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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 OSTI2022

A computationally efficient algorithm for computing convex hull prices

Electricity markets worldwide allow participants to bid non-convex production offers. While non-convex offers can more accurately reflect a resource's capabilities, they create challenges for market clearing processes. For example, system operators may be required to execute side payments to participants whose costs are not covered through energy sales as determined via traditional locational marginal pricing schemes. Convex hull pricing minimizes this and other types of side payments while providing uniform (i.e., locationally and temporally consistent) prices. Computing convex hull prices involves solving either a large-scale linear program or the Lagrangian dual of the corresponding non-convex scheduling problem. Further, the former approach requires explicit descriptions of market participants' convex hulls. While linear programs for computing convex hull prices are large, their structure is naturally decomposable by generators. Here, in this work, we propose and empirically analyze a Benders decomposition approach to computing convex hull prices that leverages recent advances in convex hull formulations for thermal generating units. We demonstrate across a large set of test instances that our decomposition approach only requires modest computational effort, obtaining solutions at least an order of magnitude faster than the equivalent large-scale linear programming approach. Overall, we provide a computationally feasible method for computing convex hull prices for industrial scale market clearing problems, enabling the possibility of practical adoption of this advanced pricing mechanism.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

A Computationally Efficient Algorithm for Computing Convex Hull Prices

Electricity markets worldwide allow participants to bid non-convex production offers. While non-convex offers can more accurately reflect a resource's capabilities, they create challenges for market clearing processes. For example, system operators may execute side payments when a participant’s cost is not covered through energy sale settlements from locational marginal pricing schemes, or when a participant incurs lost opportunity costs to follow the dispatch signal. Convex hull pricing minimizes these and other types of side payments while providing uniform (i.e., locationally and temporally consistent) prices. However, computing convex hull prices involves solving either a large-scale linear program - which in turn requires explicit descriptions of market participants’ convex hulls -or the Lagrangian dual of the corresponding non-convex scheduling problem. Here, we propose a computationally feasible and industrially scalable Benders decomposition approach to computing convex hull prices at least an order of magnitude faster than the current state-of-the-art while leveraging recent advances in convex hull formulations for thermal generating units.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2024

Fast, Nondestructive and Precise Biomass Measurements Are Possible Using Lidar-Based Convex Hull and Voxelization Algorithms

Light detection and ranging (lidar) scanning tools are available that can make rapid digital estimations of biomass. Voxelization and convex hull are two algorithms used to calculate the volume of the scanned plant canopy, which is correlated with biomass, often the primary trait of interest. Voxelization splits the scans into regular-sized cubes, or voxels, whereas the convex hull algorithm creates a polygon mesh around the outermost points of the point cloud and calculates the volume within that mesh. In this study, digital estimates of biomass were correlated against hand-harvested biomass for field-grown corn, broom corn, and energy sorghum. Voxelization (r = 0.92) and convex hull (r = 0.95) both correlated well with plant dry biomass. Lidar data were also collected in a large breeding trial with nearly 900 genotypes of energy sorghum. In contrast to the manual harvest studies, digital biomass estimations correlated poorly with yield collected from a forage harvester for both voxel count (r = 0.32) and convex hull volume (r = 0.39). However, further analysis showed that the coefficient of variation (CV, a measure of variability) for harvester-based estimates of biomass was greater than the CV of the voxel and convex-hull-based biomass estimates, indicating that poor correlation was due to harvester imprecision, not digital estimations. Overall, results indicate that the lidar-based digital biomass estimates presented here are comparable or more precise than current approaches.

Environmental Sciences & Ecology↗
NASA NTRS1991

A fast adaptive convex hull algorithm on two-dimensional processor arrays with a reconfigurable BUS system

A bus system that can change dynamically to suit computational needs is referred to as reconfigurable. We present a fast adaptive convex hull algorithm on a two-dimensional processor array with a reconfigurable bus system (2-D PARBS, for short). Specifically, we show that computing the convex hull of a planar set of n points taken O(log n/log m) time on a 2-D PARBS of size mn x n with 3 less than or equal to m less than or equal to n. Our result implies that the convex hull of n points in the plane can be computed in O(1) time in a 2-D PARBS of size n(exp 1.5) x n.

Olariu, S.↗
NASA NTRS1991

Rule groupings in expert systems using nearest neighbour decision rules, and convex hulls

Expert System shells are lacking in many areas of software engineering. Large rule based systems are not semantically comprehensible, difficult to debug, and impossible to modify or validate. Partitioning a set of rules found in CLIPS (C Language Integrated Production System) into groups of rules which reflect the underlying semantic subdomains of the problem, will address adequately the concerns stated above. Techniques are introduced to structure a CLIPS rule base into groups of rules that inherently have common semantic information. The concepts involved are imported from the field of A.I., Pattern Recognition, and Statistical Inference. Techniques focus on the areas of feature selection, classification, and a criteria of how 'good' the classification technique is, based on Bayesian Decision Theory. A variety of distance metrics are discussed for measuring the 'closeness' of CLIPS rules and various Nearest Neighbor classification algorithms are described based on the above metric.

