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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 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Modification of Jet Velocities in an Explosively Loaded Copper Target with a Conical Cavity

Here, in this work, the design and execution of an experiment with the goal of demonstrating control over the evolution of a copper jet is described. Simulations show that when using simple multi-material buffers placed between a copper target with a conical cavity and a cylinder of high-explosive, a variety of jetting behaviors occur based on material placement, including both jet velocity augmentation and mitigation. A parameter sweep was performed to determine optimal buffer designs in two configurations. Experiments using the optimal buffer designs verified the effectiveness of the buffers at altering jet velocities. Similar trends were shown between the experimental results and the modeling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

A Class of Sparse Johnson–Lindenstrauss Transforms and Analysis of their Extreme Singular Values

The Johnson–Lindenstrauss (JL) lemma is a powerful tool for dimensionality reduction in modern algorithm design. The lemma states that any set of high-dimensional points in a Euclidean space can be projected into lower dimensions while approximately preserving pairwise Euclidean distances. Random matrices satisfying this lemma are called JL transforms (JLTs). Inspired by existing $s$-hashing JLTs with exactly $s$ nonzero elements on each column, the present work introduces an ensemble of sparse matrices encompassing so-called $s$-hashing-like matrices whose expected number of nonzero elements on each column is $s$. The independence of the sub-Gaussian entries of these matrices and the knowledge of their exact distribution play an important role in their analyses. Using properties of independent sub-Gaussian random variables, these matrices are demonstrated to be JLTs, and their smallest nontrivial singular values and largest singular values are estimated nonasymptotically using a technique from geometric functional analysis. As the dimensions of the matrix grow to infinity, these singular values are proved to converge almost surely to fixed quantities (by using the universal Bai–Yin law) and in distribution to the Gaussian orthogonal ensemble Tracy–Widom law after proper rescalings. Understanding the behaviors of extreme singular values is important in general because they are often used to define a measure of stability of matrix algorithms. For example, JLTs were recently used in derivative-free optimization algorithmic frameworks to select random subspaces in which are constructed random models or poll directions to achieve scalability, and hence estimating their smallest singular value in particular helps determine the dimension of these subspaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Machine learning models for PDE constrained optimization

Partial differential equation (PDE)-constrained optimization problems arise in a variety of scientific and engineering applications, such as topology optimization, electrodynamics, fluid dynamics, and structural dynamics. However, these problems are often challenging and computationally expensive to solve, due to the need to solve the PDEs within the optimization loop. One approach to reducing the computational cost of these methods while providing convergence guarantees is through inexact trust region methods; this method uses lower fidelity solutions of the PDE at early stages of the optimization and adjusts the required accuracy of inexact PDE solvers as the optimization progresses. In this work, we explore the use of machine learning based surrogate models with these inexact trust region methods. We first demonstrate the potential of this approach by using Gaussian processes as the surrogate model and test this on a simple PDE-constrained optimization problem. We then document explorations into improving the computational costs of evolutional deep neural network / neural Galerkin methods, with the eventual goal of using these methods with the inexact trust region algorithms. We are able to speed up these approaches, albeit at the cost of lower accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Co-Simulation Meets AI: MCP-Driven Power System Analysis

GridGPT, a fine-tuned Generative AI model is designed for on-premise use in grid control rooms. This presentation will demonstrate how eGridGPT can seamlessly integrate with control room solutions to offer operators, engineers, and corporate users enhanced guidance and decision support. It is to show how this innovative AI solution can improve state estimation, boost variable energy forecasting, and optimize grid operations. By leveraging eGridGPT's unique features, audience will learn to unlock new levels of automation, predictive analytics, and reliability within their power systems, ultimately leading to reduced downtime and improved operational efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Contextually-Aware Sensitivity Analysis to Guide the Design of Randomized Least Squares Solvers in Applications

