed us to develop computationally efficient approaches for evaluating complex-valued matrix exponential propagators based on Padé approximants. To assess the computational performance of our GPU-accelerated VAN-DAMME code, we carried out QOC calculations of systems containing 10 - 15 qubits, which showed that our GPU implementation is 18.4× faster than the corresponding CPU implementation. Our GPU-accelerated enhancements allow efficient calculations of multi-qubit systems, which can be used for the efficient implementation of QOC applications across multiple domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Once-Through Steam Generator Model Analysis Using Python and Advanced Optimization Tools (Summer Internship Report)

This study focuses on the parametric analysis of design parameters for a once-through steam generator (OTSG) model, using python and advanced optimization tools to facilitate applications such as the flowing autoclave steam generator (FASG) test cases. Building on previous research involving another OTSG with a different design, this project aims to enhance our understanding of how steam generators (SGs) behave and how their outputs are influenced by changes in design. The reason for this design change is to allow for more precise modeling and optimization of SG performance, to provide a comparative analysis between the two designs, and to set up the model for integration with the FASG test case. The OTSG python-model is a mathematical representation (including fluid flow and heat transfer equations/models/correlations) of a steam-generating unit in a pressurized water reactor-type small modular reactor system. Design studies involve changing the model’s input design parameters to observe the resulting effects on the output of the system. By using advanced optimization tools, such as the Risk Analysis Virtual Environment (RAVEN) developed at Idaho National Laboratory, detailed design parametric studies and model optimization were performed. Six input parameters—pressure, temperature, and mass flow rate for the inlet of the primary-side (hot fluid) and secondary-side (cold fluid), respectively, of the SG—were randomly perturbed via RAVEN’s Monte Carlo Sampler module, using uniform distributions (i.e., ±1%, ±5% and ±10% relative changes) for 600 samples. The analysis provides valuable insights into SG optimization and can be used for sensor placement optimization to effectively monitor and obtain experimental data in other tests.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2025

Universal method for the optimization of HDC coating uniformity on non-planar, non-stationary substrates for inertial confinement fusion targets

The thickness uniformity of chemical vapor deposited (CVD) diamond coatings on non-planar, non-stationary substrates depends on both the intrinsic instantaneous coating thickness distribution (ICTD) of the coating conditions used and, if applicable, on the frequency of substrate reorientation. While important for many CVD diamond applications, the relative impact of the ICTD and substrate reorientation on the coating thickness uniformity has not been studied. In this work, we systematically investigate the effect of these factors for microwave-plasma chemical vapor deposition (MPCVD) of diamond (referred to as high density carbon (HDC) in the inertial confinement fusion (ICF) community) coatings on spherical, rolling substrates. This coating technique is used to fabricate capsules for ICF experiments, which require extreme coating uniformity with <0.3 % thickness variation (so-called Mode 1 or M1) to ensure symmetric compression of imploding targets. To extract the otherwise unobservable reorientation timescale (Δt), Monte Carlo simulations were performed using experimental ICTD data as input. This combined approach confirms scaling relationships between the substrate reorientation timescale as well as coating thickness and coating uniformity, as expected from a 3D random walk. Simulations confirm that M1 is Rayleigh-distributed and scales as (Δt) 1/2 , consistent with the randomization of two angles that determine orientation of a sphere. We also demonstrate that, under the conditions studied, Δt is the dominant factor in determining thickness uniformity while the intrinsic ICTD has minimal impact. Finally, experiments show that Δt can be affected by total batch size under constant agitation conditions due to space constraints that limit the capsule reorientation kinetics. In conclusion, this study highlights the utility of a combined experiment-simulation approach as a general methodology for understanding and improving coating uniformity on non-planar, non-stationary substrates.

Capsule↗
DOE OSTI2024

Level-set topology optimization with PDE generated conformal meshes

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

42 ENGINEERING↗
DOE OSTI2024

Automatic Loss Factor Modeling and Attribution on Unlabeled PV Energy Data

We present a novel approach for modeling the loss factors of photovoltaic power generation systems (PV systems). This method is a white-box machine learning model built on convex optimization that is fast, interpretable, and auditable. It takes as an input the measured daily energy produced by the system, over a multi-year period, and returns a multiplicative decomposition model of the daily energy signal and full attribution of the total energy loss to each feature. The methods section of this paper has two major components: (1) the description of the signal decomposition (SD) model, expressed in the SD framework, and (2) the attribution of total energy losses via Shapley values. We validate the method on synthetic and open-source data sets and compare to similar methods from the literature.

