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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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33 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Piecewise linear approximation with minimum number of linear segments and minimum error: A fast approach to tighten and warm start the hierarchical mixed integer formulation

In several areas of economics and engineering, it is often necessary to fit discrete data points or approximate nonlinear functions with continuous functions. Piecewise linear (PWL) functions are a convenient way to achieve this. PWL functions can be modeled in mathematical problems using only linear and integer variables. Moreover, there is a computational benefit in using PWL functions that have the least possible number of segments. This work proposes a novel hierarchical mixed integer linear programming (MILP) formulation that identifies a continuous PWL approximation with minimum number of linear segments for a given target maximum error. The proposed MILP formulation also identifies the solution with the least maximum error among the solutions with minimum number of segments. Then, this work proposes a fast iterative algorithm that identifies non necessarily continuous PWL approximations by solving O(S log N) linear programming (LP) problems, where N is the number of data points and S is the minimum number of segments in the non necessarily continuous case. This work demonstrates that tight bounds for the MILP problem can be derived from these approximations. Next, a fast algorithm is introduced to transform a non necessarily continuous PWL approximation into a continuous one. Finally, the tight bounds and the continuous PWL approximations are used to tighten and warm start the MILP problem. The tightened formulation is shown in experimental results to be more efficient, especially for large data sets, with a solution time that is up to two orders of magnitude less than the existing literature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

NREL Price Series Developed for the ARPA-E FLECCS Program

The price data for four regions (CAISO, ERCOT, MISO-W, and PJM-W) are developed using the ReEDS to PLEXOS conversion as described in (Gagnon et al. 2020). The reference ReEDS case chosen is based on the 2020 Standard Scenario Mid-case, which uses the 2020 ReEDS model version (Cole et al. 2020; Ho et al. 2021). All ReEDS model inputs use 2020 Standard Scenarios Mid-case assumptions except for CO2 prices, which are implemented as linearly increasing CO2 price trajectories beginning at $0/tCO2 in 2020 and ending at either $100/tCO2 or $150/tCO2 in 2035 to dive capacity expansion towards a low-carbon system that could support CCS deployment. However, these scenarios also prohibit CCS deployment in this time frame so that resulting price data are not influenced by the deployment and operation of CCS itself. Implementing the ReEDS to PLEXOS conversion tool, PLEXOS is then simulated using the 2035 ReEDS infrastructure for both CO2 price scenarios, with the following model version and setup: PLEXOS Version: 8.2 Solver: Xpress-MP 35.01.01 Mixed integer optimization relative gap 1% System configuration: • Total number of nodes: 134 (consistent with ReEDS balancing areas) • Line losses enforced using piecewise linear approximation • Energy dump was enabled Price data is aggregated to the ISO/RTO level using load-weighted averages. References: Cole, Wesley, Sean Corcoran, Nathaniel Gates, Daniel Mai, Trieu, and Paritosh Das. 2020. “2020 Standard Scenarios Report: A U.S. Electricity Sector Outlook.” NREL/TP-6A20-77442. Golden, CO: National Renewable Energy Laboratory. https://www.nrel.gov/docs/fy21osti/77442.pdf. Gagnon, Pieter, Will Frazier, Elaine Hale, and Wesley Cole. 2020. “Cambium Documentation: Version 2020.” NREL/TP-6A20-78239. National Renewable Energy Lab. (NREL), Golden, CO (United States). https://doi.org/10.2172/1734551. Ho, Jonathan, Jonathon Becker, Maxwell Brown, Patrick Brown, Ilya (ORCID:0000000284917814) Chernyakhovskiy, Stuart Cohen, Wesley (ORCID:000000029194065X) Cole, et al. 2021. “Regional Energy Deployment System (ReEDS) Model Documentation: Version 2020.” NREL/TP-6A20-78195. Golden, CO: National Renewable Energy Laboratory. https://doi.org/10.2172/1788425.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

ASP (Adaptive Splines for Prediction) [SWR-22-66]

This software package provides functionality to fit piecewise cubic splines to model the relationship between a univariate X (independent variable) and a univariate Y (dependent variable). The output is akin to linear regression but has higher "capacity" in that it can learn more complicated relationships despite leveraging only a single predictor. It thus can learn very reasonable relationships between X and Y with minimal effort. The canonical intended use case is for predicting electric demand (Y) from temperature (X). There can be complicated, non-linear relationships between these two variables, but these can be reasonably approximated by the sum of: 1) an "aggregate" relationship between daily average temperature and daily average demand, and 2) intra-day patterns represented as hourly offsets from the daily average load. The spline functionality is used for learning a robust "aggregate" relationship without the inconvenience of manual feature engineering while still ensuring robust results. The model fitting workhorse is R's built-in smooth.spline. This package provides a suite of options for controlling how smooth.spline fits a spline to the data. In particular, it is designed to return a model with a single critical point (i.e., a single location along the domain/support where the first derivative is zero). This is to ensure that predicted changes in electric demand are always positive as temperatures become more extreme. This helps to prevent overfitting, particularly when the input data has few observations or has significant uncertainty from other sources.