Anastasiadis, Stergios↗
DOE OSTI2021

Extended convex hull-based distributed optimal energy flow of integrated electricity-gas systems

Integrated electricity and gas systems are constructed to facilitate the gas-fired generation, and the distributed operation of these integrated systems have received much attention due to the increased emphasis on data security and privacy between different agencies. This paper proposes an extended convex hull based method to address optimal energy flow problems for the integrated electricity and gas systems in a distributed manner. First, a multi-block electricity-gas system model is constructed by dividing the whole system into N blocks considering both physical and regional differences. This multi-block model is then convexified by replacing the nonconvex gas transmission equation with the extended convex hull-based constraints. The Jacobi-Proximal alternating direction method of multipliers algorithm is adopted to solve the convexified model and minimize its operation cost. Finally, the feasibility of the optimal solution for the convexified model is checked, and a sufficient condition is developed. If the sufficient condition is satisfied, the optimal solution for the original nonconvex problem can be recovered from that for the convexified problem. Simulation results demonstrate that the proposed method is tractable and effective in obtaining feasible optimal solutions for multi-block optimal energy flow problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Computational discovery of stable and metastable ternary oxynitrides

Materials design from first principles enables exploration of uncharted chemical spaces. Extensive computational searches have been performed for mixed-cation ternary compounds, but mixed-anion systems are gaining increased interest as well. Central to computational discovery is the crystal structure prediction, where the trade-off between reliance on prototype structures and size limitations of unconstrained sampling has to be navigated. We approach this challenge by letting two complementary structure sampling approaches compete. We use the kinetically limited minimization approach for high-throughput unconstrained crystal structure prediction in smaller cells up to 21 atoms. On the other hand, ternary—and, more generally, multinary—systems often assume structures formed by atomic ordering on a lattice derived from a binary parent structure. Thus, we additionally sample atomic configurations on prototype lattices with cells up to 56 atoms. Using this approach, we searched 65 different charge-balanced oxide–nitride stoichiometries, including six known systems as the control sample. The convex hull analysis is performed both for the thermodynamic limit and for the case of synthesis with activated nitrogen sources. We identified 34 phases that are either on the convex hull or within a viable energy window for potentially metastable phases. We further performed structure sampling for “missing” binary nitrides whose energies are needed for the convex hull analysis. Among these, we discovered metastable Ce3N4 as a nitride analog of the tetravalent cerium oxide, which becomes stable under slightly activated nitrogen condition µN > +0.07 eV. Given the outsize role of CeO2 in research and application, Ce3N4 is a potentially important discovery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Sequence of polyhedral relaxations for nonlinear univariate functions

Here, given a nonlinear, univariate, bounded, and differentiable function f(x), this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of f(x) and its convex hull, respectively. Theoretical convergence of the sequence of relaxations to the graph of the function and its convex hull is established. For nonlinear non-convex optimization problems, the relaxations presented in this article can be used to construct tight MILP and LP relaxations. These MILP and the LP relaxations can also be used with MILP-based and spatial branch-and-bound based global optimization algorithms, respectively.

42 ENGINEERING↗
DOE OSTI2025

Machine learning guided search for energetically favorable metal borocarbide ternary compounds

In this work, we employ machine-learning (ML) combined with first principles calculations to efficiently search for the energetically favorable metal borocarbide (M-B-C) ternary compounds with M being the group 1–3 metal elements. Using a crystal graph convolutional neural network (CGCNN) ML approach followed by first-principles calculations, we predicted 47 energetically favorable stable and metastable ternary Na-B-C, Ca-B-C, and La-B-C ternary compounds with their decomposition energy (E d ) below or within 100 meV/atom from the currently known convex hulls. Phonon spectra and electronic structures of the 14 energetically favorable stable structures are also investigated by first-principles calculations. By substituting the metal atoms in the 29 energetically favorable non-equivalent template structures of Na (Ca, La)-B-C with other group 1–3 elements in the periodic table, we further obtain 22 stable structures and 52 metastable structures (E d ≤100 meV/atom with respect to the known convex hulls) for Li-B-C, K-B-C, Rb-B-C, Mg-B-C, Sr-B-C, Ba-B-C, Sc-B-C and Y-B-C ternary compounds. New convex hulls including our newly predicted stable ternary structures and the known stable structures are constructed for the M-B-C systems. The results obtained by our ML guided first-principles calculations enrich our knowledge in the structure and energy landscape of metal borocarbide ternary compounds and provide useful guidance for further experimental synthesis and discovery.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Data mining the missing ordered phases of Li/Na metal oxides