artificial intelligence↗
DOE OSTI2025

Flexibility Options: A Proposed Product for Managing Imbalance Risk

The presence of variable renewable energy resources with uncertain outputs in day-ahead electricity markets results in additional balancing needs in real-time. Addressing those needs cost-effectively and reliably within a competitive market with unbundled products is challenging as both the demand for and the availability of flexibility depends on day-ahead energy schedules. Existing approaches for reserve procurement usually rely either on oversimplified demand curves that do not consider how system conditions that particular day affect the value of flexibility, or on bilateral trading of hedging instruments that are not co-optimized with day-ahead schedules. This article proposes a new product, ‘Flexibility Options', to address these two limitations. The demand for this product is endogenously determined in the day-ahead market and it is met cost-effectively by considering real-time supply curves for product providers, which are co-optimized with the energy supply. As we illustrate with numerical examples and mathematical analysis, the product addresses the hedging needs of participants with imbalances cost-effectively, provides a less intermittent revenue stream for participants with flexible outputs, promotes value-driven pricing of flexibility, and ensures that the system operator is revenue-neutral. This article provides a comprehensive design that can be further tested and applied in large-scale systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Landscaper v1

Understanding the inner workings of machine learning models through their loss landscapes offers crucial insights into model properties, optimization dynamics, and generalizability. However, accessing these insights has traditionally required specialized mathematical expertise, limiting broader adoption. Landscaper is an open-source Python package designed to bridge this gap. Landscaper seamlessly integrates a suite of multi-dimensional loss landscape analyses with cutting-edge topological data analysis (TDA) methods. This powerful combination makes both fundamental loss landscape analysis and advanced TDA techniques accessible to the broader scientific ML community, without requiring deep pre-existing mathematical knowledge. Landscaper offers three key functionalities: * Construction: Builds detailed loss landscape representations through versatile low and high-dimensional sampling techniques. * Quantification: Applies advanced metrics, including a novel topological data analysis (TDA) based smoothness metric, enabling new perspectives on model behavior. * Visualization: Offers intuitive tools to visualize and interpret loss landscapes, providing actionable insights beyond traditional performance metrics.

Weber, Gunther [Lawrence Berkeley National Laborat↗
DOE OSTI2024

Modeling and Analysis of a Heat Pump Clothes Dryer with Thermal Energy Storage

Clothes drying is an energy-intensive process that causes significant electricity consumption and carbon emissions in the US. Approximately 83% of Households in the US own a tumble clothes dryer at home and 80% of dryers are electrical resistance dryers with low energy efficiency. Heat pump technology makes it possible for highly efficient and clean drying. Additionally, the ventless design of heat pump clothes dryers (HPCD) provides more installation flexibility. HPCD involves three primary mediums: wet clothes, a closed air loop, and a refrigerant circuit. The evaporator is used to dehumidify the wet air and the condenser is used to re-heat the dry air. One of the critical technological barriers to HPCD market penetration is its long drying time, primarily due to the relatively low discharging temperature and the slow response during the warm-up period. In this study, the thermal energy storage (TES) technology is adopted to address this challenge by providing pre-heating of air prior to the condenser to increase the operating temperature of the process air. The heat pump will charge the phase change material (PCM) in the TES device with heating energy during clothes washing and the PCM will discharge the stored heat to facilitate air heating during clothes drying. To analyze the optimal design and potential for energy saving and drying time reduction, a mathematical model of the HPCD system was developed. The HPCD is a highly dynamic system with a coupled heat and mass transfer and heat pumping cycle. This paper provides solutions to simulate the transient behavior of the system while maintaining low computational cost. The modeling result indicates reduced energy consumption and drying time by integrating TES with HPCD, as compared to electrical resistance dryers. The study can provide significant insights into improving building flexibility with TES and smart appliances.

Liu, Xiaoli↗
DOE OSTI2026

Optimality of Gradient-MUSIC for Spectral Estimation

We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm performs a computationally expensive search over a fine grid, Gradient-MUSIC is significantly more efficient and eliminates the need for discretization over a fine grid by using optimization techniques. It coarsely scans the 1D landscape to find initialization simultaneously for all frequencies followed by parallelizable local refinement via gradient descent. We also analyze its performance when the noise level is sufficiently small and the signal frequencies are separated by at least 8π/m, where π/m is the standard resolution of this problem. Even though the 1D landscape is nonconvex, we prove a global convergence result for Gradient-MUSIC: coarse scanning provably finds suitable initialization and gradient descent converges at a linear rate. In addition to convergence results, we also upper bound the error between the true signal frequencies and amplitudes with those found by Gradient-MUSIC. For example, if the noise has $\ell^\infty$ norm at most ϵ, then the frequencies and amplitudes are recovered up to error at most Cϵ/m and Cϵ respectively, which are minimax optimal in m and ϵ. Our theory can also handle stochastic noise with performance guarantees under nonstationary independent Gaussian noise. Our main approach is a comprehensive geometric analysis of the landscape, a perspective that has not been explored before.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

