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Results for “constraint energy minimization”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Online Adaptive Algorithm for Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method

Here in this research, we propose an online basis enrichment strategy within the framework of a recently developed constraint energy minimizing generalized multiscale discontinuous Galerkin method. Combining the technique of oversampling, one makes use of the information of the current residuals to adaptively construct basis functions in the online stage to reduce the error of multiscale approximation. A complete analysis of the method is presented, which shows the proposed online enrichment leads to a fast convergence from multiscale approximation to the fine-scale solution. The error reduction can be made sufficiently large by suitably selecting oversampling regions and the number of oversampling layers. Further, the convergence rate of the enrichment algorithm depends on a factor of exponential decay regarding the number of oversampling layers and a user-defined parameter. Numerical results are provided to demonstrate the effectiveness and efficiency of the proposed online adaptive algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced order methods are demanded. Combining these techniques with nonlinearity, we will consider in this paper a dual-continuum model which is generalized as a multi-continuum model for a coupled system of nonlinear Richards equations as unsaturated flows, in complex heterogeneous fractured porous media; and we will solve it by a novel multiscale approach utilizing the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). In particular, such a nonlinear system will be discretized in time and then linearized by Picard iteration (whose global convergence is proved theoretically). Subsequently, we tackle the resulting linearized equations by the CEM-GMsFEM and obtain proper offline multiscale basis functions to span the multiscale space (which contains the pressure solution). More specifically, we first introduce two new sources of samples, and the GMsFEM is used over each coarse block to build local auxiliary multiscale basis functions via solving local spectral problems, that are crucial for detecting high-contrast channels. Second, per oversampled coarse region, local multiscale basis functions are created through the CEM as constrainedly minimizing an energy functional. Various numerical tests for our approach reveal that the error converges with the coarse-grid size and that only few oversampling layers as well as basis functions are needed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Single-channel and single-energy partial-wave analysis with continuity improved through minimal phase constraints

Single-energy partial-wave analysis has often been applied as a way to fit data with minimal model dependence. However, remaining unconstrained, partial waves at neighboring energies will vary discontinuously because the overall amplitude phase cannot be determined through single-channel measurements. This problem can be mitigated through the use of a constraining penalty function based on an associated energy-dependent fit. However, the weight given to this constraint results in a biased fit to the data. In this paper, for the first time, we explore a constraining function which does not influence the fit to data. The constraint comes from the overall phase found in multichannel fits which, in the present study, are the Bonn-Gatchina and Jülich-Bonn multichannel analyses. The data are well reproduced and weighting of the penalty function does not influence the result. The method is applied to K⁢Λ photoproduction data and all observables can be maximally well reproduced. While the employed multichannel analyses display very different multipole amplitudes, we show that the major difference between two sets of multipoles can be related to the different overall phases.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Multistage economic MPC for systems with a cyclic steady state: A gas network case study

Multistage model predictive control (MPC) provides a robust control strategy for dynamic systems with uncertainties and a setpoint tracking objective. Moreover, extending MPC to minimize an economic cost instead of tracking a pre-calculated optimal setpoint improves controller performance. This paper presents a novel multistage economic nonlinear model predictive control (E-NMPC) framework for dynamic systems operating under uncertainty, with specific application to natural gas transmission networks. A key innovation lies in the integration of cyclic steady-state (CSS) constraints within the multistage MPC formulation, enabling the controller to manage periodic operating conditions commonly observed in energy systems. A Lyapunov-based descent condition is enforced to ensure robust stability of the controller. The multistage economic MPC framework is validated on two gas pipeline case studies, where it successfully minimizes net energy consumption, respects operational constraints under uncertain demand profiles, and guides the network to optimal cyclic operation. The Lyapunov function remains bounded in both case studies, validating the robust stability of multistage E-NMPC.

