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Results for “variational and sequential methods”

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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NASA NTRS1989

An optimal momentum management controller for the Space Station

This paper presents a new sequential design procedure for determining an optimal CMG (control moment gyro) momentum management and attitude control system for the Space Station Freedom. First, the Space Station equations of motion are linearized and uncoupled, and the associated state space equations are defined. Next, a new sequential procedure is used for the development of a continuous quadratic regulator with eigenvalue placement in a specified region of the complex plane. The regional pole assignment method is utilized since it is best suited for tradeoffs between eigenvalue locations and robustness with respect to parameter variations, sensor failures, implementation accuracies and gain reductions. The matrix sign function is used for solving the Riccati equations which appear in the design procedure. Simulation results are given which show that the resultant design provides desired system performance.

Sunkel, J. W.↗

NASA NTRS1991

Improved self arbitrated VLSI asynchronous circuits

This paper introduces an improved method for designing the class of CMOS VLSI asynchronous sequential circuits introduced in the paper by Sterling R. Whitaker and Gary K. Maki, 'Self Arbitrated VLSI Asynchronous Circuits.' Of main interest here is the simple design by inspection rules that arise from these circuits. This paper presents a variation on these circuits which reduces the number of transistors required.

Winterrowd, P.↗

NASA NTRS1986

The expanded LaGrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrainted optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗

NASA NTRS1988

The expanded Lagrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrained optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗

NASA NTRS2021

Decoding the effects of synonymous variants

Synonymous single nucleotide variants (sSNVs) are common in the human genome but are often overlooked. However, sSNVs can have significant biological impact and may lead to disease. Existing computational methods for evaluating the effect of sSNVs suffer from the lack of gold-standard training/evaluation data and exhibit over-reliance on sequence conservation signals. We developed synVep (synonymous Variant effect predictor), a machine learning-based method that overcomes both of these limitations. Our training data was a combination of variants reported by gnomAD (observed) and those unreported, but possible in the human genome (generated). We used positive-unlabeled learning to purify the generated variant set of any likely unobservable variants. We then trained two sequential extreme gradient boosting models to identify subsets of the remaining variants putatively enriched and depleted in effect. Our method attained 90% precision/recall on a previously unseen set of variants. Furthermore, although synVep does not explicitly use conservation, its scores correlated with evolutionary distances between orthologs in cross-species variation analysis. synVep was also able to differentiate pathogenic vs. benign variants, as well as splice-site disrupting variants (SDV) vs. non-SDVs. Thus, synVep provides an important improvement in annotation of sSNVs, allowing users to focus on variants that most likely harbor effects.

Zishuo Zeng↗

NASA NTRS1969

Remote sensing of winds and atmospheric turbulence by cross correlation of passive optical signals

A new method is described for the remote measurement of winds and atmospheric turbulence by the cross-correlation of passive optical signals. If small local variations in atmospheric density, temperature or other parameters cause fluctuations in scattered or thermal radiation detected by a radiometer on the ground, then the cross-correlation of fluctuations detected by two radiometers with crossed fields of view can yield turbulence information pertaining to the region about this intersection point. When the fields of view are not quite crossed turbulent eddies will be convected through the fields of view sequentially, and the transit times of the eddies identified by the correlation procedure will yield wind information. The successful application of this technique, detecting fluctuations in scattered sunlight, has demonstrated both the potential, and the present limitations of the method, which are discussed. Results for the power spectrum of the fluctuations and for winds at an altitude of 61 meters are shown.

Montgomery, A. J.↗

NASA NTRS2003

Reliability Sensitivity Analysis and Design Optimization of Composite Structures Based on Response Surface Methodology

This report discusses the development and application of two alternative strategies in the form of global and sequential local response surface (RS) techniques for the solution of reliability-based optimization (RBO) problems. The problem of a thin-walled composite circular cylinder under axial buckling instability is used as a demonstrative example. In this case, the global technique uses a single second-order RS model to estimate the axial buckling load over the entire feasible design space (FDS) whereas the local technique uses multiple first-order RS models with each applied to a small subregion of FDS. Alternative methods for the calculation of unknown coefficients in each RS model are explored prior to the solution of the optimization problem. The example RBO problem is formulated as a function of 23 uncorrelated random variables that include material properties, thickness and orientation angle of each ply, cylinder diameter and length, as well as the applied load. The mean values of the 8 ply thicknesses are treated as independent design variables. While the coefficients of variation of all random variables are held fixed, the standard deviations of ply thicknesses can vary during the optimization process as a result of changes in the design variables. The structural reliability analysis is based on the first-order reliability method with reliability index treated as the design constraint. In addition to the probabilistic sensitivity analysis of reliability index, the results of the RBO problem are presented for different combinations of cylinder length and diameter and laminate ply patterns. The two strategies are found to produce similar results in terms of accuracy with the sequential local RS technique having a considerably better computational efficiency.