We introduce a safe extremum-seeking (Safe ES) algorithm which achieves the minimization of an unknown objective function while ensuring that an unknown, yet measured, control barrier function (CBF) remains above an arbitrarily small negative value for all time. In other words, “practical safety” is maintained during the entire period of convergence to the constrained extremum. Our design is based on quadratic program (QP) CBF style filters for safety, which is applied in an average and estimated sense. Using nonsmooth analysis tools, we guarantee semiglobal practical asymptotic (SPA) stability of the global constrained optimum, practical convergence to the safe set if starting in a condition violating the CBF, and practical safety for all time—semiglobally—if starting in safe set. The safety result of the paper is analogous with modern notions of SPA stability, guaranteeing that, for any small violation of safety, there exist design coefficients which guarantee that such a small violation is not exceeded. The paper outlines a set of sufficient conditions on the barrier and objective functions, and by way of a Lyapunov argument, we demonstrate that nonconvex constrained optimization problems can be solved. We present these results in the setting of a static map and a dynamical system. A simulation example illustrates the results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Topology optimization for the full-cell design of porous electrodes in electrochemical energy storage devices

In this paper, we introduce a density-based topology optimization framework to design porous electrodes for maximum energy storage. We simulate the full cell with a model that incorporates electronic potential, ionic potential, and electrolyte concentration. The system consists of three materials, namely pure liquid electrolyte and the porous solids of the anode and cathode, for which we determine the optimal placement. We use separate electronic potentials to model each electrode, which allows interdigitated designs. As a result, a penalization is required to ensure that the anode and cathode do not touch, i.e., causing a short circuit. We compare multiple 2D designs generated for different fixed conditions, e.g. material properties. A 3D design with complex channel and interlocked structure is also created. All optimized designs are far superior to the traditional monolithic electrode design with respect to energy storage metrics. We observe up to a 750% increase in energy storage for cases with slow effective ionic diffusion within the porous electrode.

25 ENERGY STORAGE↗
DOE OSTI2024

Optimization of the artificial viscosity in Lagrangian staggered discretization codes. Modeling 1D stand-alone shock - case study

We have developed new measures of errors for numerical shock. The new approach is based on analysis of the structure function, and separation of the errors related to oscillations and shock width, which also include error in the position of the ”center” of the numerical shock. We have demonstrated that those measures correctly characterize the numerical solution. We introduced an objective function in, which both types of errors are weighted, and presented optimal values of the coefficients of the linear and quadratic viscosity for different weights and different Mach numbers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Structure-aware Initialization via Numerical Continuation and Informed Priors

Scientific machine learning (SciML) often operates in ill-conditioned, weakly identifiable regimes due to limited data or indirect observations. In such settings, optimization and inference are highly sensitive to the starting point, making initialization--often under-reported--a consequential degree of freedom. Random initialization is not a neutral default as it induces an implicit prior over candidate solutions and can systematically bias the result, producing large run-to-run variability. Here, we formalize this view by treating initialization as a hidden confounder in SciML and develop a unifying theory for structure-aware initialization via numerical continuation, constructing warm starts from related problem instances. Across representative tasks, including physics-informed neural networks, maximum likelihood estimation, and variational inference, warm starts have been shown to consistently reduce optimization effort and improve reliability.

Data integrity↗
DOE OSTI2026

Explainable physics-based constraints on reinforcement learning for accelerator optimization

We present a reinforcement learning (RL) framework for optimizing particle accelerator experiments that builds explainable physics-based constraints on agent behavior. The goal is to increase transparency and trust by letting users verify that the agent’s decision-making process incorporates suitable physics. Our algorithm uses a learnable surrogate function for physical observables, such as energy, and uses them to fine-tune how actions are chosen. This surrogate can be represented by a neural network or by an interpretable sparse dictionary model. We test our algorithm on a range of particle accelerator optimization environments designed to emulate the Continuous Electron Beam Accelerator Facility at Jefferson Lab. By examining the mathematical form of the learned constraint function, we are able to confirm the agent has learned to use the established physics of each environment. In addition, we find that the introduction of a physics-based surrogate enables our RL algorithms to reliably converge for difficult high-dimensional accelerator optimization environments.

explainability↗
DOE OSTI2026

Demand Response Under Stochastic, Price-Dependent User Behavior

This letter focuses on price-based demand response (DR) implemented through dynamic adjustments of electricity prices. It extends existing DR models to a stochastic framework in which customer response is represented by price-dependent random variables, leveraging models and tools from the theory of stochastic optimization with decision-dependent distributions. The inherent epistemic uncertainty in the customers' responses renders open-loop, model-based DR strategies impractical. We propose a stochastic, feedback-based pricing strategy to compensate for estimation errors and uncertainty in customer response, establish theoretical results demonstrating the stability and near-optimality of the proposed approach, and validate its effectiveness through numerical simulations.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