Data-driven discovery of Li-ion and Na-ion battery materials has been pioneered by generic materials data platforms such as the Materials Project. After decades of progress, it is timely to ask whether there remain underexplored compositional spaces. Here, in this work, we present a systematic data-mining effort to uncover missing ordered binary, ternary and quaternary Li/Na-containing metal oxides using high-throughput density functional theory (DFT). Building on 19,120 stable and metastable oxides entries from the Materials Project, we performed 13,245 additional calculations through isovalent substitutions of known ground states, experimentally reported compounds, and specific prototype structures. Our study identifies 36 new ground states within the GGA/GGA + U convex hull and 45 within the r 2 SCAN convex hull. Additionally, we identified 840 metastable compounds from GGA/GGA + U and 979 from r 2 SCAN that are absent in the present Materials Project databases. Moreover, we have tripled the metastable materials in compositional spaces with a molar ratio of cation/anion >1, highlighting the overlooked opportunities in this compositional space.

25 ENERGY STORAGE↗
DOE OSTI2020

Crystal Structure Prediction of Binary Alloys via Deep Potential

Predicting crystal structure has been a challenging problem in physics and materials science for a long time. A reliable energy calculation engine combined with an efficient global search algorithm, such as particle swarm optimization algorithm or genetic algorithm, is needed to conduct crystal structure prediction. In recent years, machine learning-based interatomic potential energy surface models have been proposed, potentially allowing us to perform crystal structure prediction for systems with the accuracy of density functional theory (DFT) and the speed of empirical force fields. In this paper, we employ a previously developed Deep Potential model to predict the intermetallic compound of the aluminum–magnesium system, and find six meta-stable phases with negative or nearly zero formation energy. In particular, Mg 12 Al 8 shows excellent ductility and Mg 5 Al 27 has a high Young's modulus. Based on our benchmark results, we propose a relatively robust structure screening criterion that selects potentially stable structures from the Deep Potential-based convex hull and performs DFT refinement. By using this criterion, the computational cost needed to construct the convex hull with ab initio accuracy can be dramatically reduced.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Remark on Algorithm 1012: Computing Projections with Large Datasets

In ACM TOMS Algorithm 1012, the DELAUNAYSPARSE software is given for performing Delaunay interpolation in medium to high dimensions. When extrapolating outside the convex hull of the training set, DELAUNAYSPARSE calls the nonnegative least squares solver DWNNLS to compute projections onto the convex hull. However, DWNNLS and many other available sum-of-squares optimization solvers were not intended for usage with many variable problems, which result from the large training sets that are typical in machine learning applications. Thus, a new PROJECT subroutine is given, based on the highly customizable quadratic program solver BQPD. This solution is shown to be as robust as DELAUNAYSPARSE for projection onto both synthetic and real-world datasets, where other available solvers frequently fail. Although it is intended as an update for DELAUNAYSPARSE, due to the difficulty and prevalence of the problem, this solution is likely to be of external interest as well.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Machine Learning-Guided Discovery of Ternary Compounds Containing La, P, and Group 14 Elements

In this work, we integrate a deep machine learning (ML) method with first-principles calculations to efficiently search for the energetically favorable ternary compounds. Using La–Si–P as a prototype system, we demonstrate that ML-guided first-principles calculations can efficiently explore crystal structures and their relative energetic stabilities, thus greatly accelerate the pace of material discovery. A number of new La–Si–P ternary compounds with formation energies less than 30 meV/atom above the known ternary convex hull are discovered. Among them, the formation energies of La 5 SiP 3 and La 2 SiP phases are only 2 and 10 meV/atom, respectively, above the convex hull. These two compounds are dynamically stable with no imaginary phonon modes. Moreover, by replacing Si with heavier-group 14 elements in the eight lowest-energy La–Si–P structures from our ML-guided predictions, a number of low-energy La–X–P phases (X = Ge, Sn, Pb) are predicted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Ellipsoidal Fitting Methodology for Defect Clusters in Gallium Arsenide

In assessing the initial spatial distribution of defects from neutron or heavy ion irradiation, it is useful to have a reliable, automated, and fast-running tool to evaluate characteristic metrics such as the number of sub-clusters or the overall cluster volume. The latter metric, for instance, can be utilized to estimate a reference neutron fluence level at which inter-cluster interaction effects begin to become significant. This paper details a methodology to fit an arbitrarily complex defect map with a set of ellipsoids (one per identified sub-cluster) in which the constituent defects of a sub-cluster are determined using fuzzy degree-of-membership analysis. Specifically, a parameterized model is developed for point defects in gallium arsenide. Cluster volume calculations based on the model are compared against convex hull and single- ellipsoid representations. Results show that the parameterized sub-cluster model begins to deviate from the two reference models at a recoil energy of about 100 keV in GaAs, with the convex hull and single-ellipsoid representations increasingly overestimating the volume thereafter.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