Murphy, Sinnott↗
DOE OSTI2020

Piecewise Linear Optimization for Public EV Charging Depots in Different Utility Environments

With the proliferation of electric vehicles (EVs), EV supply equipment technology is being pushed to increasingly higher power levels, such as extreme fast charging (XFC) at 300kW or more. As more public XFC depots are connected to electric distribution systems, utility operators will mitigate their impact with pricing schemes and programs such as demand response, demand charges, and time-varying prices. In this paper we describe an XFC management system that combines an on-site battery energy storage system and an optimization application that minimizes the cost to operate the depot in light of the utility pricing programs. We have designed the optimizer specially to use fast and simple linear programming so that it can be deployed to low-cost computing platforms. We also describe how several utility pricing schemes are integrated into a single piecewise model, reducing the engineering effort to implement the optimizer in different utility environments.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Adiabatic behavior of an elliptical vortex in a time-dependent external strain flow

The adiabatic behavior of two-dimensional (2D) fluid vortices subject to slowly varying, time-dependent external strain flows is studied theoretically, and experimentally using magnetized non-neutral electron plasmas. Here the E × B drift dynamics of the electrons perpendicular to the magnetic field are analogous to the motion of fluid vorticity under the 2D Euler equations describing ideal fluids. A low-dimensional elliptical vortex patch model is used along with a WKB approximation to derive a formula for the breaking of an adiabatic invariant due to the changing external flow. The invariant is interpreted as the amplitude of a perturbative oscillation about a stable fixed point corresponding to a steady elliptical vortex. Smooth, hyperbolic tangent and piecewise linear ramp functions are considered for the external strain time dependence. Standard exponential breaking is observed in the former case, whereas the latter exhibits a power-law breaking curve with periodic modulation. It is found that a driving term in the equations of motion contributes the majority of the breaking whereas the frequency variation plays a weaker, but significant role. The experimental data agree closely with the theoretical model. The most significant deviation is due to inviscid damping behavior associated with the smooth edges of the experimental vortices, which tends to reduce the amplitude of the oscillation. Finally, the results are compared and contrasted with other related experimental, numerical, and theoretical work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Factorization Machine‐Based Active Learning for Functional Materials Design with Optimal Initial Data

The optimization of functional materials is important to enhance their properties, but their complex geometries pose great challenges to optimization. Data-driven algorithms efficiently navigate such complex design spaces by learning relationships between material structures and performance metrics to discover high-performance functional materials. Surrogate-based active learning, continually improving its surrogate model by iteratively including high-quality data points, has emerged as a cost-effective data-driven approach. Furthermore, it can be coupled with quantum computing to enhance optimization processes, especially when paired with a special form of surrogate model (i.e., quadratic unconstrained binary optimization), formulated by factorization machine (FM). However, current practices often overlook the variability in design space sizes when determining the initial data size for optimization. In this work, we investigate the optimal initial data sizes required for efficient convergence across various design space sizes. By employing averaged piecewise linear regression, we identify initiation points where convergence begins, highlighting the crucial role of employing adequate initial data in achieving efficient optimization. These results contribute to the efficient optimization of functional materials by ensuring faster convergence and reducing computational costs in FM-based active learning.

active learning↗
DOE OSTI2020

Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the embedded discrete fracture model (EDFM) and the embedded finite element method (EFEM) for the flow and the mechanics, respectively. This nonconforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finite volumes that exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an extended finite element approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

