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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗
DOE OSTI2024

Supporting ARPA-E Power Grid Optimization (Final Report)

Pacific Northwest National Laboratory (PNNL), Arizona State University (ASU), Georgia Institute of Technology (Georgia Tech), Los Alamos National Laboratory (LANL), National Renewable Energy Laboratory (NREL), Texas A&M University (TAMU), The University of Texas at Austin (UT), and the University of Wisconsin-Madison (UW-M) supported the ARPA-E Grid Optimization (GO) Competition by providing a common problem formulation, data format, datasets, evaluation mechanism, scoring, rules, and results that resulted in the awarding of $\$9.24$ million dollars to teams from academia, industry, and national labs for solving three sets of increasingly difficult non-linear, security- constrained AC Optimal Powerflow (AC-OPF) optimization problems in order to increase the efficiency of the US Electric Grid. It is estimated that a 1% increase in efficiency can save $\$1$ billion. Current industry practices typically use a linear DC model (DC-OPF) in order solve the OPF problem within the time constraints of the operation schedule. The GO Competition challenges the best power engineers, mathematicians, and computer scientists to make possible operational decisions based on accurate physical models. To accomplish this, the GO Competition created a series of Challenges and funded teams to produce the best solver. Challenge 1 was to solve the security constrained Alternating Current Optimal Power Flow (ACOPF) problem. Challenge 2 extended that to by adding adjustable transformer tap ratios, phase shifting transformers, switchable shunts, price-responsive demand, ramp rate constrained generators and loads, and fast-start unit commitment (UC). Furthermore, Challenge 2 was a maximization problem while Challenge 1 was a minimization problem. While Challenge 3 was being developed, the entrants were invited to find better solutions to the Challenge 2 synthetic datasets with no restrictions on time, hardware, or algorithms. The Challenge 2 solutions turned out to be very good. Challenge 3 expanded the Challenge 2 problem further by using multiperiod dynamic markets, including advisory models for extreme weather events, day-ahead markets, and the real-time markets with an extended look-ahead. These problems included active bid-in demand and topology optimization. Together the Challenges used nearly 30 million CPU hours. Since each team was working on the same problem, using the same data, and running on the same hardware, fair comparisons could be drawn as to the best solver. The datasets were varied enough, however, that the best solver for one dataset was not necessarily the best at another, so cumulative scores were used. The process was managed by the PNNL maintained website https://GOCompetition.energy.gov, where Entrants could find information about the problem, the data, the rules, submit their solver for evaluation, and see the scores of all the competing teams on a Leaderboard. Interest was world-wide but only American teams were eligible for prizes. The Competition has produced 34 journal articles 115 papers and been cited over 500 times in the literature, including 12 dissertations (4 from foreign countries; Columbia (2), Germany, and Italy) and 3 from the DOE ExaScale project. Software developed by Pearl Street Technologies for Challenges 1 and 2 is now deployed by Southwest Power Pool (SPP) and Midcontinent Independent Service Operator (MISO). Other teams have received inquiries from venture capitalists. Google DeepMind has thanked the Competition for making the datasets developed for the Competition public. They are using it to train machine learning models. The larger datasets have billions of unknowns to be solved for, but only a small percent matter in the final solution. Knowing what unknowns are important can dramatically speedup the solution.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Stochastic projective splitting

Here, we present a new, stochastic variant of the projective splitting (PS) family of algorithms for inclusion problems involving the sum of any finite number of maximal monotone operators. This new variant uses a stochastic oracle to evaluate one of the operators, which is assumed to be Lipschitz continuous, and (deterministic) resolvents to process the remaining operators. Our proposal is the first version of PS with such stochastic capabilities. We envision the primary application being machine learning (ML) problems, with the method’s stochastic features facilitating “mini-batch” sampling of datasets. Since it uses a monotone operator formulation, the method can handle not only Lipschitz-smooth loss minimization, but also min–max and noncooperative game formulations, with better convergence properties than the gradient descent-ascent methods commonly applied in such settings. The proposed method can handle any number of constraints and nonsmooth regularizers via projection and proximal operators. We prove almost-sure convergence of the iterates to a solution and a convergence rate result for the expected residual, and close with numerical experiments on a distributionally robust sparse logistic regression problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Internal calibration of transient kinetic data via machine learning