Our work on the DOE-sponsored project “A Contextually-Aware Sensitivity Analysis to Guide the Design of Randomized Least Squares Solvers in Applications,” was an effort to address critical challenges in nu merical computing and its applications to optimization. The increasing demand for robust and scalable solutions to large-scale linear algebra problems has highlighted the limitations of traditional approaches, particularly in heterogeneous and extreme-scale computing environments. Randomized Numerical Linear Algebra (RandNLA) offers a promising framework to address these challenges, and this proposal builds on this foundation by introducing innovations in sensitivity analysis and computational adaptability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Quantifying Epistemic Uncertainty in Binary Classification via Accuracy Gain

ABSTRACT Recently, a surge of interest has been given to quantifying epistemic uncertainty (EU), the reducible portion of uncertainty due to lack of data. We propose a novel EU estimator in the binary classification setting, as the posterior expected value of the empirical gain in accuracy between the current prediction and the optimal prediction. In order to validate the performance of our EU estimator, we introduce an experimental procedure where we take an existing dataset, remove a set of points, and compare the estimated EU with the observed change in accuracy. Through real and simulated data experiments, we demonstrate the effectiveness of our proposed EU estimator.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method

Abstract An interface-modified reproducing kernel particle method (IM-RKPM) is introduced in this work to allow for a direct model construction from image pixels of heterogeneous polycrystalline Li-ion battery microstructures. The interface-modified reproducing kernel (IM-RK) approximation is constructed through scaling of a kernel function by a regularized distance function in conjunction with strategic placement of interface node locations. This leads to RK shape functions with either weak or strong discontinuities across material interfaces, suitable for modeling various interface mechanics. With the placement of a triple junction node and distance-based scaling of kernel functions, the resulting IM-RK shape function also possesses proper discontinuities at the triple junctions. This IM-RK approximation effectively remedies the well-known Gibb’s oscillation in the smooth approximation of discontinuities. Different from the conventional meshfree approaches for interface discontinuities, this IM-RK approach is done without additional degrees of freedom associated with the enrichment functions, and it is formulated with the standard procedures in the RK shape function construction. This work focuses on identifying the accuracy and convergence properties of IM-RKPM for modeling the coupled electro-chemo-mechanical system. A linear patch test is formulated and numerically tested for the electro-chemo-mechanical coupled problem with a Butler–Volmer boundary condition representing the physical conditions in Li-ion battery microstructures. This is followed by verification of the optimal rates of convergence of IM-RKPM for solving the coupled problem with higher order solutions. The image-based modeling of Li-ion battery microstructures in the numerical examples demonstrates the applicability of the proposed method to realistic Li-ion battery materials modeling.

25 ENERGY STORAGE↗
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↗
DOE OSTI2025

CAMEO: A Co-design Architecture for Multi-objective Energy System Optimization (Project Report)

CAMEO (Codesign Architecture for Multi-objective Energy System Optimization) is a modular workflow management framework that abstracts co-design problems as Directed Acyclic Graphs (DAG). The framework employs JSON-based workflow specifications that enable systematic decomposition of complex optimization problems into reusable, interchangeable components including data loaders, scenario generators, optimization solvers, and result summarizers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Project PARETO—DOE’s Produced Water Optimization Initiative

The Texas Produced Water Consortium invited Project PARETO to contribute a write-up about the project to an update report they are preparing for the Texas legislature. The article we have prepared presents a high-level overview of the PARETO produced water management framework, and includes sections dedicated to going into more detail about PARETO’s strategic model and water sharing portals (AquaShare and AquaTrade).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A mathematical design framework for membrane pre-concentration in energy-efficient recovery of fermentation products