58 GEOSCIENCES↗
DOE OSTI2023

Reduced-Order Models of Static Power Grids based on Spectral Clustering

For large-scale interconnected power systems that cover large geographical areas, certain electrical studies are required so that appropriate decisions ensure system reliability and low cost. For such studies, it is often neither practical nor necessary to model in detail the entire power system, which is increasingly complex due to a more diverse range of grid assets to choose from in both short and long-term planning. The goal of this paper is to present a methodology to reduce the order of large-scale power networks based on spectral graph theory given that current methods for static network reduction are not scalable. A brief analysis of some spectral clustering properties to determine which graph Laplacian matrix should be used and why is included. The analysis shows that the utilization of the normalized graph Laplacian is more advantageous for clustering purposes. Techniques are proposed to approximate cost functions for the aggregated generators. This is done via linear regression. The reduced-order model obtained with the proposed methodology has an accuracy above 94% and solves the scalability issue commonly present in other reduction methods. If the utilization of the reduced-order model is either constrained to load levels above mid-peak demand, or cost functions of aggregated units are approximated via a piecewise quadratic approach, then the error distribution is in the order of 10^-3. .

Baquedano-Aguilar, Mario D.↗
DOE OSTI2023

Diffusion in intact secondary cell wall models of plants at different equilibrium moisture content

Secondary plant cell walls are composed of carbohydrate and lignin polymers, and collectively represent a significant renewable resource. Leveraging these resources depends in part on a mechanistic understanding for diffusive processes within plant cell walls. Common wood protection treatments and biomass conversion processes to create biorefinery feedstocks feature ion or solvent diffusion within the cell wall. X-ray fluorescence microscopy experiments have determined that ionic diffusion rates are dependent on cell wall hydration as well as the ionic species through non-linear relationships. In this work, we use classical molecular dynamics simulations to map the diffusion behavior of different plant cell wall components (cellulose, hemicellulose, lignin), ions (Na + , K + , Cu2 + , Cl - ) and water within a model for an intact plant cell wall at various hydration states (3-30 wt% water). From these simulations, we analyze the contacts between different plant cell wall components with each other and their interaction with the ions. Generally, diffusion increases with increasing hydration, with lignin and hemicellulose components increasing diffusion by an order of magnitude over the tested hydration range. Ion diffusion depends on charge. Positively charged cations preferentially interact with hemicellulose components, which include negatively charged carboxylates. As a result, positive ions diffuse more slowly than negatively charged ions. Measured diffusion coefficients are largely observed to best fit piecewise linear trends, with an inflection point between 10 and 15% hydration. These observations shed light onto the molecular mechanisms for diffusive processes within secondary plant cell walls at atomic resolution.

09 BIOMASS FUELS↗
DOE OSTI2026

A robust framework for frictional fault contact in geological formations using a stabilized augmented Lagrangian approach

Numerical simulations are essential to evaluate the performance and safety of engineered subsurface systems such as geological carbon storage sites, enhanced geothermal fields, and oil and gas reservoirs. A key challenge lies in accurately modeling the frictional contact behavior along fault surfaces. This problem involves inequality constraints that arise from the physics of frictional slip, requiring specialized numerical methods to handle the resulting highly nonlinear and path-dependent behavior. Here, in this work, we address this challenge using an Augmented Lagrangian Method (ALM) implemented via the Uzawa algorithm. The formulation employs mixed finite element spaces, combining low-order piecewise linear displacements within the 3D domain cells with piecewise constant tractions defined on the fault surfaces. Furthermore, to ensure stability and satisfy the inf-sup condition, the discrete displacement space is enriched with face bubble functions on both sides of the contact interfaces. This approach offers several advantages over other stabilization techniques that rely on additional terms, and it integrates naturally in the Uzawa framework.

58 GEOSCIENCES↗
DOE OSTI2021

The White Dwarfs of the Old, Solar-metallicity Open Star Cluster Messier 67: Properties and Progenitors

The old, solar-metallicity open cluster Messier 67 has long been considered a lynchpin in the study and understanding of the structure and evolution of solar-type stars. The same is arguably true for stellar remnants; the white dwarf population of M67 provides crucial observational data for understanding and interpreting white dwarf populations and evolution. In this work, we determine the white dwarf masses and derive their progenitor star masses using high signal-to-noise spectroscopy of warm (≳10,000 K) DA white dwarfs in the cluster. From this, we are able to derive each white dwarf’s position on the initial–final mass relation (IFMR), with an average M {sub WD} = 0.60 ± 0.01 M {sub ⊙} and progenitor mass M {sub i} = 1.52 ± 0.04 M {sub ⊙}. These values are fully consistent with recently published linear and piecewise linear fits to the semiempirical IFMR and provide a crucial, precise anchor point for the IFMR for solar-metallicity, low-mass stars. The mean mass of M67 white dwarfs is also consistent with the sharp narrow peak in the local field white dwarf mass distribution, indicating that a majority of recently formed field white dwarfs come from stars with progenitor masses of ≈1.5 M {sub ⊙}. Our results enable more precise modeling of the Galactic star formation rate encoded in the field white dwarf mass distribution.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Density functional theory of material design: fundamentals and applications—II