03 NATURAL GAS↗
DOE OSTI2023

Framework for phase transitions between the Maxwell and Gibbs constructions

By taking the nucleon-to-quark phase transition within a neutron star as an example, we present a thermodynamically consistent method to calculate the equation of state of ambient matter so that transitions that are intermediate to those of the familiar Maxwell and Gibbs constructions can be described. This method does not address the poorly known surface tension between the two phases microscopically (as, for example, in the calculation of the core pasta phases via the Wigner-Seitz approximation) but instead combines the local and global charge neutrality conditions characteristic of the Maxwell and Gibbs constructions, respectively. Overall charge neutrality is achieved by dividing the leptons to those that obey local charge neutrality (Maxwell) and those that maintain global charge neutrality (Gibbs). The equation of state is obtained by using equilibrium constraints derived from minimizing the total energy density. The results of this minimization are then used to calculate neutron star mass-radius curves, tidal deformabilities, equilibrium and adiabatic sound speeds, and nonradial g-mode oscillation frequencies for several intermediate constructions. Various quantities of interest transform smoothly from their Gibbs structures to those of Maxwell as the local-to-total electron ratio η, introduced to mimic the hadron-to-quark interface tension from 0 (Gibbs) to ∞ (Maxwell), is raised from 0 to 1. As a result, a notable exception is the g-mode frequency for the specific case of η = 1 for which a gap appears between the quark and hadronic branches.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Including Physics-Informed Atomization Constraints in Neural Networks for Reactive Chemistry

Machine learning interatomic potentials (MLIPs) have emerged as powerful tools for investigating atomistic systems with high accuracy and a relatively low computational cost. However, a common and unaddressed challenge with many current neural network (NN) MLIP models is their limited ability to accurately predict the relative energies of systems containing isolated or nearly isolated atoms, which appear in various reactive processes. To address this limitation, we present a mathematical technique for modifying any existing atom-centered NN architecture to account for the energies of isolated atoms. The result produces a consistent prediction of the atomization energy (AE) of a system using minimal constraints on the model. Using this technique, we build a model architecture that we call hierarchically interacting particle neural network (HIP-NN)-AE, an AE-constrained version of the HIP-NN, as well as ANI-AE, the AE-constrained version of the accurate NN engine for molecular energies (ANI). Our results demonstrate AE consistency of AE-constrained models, which drastically improves the AE predictions for the models. We compare the AE-constrained approach to unconstrained models as well as models from the literature in other scenarios, such as bond dissociation energies, bond dissociation pathways, and extensibility tests. These results show that the constraints improve the model performance in some of these tasks and do not negatively affect the performance on any tasks. The AE constraint approach thus offers a robust solution to the challenges posed by isolated atoms in energy prediction tasks.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

A kinetic-based regularization method for data science applications

We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce corrections that impose constraints on the lower-order moments of the data distribution. This minimizes the discrepancy between the discrete and continuum representations of the data, in turn allowing to access more favorable energy landscapes, thus improving the accuracy of the interpolator. Our approach improves performance in both interpolation and regression tasks, even in high-dimensional spaces. Unlike traditional methods, it does not require empirical parameter tuning, making it particularly effective for handling noisy data. We also show that thanks to its local nature, the method offers computational and memory efficiency advantages over Radial Basis Function interpolators, especially for large datasets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A novel technique for minimizing energy functional using neural networks

An energy functional describes the equilibrium state of a system. In this work, we present a novel technique, Functional Optimization using Neural Networks (FONN), for minimizing the system’s energy. FONN utilizes neural networks to process information at discrete grid points, considering their interactions with neighboring grid points, to update the state of the system. The training process involves formulating a loss function based on the system’s energy, and with the help of multiple fine-tuning steps, the method employs a progressive energy reduction technique that decreases the energy in multiple steps. FONN’s effectiveness is demonstrated across various problems, including the minimization of the heat and Lyapunov energy. Furthermore, the paper explores the minimization of the elastic bending energy with an area constraint.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantum Many-Body Theory from a Solution of the N -Representability Problem