Due to the dilute nature of products manufactured via fermentation and cell-free bioprocessing, dewatering is a common unit operation in downstream processing (DSP) for bioproduct recovery, but it is typically energy intensive. To improve DSP energy efficiency for bio-based small molecules, integrating high-pressure membrane pre-concentration is a promising process option. However, this approach is typically constrained by a tradeoff between concentration factor (CF) and product recovery (PR), namely increasing the CF typically results in greater product loss, and vice versa. Here we developed a model that enables process design guidelines to: (i) identify scenarios in which the additional energy consumption and product loss from membrane pre-concentration are justified for use in DSP, and (ii) determine the optimal CF that minimizes process specific energy consumption. We compared the energy consumption of high-pressure membrane-integrated processes to evaporation-only processes and applied the model to an experimental case study for the separation and purification of butyric acid from Clostridium tyrobutyricum fermentation using an in situ product recovery (ISPR) process. The model estimated that integrating a tangential-flow reverse osmosis (RO) pre-concentration unit could reduce process energy consumption up to 45%. The use of advanced membrane pre-concentration technologies, such as negative rejection membranes and organic solvent reverse osmosis (OSRO), have the potential to further reduce the overall process specific energy consumption up to 96%, projected based on modeling. Overall, membrane pre-concentration, especially when strategically integrated prior to an evaporation step with optimized process conditions, holds significant potential for improving DSP energy efficiency, particularly in applications requiring substantial solvent removal for product recovery from dilute mixtures.

09 BIOMASS FUELS↗
DOE OSTI2024

Analysis of heat transfer and AuNPs-mediated photo-thermal inactivation of E. coli at varying laser powers using single-phase CFD modeling

In the wake of the COVID-19 pandemics, the demand for innovative and effective methods of bacterial inactivation has become a critical area of research, providing the impetus for this study. The purpose of this research is to analyze the AuNPs-mediated photothermal inactivation of E. coli. Gold nanoparticles irradiated by laser represent a promising technique for combating bacterial infection that combines high-tech and scientific progress. The intermediate aim of the work was to present the calibration of the model with respect to the gold nanorods experiment. The purpose of this work is to study the effect of initial concentration of E. coli bacteria, the design of the chamber and the laser power on heat transfer and inactivation of E. coli bacteria. Using the CFD simulation, the work combines three main concepts. 1. The conversion of laser light to heat has been described by a combination of three distinctive approximations: a- Discrete particle integration to take into account every nanoparticle within the system, b- Rayleigh-Drude approximation to determine the scattering and extinction coefficients and c- Lambert–Beer–Bourger law to describe the decrease in laser intensity across the AuNPs. 2. The contribution of the presence of E. coli bacteria to the thermal and fluid-dynamic fields in the microdevice was modeled by single-phase approach by determining the effective thermophysical properties of the water-bacteria mixture. 3. An approach based on a temperature threshold attained at which bacteria will be inactivated, has been used to predict bacterial response to temperature increases. The comparison of the thermal fields and temporal temperature changes obtained by the CFD simulation with those obtained experimentally confirms the accuracy of the light-heat conversion model derived from the aforementioned approximations. The results show a linear relationship between maximum temperature and variation in laser power over the range studied, which is in line with previous experimental results. It was also found that the temperature inside the microchamber can exceed 55 °C only when a laser power higher than 0.8 W is used, so bacterial inactivation begins. The experimental data allows to determinate the concentration of nanoparticles. This parameter is introduced into the mathematical model obtaining the same number of AuNPs. However, this assumption introduces a certain simplification, as in the mathematical model the distribution of nanoparticles is uniform. This work is directly connected to the use of gold nanoparticles for energy conversion, as well as the field of bacterial inactivation in microfluidic systems such as lab-on-a-chip. Presented mathematical and numerical models can be extended to the entire spectrum of wavelengths with particular use of white light in the inactivation of bacteria. This work represents a significant advancement in the field, as to the best of the authors’ knowledge, it is the first to employ a single-phase computational fluid dynamics (CFD) approach specifically combined with the thermal inactivation of bacteria. Moreover, this research pioneers the use of a numerical simulation to analyze the temperature threshold of photothermal inactivation of E. coli mediated by gold nanorods (AuNRs). The integration of these methodologies offers a new perspective on optimizing bacterial inactivation techniques, making this study a valuable contribution to both computational modeling and biomedical applications.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Novel artificial neural network model for instantaneous power losses and operational efficiency mapping of MW-scale vanadium redox flow battery for improved technoeconomic analysis