Abstract This is the second and the final part of the review on density functional theory (DFT), referred to as DFT-II. In the first review, DFT-I, we have discussed wavefunction-based methods, their complexity, and basics of density functional theory. In DFT-II, we focus on fundamentals of DFT and their implications for the betterment of the theory. We start our presentation with the exact DFT results followed by the concept of exchange-correlation (xc) or Fermi-Coulomb hole and its relationship with xc energy functional. We also provide the exact conditions for the xc-hole, xc-energy and xc-potential along with their physical interpretation. Next, we describe the extension of DFT for non-integer number of electrons, the piecewise linearity of total energy and discontinuity of chemical potential at integer particle numbers, and derivative discontinuity of the xc potential, which has consequences on fundamental gap of solids. After that, we present how one obtains more accurate xc energy functionals by going beyond the LDA. We discuss the gradient expansion approximation (GEA), generalized gradient approximation (GGA), and hybrid functional approaches to designing better xc energy functionals that give accurate total energies. However, these functionals fail to predict properties like the ionization potential and the band gap. Thus, we next describe different methods of modelling these potentials and results of their application for calculation of the band gaps of different solids to highlight accuracy of different xc potentials. Finally, we conclude with a glimpse on orbital-free density functional theory and the machine learning approach.

36 MATERIALS SCIENCE↗
DOE OSTI2025

On nonlocal problems with Neumann boundary conditions: scaling and convergence for nonlocal operators and solutions

Formulations of Neumann-type boundary conditions for boundary value problems in the nonlocal framework are beset with difficulties, some related to the choice of a proper scaling. Here we identify a space-dependent scaling for a nonlocal Neumann operator, for which we prove linear in δ (δ being the radius for the support for the kernel) convergence of the Neumann operator and $\mathcal{O}$(δ 2 ) convergence of solutions to their classical counterparts. The pointwise-like convergence of the nonlocal normal operator is cast as a new type of two-scale operator-point convergence, which we call condensated convergence . The results hold for general integrable kernels, a setting which is favored in numerical simulations. We support this analysis with numerical convergence studies using a piecewise linear discontinuous Galerkin discretization and show an $\mathcal{O}$(δ 2 ) rate of convergence of solutions, also exhibiting an $\mathcal{O}$(h 2 ) convergence, where h is the mesh size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Machine Learning-Driven Conservative-to-Primitive Conversion in Hybrid Piecewise Polytropic and Tabulated Equations of State

We present a novel machine learning (ML)-based method to accelerate conservative-to-primitive inversion, focusing on hybrid piecewise polytropic and tabulated equations of state. Traditional root-finding techniques are computationally expensive, particularly for large-scale relativistic hydrodynamics simulations. To address this, we employ feedforward neural networks (NNC2PS and NNC2PL), trained in PyTorch (2.0+) and optimized for GPU inference using NVIDIA TensorRT (8.4.1), achieving significant speedups with minimal accuracy loss. The NNC2PS model achieves 𝐿 1 and 𝐿 ∞ errors of 4.54 × 10 −7 and 3.44 × 10−6, respectively, while the NNC2PL model exhibits even lower error values. TensorRT optimization with mixed-precision deployment substantially accelerates performance compared to traditional root-finding methods. Specifically, the mixed-precision TensorRT engine for NNC2PS achieves inference speeds approximately 400 times faster than a traditional single-threaded CPU implementation for a dataset size of 1,000,000 points. Ideal parallelization across an entire compute node in the Delta supercomputer (dual AMD 64-core 2.45 GHz Milan processors and 8 NVIDIA A100 GPUs with 40 GB HBM2 RAM and NVLink) predicts a 25-fold speedup for TensorRT over an optimally parallelized numerical method when processing 8 million data points. Moreover, the ML method exhibits sub-linear scaling with increasing dataset sizes. We release the scientific software developed, enabling further validation and extension of our findings. By exploiting the underlying symmetries within the equation of state, these findings highlight the potential of ML, combined with GPU optimization and model quantization, to accelerate conservative-to-primitive inversion in relativistic hydrodynamics simulations.

conservative-to-primitive conversion↗