Here, in this study, we present a many-body theory based on a solution of the N-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an equation that re-expresses physical constraints on higher-order RDMs to generate direct constraints on the 2-RDM, which are required for its derivation from an N-particle density matrix, known as N-representability conditions. The approach produces a complete hierarchy of 2-RDM constraints that do not depend explicitly upon the higher RDMs or the wave function. By using the two-particle part of a unitary decomposition of higher order constraint matrices, we can solve the energy minimization by semidefinite programming in a form where the low-rank structure of these matrices can be potentially exploited. We illustrate by computing the ground-state electronic energy and properties of the H 8 ring.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Constrained Local Approximate Ideal Restriction for Advection-Diffusion Problems

Herein this paper focuses on developing a reduction-based algebraic multigrid (AMG) method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure advection to pure diffusion. Initial motivation comes from a new reduction-based AMG approach, $\ell \text{AIR}$ (local approximate ideal restriction), that was developed for solving advection-dominated problems. Though this new solver is very effective in the advection-dominated regime, its performance degrades in cases where diffusion becomes dominant. This is consistent with the fact that in general, reduction-based AMG methods tend to suffer from growth in complexity and/or convergence rates as the problem size is increased, especially for diffusion-dominated problems in two or three dimensions. Motivated by the success of $\ell \text{AIR}$ in the advective regime, our aim in this paper is to generalize the AIR framework with the goal of improving the performance of the solver in diffusion-dominated regimes. To do so, we propose a novel way to combine mode constraints as used commonly in energy-minimization AMG methods with the local approximation of ideal operators used in $\ell \text{AIR}$. The resulting constrained $\ell \text{AIR}$ algorithm is able to achieve fast scalable convergence on advective and diffusive problems. In addition, it is able to achieve standard low complexity hierarchies in the diffusive regime through aggressive coarsening, something that was previously difficult for reduction-based methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Pareto-optimal target definition for multi-axis random vibration testing

In random vibration testing with multiple control channels, existing control laws require specification of a complete spectral density matrix at each control frequency. Spectral density matrices include autospectral densities on the diagonal and cross-spectral densities on the off-diagonal. In practice, the off-diagonal terms are often unknown, and recent vibration testing research has focused on fixing the diagonal and specifying the off-diagonal to minimize the required control energy, subject to a constraint that the target matrix is positive semidefinite. This paper shows that, even with a fixed diagonal, off-diagonal terms strongly affect control residuals. This overlooked effect occurs in both square and rectangular systems. By jointly considering input energy and control residuals, open-loop inputs are derived directly from the diagonal without specifying the off-diagonal terms. Vibration targets that can be used in closed-loop control are then derived using the optimal inputs, with positive semidefinite constraints applied during the derivation. The result is a set of Pareto-optimal control solutions. For each solution in the set, any other possible solution produces greater control error, greater input energy, or both. A balanced solution is selected automatically, though others can be chosen based on test needs. Simulations and experiments show that the proposed method outperforms state-of-the-art energy-minimizing approaches, achieving significant reductions in both control error and input energy.

Autospectral density↗
DOE OSTI2024

Accuracy of the explicit energy-conserving particle-in-cell method for under-resolved simulations of capacitively coupled plasma discharges

The traditional explicit electrostatic momentum-conserving particle-in-cell algorithm requires strict resolution of the electron Debye length to deliver numerical stability and accuracy. The explicit electrostatic energy-conserving particle-in-cell algorithm alleviates this constraint with minimal modification to the traditional algorithm, retaining its simplicity, ease of parallelization, and acceleration on modern supercomputing architectures. In this article, we apply the algorithm to model a one-dimensional radio frequency capacitively coupled plasma discharge relevant to industrial applications. The energy-conserving approach closely matches the results from the momentum-conserving algorithm and retains accuracy even for cell sizes up to 8 times the electron Debye length. For even larger cells, the algorithm loses accuracy due to poor resolution of steep gradients within the radio frequency sheath. Accuracy can be recovered by adopting a non-uniform grid, which resolves the sheath and allows for cell sizes up to 32 times the electron Debye length in the quasi-neutral bulk of the discharge. The effect is an up to 8 times reduction in the number of required simulation cells, an improvement that can compound in higher-dimensional simulations. We therefore consider the explicit energy-conserving algorithm as a promising approach to significantly reduce the computational cost of full-scale device simulations and a pathway to delivering kinetic simulation capabilities of use to industry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Operational Simulation of Multi-Functional Charging Station for Sustainable Transportation