The temporal analysis of products (TAP) reactor provides a vast amount of transient kinetic information that may be used to describe a variety of chemical features including residence time distributions, kinetic coefficients, number of active sites, reaction mechanism, etc. However, as with any measurement device, the TAP reactor signal is convoluted with noise and drift is common. In order to reduce the uncertainty of the kinetic measurement and any derived parameters or mechanisms, proper preprocessing must be performed prior to any advanced type of analysis. This preprocessing includes baseline correction, i.e., a shift in the voltage response, and calibration, i.e., a scaling of the flux response based on prior experiments. The traditional methodology of preprocessing requires significant user discretion and reliance on separate calibration experiments that may drift over time. Herein we use machine learning techniques combined with physical constraints to understand the noise and drift that is being generated within and between experiments for enhancement of the chemical kinetic signal. As such, the proposed methodology demonstrates clear benefits over the traditional preprocessing approach by eliminating the need for separate calibration experiments or heuristic input from the user.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Uncertain characterization of reservoir fluids due to brittleness of equation of state regression

Equations of state (EoS) play a central role in modeling the phase equilibrium of fluid mixtures. Their parameterization involves fitting a model to experimental data, i.e., solving a nonlinear, non-convex, multivariate optimization problem. The latter requires one to select design variables, domains of definition for each variable, and weights assigned to individual measurements. We demonstrate that subjective choices of an optimization algorithm and an initial guess also impact the regression process. Consequently, EoS predictions are fundamentally uncertain even after the EoS tuning to a limited set of experimental data points. We demonstrate this observation for two hydrocarbon reservoir fluids, in which five properties of the heaviest carbon fraction are treated as design variables. While all the optimization algorithms and initial guesses match experimental data for the gas and liquid properties, the resulting EoS parameterizations lead to dramatically different predictions of the fluid’s thermophysical behavior in the unsampled pressure and temperature regions. In conclusion, we propose the probabilistic treatment of design variables to quantify the predictive uncertainty of the resulting fluid models.

15 GEOTHERMAL ENERGY↗
DOE OSTI2013

Compressive Sensing Based Machine Learning Strategy For Characterizing The Flow Around A Cylinder With Limited Pressure Measurements

Compressive sensing is used to determine the flow characteristics around a cylinder (Reynolds number and pressure/flow field) from a sparse number of pressure measurements on the cylinder. Using a supervised machine learning strategy, library elements encoding the dimensionally reduced dynamics are computed for various Reynolds numbers. Convex L1 optimization is then used with a limited number of pressure measurements on the cylinder to reconstruct, or decode, the full pressure field and the resulting flow field around the cylinder. Aside from the highly turbulent regime (large Reynolds number) where only the Reynolds number can be identified, accurate reconstruction of the pressure field and Reynolds number is achieved. The proposed data-driven strategy thus achieves encoding of the fluid dynamics using the L2 norm, and robust decoding (flow field reconstruction) using the sparsity promoting L1 norm.

Bright, Ido↗
DOE OSTI2015

BI-sparsity pursuit for robust subspace recovery

Here, the success of sparse models in computer vision and machine learning in many real-world applications, may be attributed in large part, to the fact that many high dimensional data are distributed in a union of low dimensional subspaces. The underlying structure may, however, be adversely affected by sparse errors, thus inducing additional complexity in recovering it. In this paper, we propose a bi-sparse model as a framework to investigate and analyze this problem, and provide as a result , a novel algorithm to recover the union of subspaces in presence of sparse corruptions. We additionally demonstrate the effectiveness of our method by experiments on real-world vision data.

47 OTHER INSTRUMENTATION↗
DOE OSTI2018

Representing Operational Flexibility in Generation Expansion Planning Through Convex Relaxation of Unit Commitment

Large shares of renewable generation in electric power systems increase the need for operational flexibility. Consideration of operational flexibility in generation expansion planning (GEP) necessitates the modeling of unit commitment (UC) in system operations. However, the UC problem itself is computationally challenging. We present a GEP model in which the embedded operational problem is a convex relaxation of the UC problem. Through a large-scale example based on the Texas system, we show the tightness and tractability of our relaxation, as well as the impact of operational flexibility on GEP.

convex optimization↗
DOE OSTI2018

Joint Electricity and Natural Gas Transmission Planning with Endogenous Market Feedbacks