A novel data-driven, machine-learning-based method for modeling the instantaneous power losses of a distribution-sited 2 MW/8MWh vanadium redox flow battery (VRFB), a grid-scale electrochemical storage technology, is introduced and compared against benchmark empirical modeling approaches, including symmetric and asymmetric models, as well as a recent convex hull modeling approach. The novel loss modeling method introduces several advantages over the benchmark models and over simplistic efficiency estimates, the most significant of which is that the model can accurately reflect the stepwise and non-linear parasitic losses associated with the duty cycles of mechanical auxiliary systems like pump motor drives and blower fans. Residuals of the models are compared; the proposed data driven model features significantly improved accuracy over the benchmark models. The model's coefficient of determination is also improved relative to that of the benchmark models. Furthermore, a novel method for visualization of operational efficiency of the grid-scale storage technology is introduced. To demonstrate the benefits of the novel data-driven method for modeling the VRFB, the benchmark models and the proposed models are embedded into an Open DSS distribution network model to study two applications of the grid-scale electrical storage system: load leveling for grid support and energy arbitrage. This article demonstrates that the accuracy of the instantaneous power loss model significantly impacts the understanding of the state of charge of the VRFB. In turn, the accuracy of the efficiency modeling of the VRFB impacts the understanding of the potential economic value and technical benefits to the distribution network operators. In conclusion, the presented power loss modeling approach is, therefore, highly relevant for utility-stakeholders, battery asset owners, system engineers, system designers, and financial planners interested in evaluating or optimizing the operation of grid-scale VRFBs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Modular Hydronic Room Conditioning System (CRADA NFE-24-10120 Final Report)

This project presents the development and validation of high-fidelity numerical models for fin-tube heat exchangers to enable accurate performance prediction and informed design optimization. The modeling framework integrates detailed geometric specifications, thermophysical property data, and system-level constraints to simulate the heat exchanger’s behavior under a range of operating conditions. The model is calibrated using real-world product specifications and validated against experimental data collected from controlled cooling and heating tests. In cooling mode, the model captures the overall trends in capacity and outlet air temperature but tends to underpredict latent effects, especially at lower air flow rates. In heating mode, the simulation consistently overestimates both the thermal capacity and outlet air temperature, indicating the need for refinement in air-side heat transfer assumptions. Despite these deviations, the model provides a solid foundation for optimization, allowing key design variables to be tuned within physical and performance-based constraints. This research advances the ability to simulate, validate, and optimize fin-tube heat exchanger designs with greater confidence and efficiency.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Acceleration of Thermochemistry Solves in MOOSE and Pronghorn

This work focuses on the development and implementation of strategies to accelerate thermochemical calculations within MOOSE-based multiphysics simulations, particularly for applications in MSRs. We highlight the inherent complexity of nuclear materials, which require a multiscale approach to accurately model their behavior across various physical domains, including mechanical, chemical, and thermal phenomena. Thermochemical equilibrium calculations are crucial for predicting material properties and enhancing the fidelity of these simulations. The integration of Thermochimica, a Gibbs energy minimizer, into MOOSE allows for the direct minimization of Gibbs energy at every point on the mesh. However, the computational cost of such integration is significant. To address this, we explored acceleration strategies such as multi-threading support and the use of a thermodynamic ValueCache to reduce redundant calculations. Additionally, we investigated modifications to Thermochimica to enable phase constraints and improve its coupling with phase-field models, which are essential for simulating microstructural evolution and corrosion in MSR. These efforts aim to optimize the computational efficiency and accuracy of multiphysics simulations, thereby supporting the development of reliable and efficient nuclear materials for next-generation reactor technologies.

36 - MATERIALS SCIENCE↗
DOE OSTI2024

ACOPF Transmission Switching Using Open-Source MINLP Solvers

The optimal transmission switching (OTS) problem with AC physics represents a mixed integer non-linear non-convex optimization problem which can provide benefits to transmission level power system operations. In this paper we benchmark a set of open-source mixed integer non-linear programming (MINLP) solvers on the OTS problem with AC physics using the pglib set of power system test cases. Results characterizing the performance of the different solvers are reported and discussed.

ACOPF↗