As transportation systems move toward electrification and decarbonization, multifunctional charging stations (MFCS) are emerging as key infrastructure for electric vehicles (EVs) and hydrogen fuel cell vehicles (HFCVs). This paper presents a simulation model of an MFCS that integrates solar photovoltaic (PV), wind power, battery storage, hydrogen (\mathrm{H}_{2}) production, dual-pressure \mathrm{H}_{2} storage, fuel cells, and dynamic grid interactions. The model simulates daily operations using 5 -minute resolution data to capture realtime variability in renewable energy (RE), demand, and electricity prices. A flexible dispatch algorithm dynamically allocates energy for EV charging, \mathrm{H}_{2} production, storage, and grid transactions while respecting system constraints. Results show that the MFCS effectively prioritizes RE usage, minimizes waste, meets diverse energy demands, and achieves net operational profit. The model serves as a valuable decision-support tool for designing and optimizing integrated clean energy hubs for zero-emission transportation.

Gbadegoye, Jeremiah [University of Tennessee, Knox↗
DOE OSTI2022

Optimization of key energy and performance metrics for drug product manufacturing

During the development of pharmaceutical manufacturing processes, detailed systems-based analysis and optimization are required to control and regulate critical quality attributes within specific ranges, to maintain product performance. As discussions on carbon footprint, sustainability, and energy efficiency are gaining prominence, the development and utilization of these concepts in pharmaceutical manufacturing are seldom reported, which limits the potential of pharmaceutical industry in maximizing key energy and performance metrics. Based on an integrated modeling and techno-economic analysis framework previously developed by the authors, this study presents the development of a combined sensitivity analysis and optimization approach to minimize energy consumption while maintaining product quality and meeting operational constraints in a pharmaceutical process. The optimal input process conditions identified were validated against experiments and good agreement resulted between simulated and experimental data. Here, the results also allowed for a comparison of the capital and operational costs for batch and continuous manufacturing schemes under nominal and optimized conditions. Using the nominal batch operations as a basis, the optimized batch operation results in a 71.7% reduction of energy consumption, whereas the optimized continuous case results in an energy saving of 83.3%.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Optimal Management of Grid-Interactive Efficient Buildings via Safe Reinforcement Learning

Reinforcement learning (RL)-based methods have achieved significant success in managing grid-interactive efficient buildings (GEBs). However, RL does not carry intrinsic guarantees of constraint satisfaction, which may lead to severe safety consequences. Besides, in GEB control applications, most existing safe RL approaches rely only on the regularisation parameters in neural networks or penalty of rewards, which often encounter challenges with parameter tuning and lead to catastrophic constraint violations. To provide enforced safety guarantees in controlling GEBs, this paper designs a physics-inspired safe RL method whose decision-making is enhanced through safe interaction with the environment. Different energy resources in GEBs are optimally managed to minimize energy costs and maximize customer comfort. The proposed approach can achieve strict constraint guarantees based on prior knowledge of a set of developed hard steady-state rules. Simulations on the optimal management of GEBs, including heating, ventilation, and air conditioning (HVAC), solar photovoltaics, and energy storage systems, demonstrate the effectiveness of the proposed approach.

Huo, Xiang↗
DOE OSTI2026

BLING

The Bounded Linearized Iteration for Natural Gas (BLING) algorithm solves an optimization problem for gas pipeline flow scheduling that maximizes economic surplus and minimizes the energy used for gas compression subject to pressure, flow, and engineering constraints.