Recent trends in gas-fired power plant installation has increased the connections between the electric power and natural gas industries. Despite these dependencies, both industries must meet commercial, political, operational and technical requirements that often force the industries to plan and operate in isolation. As a result, undesired situations may arise, such as those experienced by both systems during the winter of 2013/2014 in the northeastern United States. In this work, we consider the technical challenges and present a Combined Electricity and Gas Expansion (CEGE) planning model. The CEGE model minimizes the cost of meeting gas and electricity demand during high stress conditions and introduces an elasticity model for analysis of gas-price volatility caused by congestion. The underlying mathematical formulation considers recent advances in convex approximations to make the problem computationally tractable when applied to large-scale CEGE instances. We conduct an indepth analysis on integrated test systems that include the New England area.

03 NATURAL GAS↗
DOE OSTI2024

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong↗
DOE OSTI2019

Model Predictive Control of a Wave Energy Converter Using Duality Techniques

In this paper, a method for implementing model predictive control for vibration energy harvesting systems with the goal of maximizing generated energy is presented. This is generally a nonconvex problem, which can be computationally expensive and converging to a global minimum cannot be guaranteed. We introduce a dual-domain method to relax the nonconvex primal problem into a convex dual optimization problem, which can be performed in real time. Based on previous work, we determine when the duality gap is zero and, by extension, whether the global optimal primal solution is found. Here, we demonstrate the algorithm on a single, buoy-type wave energy converter with energy storage constraints and power take-off force constraints.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

Scaling and Benchmarking an Evolutionary Algorithm for Constructing Biophysical Neuronal Models

Single neuron models are fundamental for computational modeling of the brain's neuronal networks, and understanding how ion channel dynamics mediate neural function. A challenge in defining such models is determining biophysically realistic channel distributions. Here, we present an efficient, highly parallel evolutionary algorithm for developing such models, named NeuroGPU-EA. NeuroGPU-EA uses CPUs and GPUs concurrently to simulate and evaluate neuron membrane potentials with respect to multiple stimuli. We demonstrate a logarithmic cost for scaling the stimuli used in the fitting procedure. NeuroGPU-EA outperforms the typically used CPU based evolutionary algorithm by a factor of 10 on a series of scaling benchmarks. We report observed performance bottlenecks and propose mitigation strategies. Finally, we also discuss the potential of this method for efficient simulation and evaluation of electrophysiological waveforms.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1988

International Conference on Advances in Communication and Control Systems, 1st, Washington, DC, June 18-20, 1987, Proceedings

Theoretical models of communication and control systems are discussed in reviews and reports. Topics addressed include smoothing and identification for random fields, the information and coding capacities of mismatched Gaussian channels, recursive least-squares estimation and Kalman filtering by systolic arrays, Kemp echo digital filters, a periodic test-scheduling scheme for communication and queuing processes, and receivers for direct-sequence systems. Consideration is given to a distributed-parameter model for detecting cracks in rotors, active control of aeroelastic systems governed by functional differential equations, robust multivariable control of large space structures, finite-rank relatively bounded perturbations of semigroup generators, and sensitivity analysis of convex optimal-control problems.

Declaris, Nicholas↗
NASA NTRS1994

Improved image decompression for reduced transform coding artifacts

The perceived quality of images reconstructed from low bit rate compression is severely degraded by the appearance of transform coding artifacts. This paper proposes a method for producing higher quality reconstructed images based on a stochastic model for the image data. Quantization (scalar or vector) partitions the transform coefficient space and maps all points in a partition cell to a representative reconstruction point, usually taken as the centroid of the cell. The proposed image estimation technique selects the reconstruction point within the quantization partition cell which results in a reconstructed image which best fits a non-Gaussian Markov random field (MRF) image model. This approach results in a convex constrained optimization problem which can be solved iteratively. At each iteration, the gradient projection method is used to update the estimate based on the image model. In the transform domain, the resulting coefficient reconstruction points are projected to the particular quantization partition cells defined by the compressed image. Experimental results will be shown for images compressed using scalar quantization of block DCT and using vector quantization of subband wavelet transform. The proposed image decompression provides a reconstructed image with reduced visibility of transform coding artifacts and superior perceived quality.

Orourke, Thomas P.↗