Zlotnik, Anatoly↗
DOE OSTI2026

Reference floating wind array designs for three representative regions

This work presents the systematic development of three open-source reference floating wind array designs. The designs are tailored to representative site conditions for three regions of the United States: Humboldt Bay off the coast of California, the Gulf of Maine, and the Gulf of America. We adopted existing reference designs for the individual 15 MW turbines, semisubmersible floating platforms, substations, mooring systems, and power cables – integrating and adapting them as needed for each location. We adapted existing dynamic cable designs to use larger conductor sizes to meet the arrays' power transmission requirements, and we set up redundant mooring systems for each substation. The layout of each array is a uniform-grid design optimized to approximately minimize the levelized cost of energy (LCOE) within a square lease area while satisfying spatial constraints. These constraints ensure adequate clearances between adjacent turbines and between underwater components during the layout optimization to prevent clashing and ensure that all components reside within the lease boundaries. Substations are included to allow accounting for intra-array cable costs. They are placed within the uniform grid to maintain the navigability of the arrays. For each feasible layout considered, annual energy production and cable routing costs are calculated and updated in the LCOE objective function. After the optimization, we refined the cable routing with a mix of algorithmic and manual methods to ensure that the cables avoid mooring system components and approach the substation with adequate clearances. We confirmed the suitability of each reference array's layout by comparing the wake losses at each wind heading angle to the wind rose, observing that the optimized layouts largely avoid wake losses in the predominant wind directions. These reference arrays provide open-source baseline designs to enable future research and innovation of floating wind technology at the array scale.

17 WIND ENERGY↗
DOE OSTI2026

First Solar Thermal Energy Planner (STEP 1) and Nationwide Industrial Heat and Power Analysis

The First Solar Thermal Energy Planner (STEP 1) and Nationwide Industrial Heat and Power Analysis (aka the STEP 1 Project or the Project) aimed to (1) developed a brand-new web tool that could provide decision support through free, rapid techno-economic analysis of behind-the-meter solar+storage systems for industrial process heat and (2) conduct high-level analyses of the cost-competitiveness of the same systems across the US in key sectors. The STEP 1 web tool collects key location, land availability, thermal load profile, proccess heat temperature and media, and other key parameters through an easy-to-use user interface (UI). The UI was designed to meet the user at their level of understanding by minimizing the number of required inputs as much as possible while including options for more nuanced inputs if the user desires. STEP 1 advises users on which solar thermal tehcnologies that could fit their needs based on the inputs provided (namely process media and temperature). The tool can model a wide range of solar thermal technologies including flat plate collectors, evacuated tubes, parabolic troughs, linear Fresnel, and molten salt towers all with corresponding thermal energy storage (TES) - solar PV with resistive heating and TES is also included. Once the parameters are collected, a nominal thermal energy production profile for the facility's location is generated using NREL's System Advisory Model (SAM) and then passed to a modified version of NREL's REopt platform to optimize the size (capacity) and dispatch of the solar+storage system to minimize lifecycle costs subject to energy balance, fuel and electricity rates, emission reductions goals, and other constraints. This entire process takes less than 20 minutes, is completely free, requires zero coding skills, and provides the user with a high-level assessment on the techno-economic feasability of deploying solar+storage systems for their energy needs. In addition to the development of the STEP 1 web tool, the project completed two complementary analyses focused on leveraging the backend code of STEP 1, public industrial facility locations and fuel consumption data, and key sector information to assess the economic opportunity of reducing fuel costs at various levels of capacity factor around the US. Both analyses found that there are key markets, locations, industrial sectors (namely food and beverage), and degrees of offset where solar thermal technologies could be cost-effectively deployed, highlighting a key market entry point for these technologies, and assessing deployment potential. In summary, the STEP 1 project improved the opportunities for solar+storage systems to expand into the industrial process heat market through breaking down barriers to assessing these technologies.

14 SOLAR ENERGY↗