Rais-Rohani, Masoud↗

DOE OSTI2021

Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control

Herein, we present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional sub-spaces whose basis functions are realizations of a sequence of neural networks. Here, the finite-dimensional subspaces are then used to define a standard Galerkin approximation of the variational equation. This approach enjoys a number of advantages, including: the sequential nature of the algorithm offers a systematic approach to enhancing the accuracy of a given approximation; the sequential enhancements provide a useful indicator for the error that can be used as a criterion for terminating the sequential updates; the basic approach is largely oblivious to the nature of the partial differential equation under consideration; and, some basic theoretical results are presented regarding the convergence (or otherwise) of the method which are used to formulate basic guidelines for applying the method.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1999

Uncertainty Modeling Via Frequency Domain Model Validation

Abstract The majority of literature on robust control assumes that a design model is available and that the uncertainty model bounds the actual variations about the nominal model. However, methods for generating accurate design models have not received as much attention in the literature. The influence of the level of accuracy of the uncertainty model on closed loop performance has received even less attention. The research reported herein is an initial step in applying and extending the concept of model validation to the problem of obtaining practical uncertainty models for robust control analysis and design applications. An extension of model validation called 'sequential validation' is presented and applied to a simple spring-mass-damper system to establish the feasibility of the approach and demonstrate the benefits of the new developments.

Waszak, Martin R.↗

DOE OSTI2021

Microseismic at HFTS2: A Story of Three Stimulated Wells

A microseismic data set was acquired at Hydraulic Fracturing Test Site 2 (HFTS2) in the Delaware Basin (Texas, USA) by the HFTS2 consortium as a part of data-collection program designed to help maximize the efficiency of hydraulic fracturing, understand the impacts of nearby depleted zones, and increase the production of hydrocarbons. Advanced methods of microseismic monitoring applied at HFTS2 include 1) native synchronization of five monitor arrays, 2) real-time location of microseismic events, 3) joint event hypocenter/ velocity-model inversion that locates microseismic events simultaneously with constructing azimuthally anisotropic velocity models, 4) high-resolution reservoir imaging, utilizing microseismic events as downhole sources. HFTS2 microseismic data set illustrated the influence of geologic complexity, variations in treatment designs, and the presence of parent wells on the efficiency of hydraulic fracturing. Three Wolfcamp wells, Boxwood 1H, 2H, and 4H, were stimulated sequentially, exhibiting very different patterns of microseismicity. When the Boxwood 1H well is stimulated, its toe stages quickly reacted to the presence of depleted Bitterroot section to the east of the Boxwood pad, extending microseismic events over 3,000 ft to the east. This behavior changes dramatically after the treatment passes the Bitterroot section at the toe, and the heel stages in 1H showed tight microseismic grouping around the stimulated well, indicative of treatment of virgin reservoir rock. The Boxwood 2H demonstrates this same pattern of behavior between the toe and heel stages of the well, suggesting that the depleted Bitterroot section remains easier to refracture than adjacent non-depleted rock. Microseismic activity associated with Boxwood 4H treatment is distinctly different from those in Boxwood wells 1H and 2H. The events generated during stimulation of 4H are hardly influenced by the depleted Bitterroot section and fill the space between the previously stimulated 1H and 2H wells. Altogether, microseismic patterns suggest that treatment fluids tend to find the weakest passages through geologic formations, and the relative well positions and treatment sequence have a significant impact on fracture geometry, as indicated by microseismic event locations.

58 GEOSCIENCES↗

DOE OSTI2021

Variational Discrete Action Theory

In this work, we propose the variational discrete action theory (VDAT) to study the ground state properties of quantum many-body Hamiltonians. VDAT is a variational theory based on the sequential product density matrix (SPD) ansatz, characterized by an integer $\mathscr{N}$, which monotonically approaches the exact solution with increasing $\mathscr{N}$. To evaluate the SPD, we introduce a discrete action and a corresponding integer time Green’s function. We use VDAT to exactly evaluate the SPD in two canonical models of interacting electrons: the Anderson impurity model and the d = ∞ Hubbard model. For the latter, we evaluate $\mathscr{N}$ = 2 – 4, where $\mathscr{N}$ = 2 recovers the Gutzwiller approximation (GA), and we show that $\mathscr{N}$ = 3, which exactly evaluates the Gutzwiller-Baeriswyl wave function, provides a truly minimal yet precise description of Mott physics with a cost similar to that of the GA. VDAT is a flexible theory for studying quantum Hamiltonians, competing both with state-of-the-art methods and simple, efficient approaches all within a single framework.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

D-Band EPR and ENDOR Spectroscopy of 15 N-Labeled Photosystem I

For billions of years, nature has optimized the photosynthetic machinery that converts light energy into chemical energy. Key primary reactions of photosynthesis occur in large membrane protein-cofactor complexes. The light-induced sequential electron transfer reactions occur through a chain of donor/acceptor cofactors embedded in the protein matrix resulting in a long-lived transmembrane charge-separated state. EPR is the method of choice to study electron transfer and the interaction of protein environment with redox-active cofactors. However, the spectra of organic cofactor radicals typically are not fully resolved and severely overlap at conventional X-band EPR. Even at Q-band EPR, this overlap is present and often a serious problem. As a result, there is a large variation of the reported EPR data and limited understanding of electronic structures of several redox-active cofactors. These serious problems can often be overcome by the excellent spectral resolution provided by high-frequency EPR (HF EPR). In this work, we study the electronic structure of the primary electron donor P 700 and the secondary electron acceptor A 1 of Photosystem I (PSI) using 130 GHz (D-band) EPR and Electron-Nuclear-Double-Resonance (ENDOR) spectroscopy. PSI was isotopically labeled with 15 N (I = $\frac{1/2}$) to avoid quadrupolar interactions in the most abundant nitrogen isotope 14 N (I = 1) and simplify the ENDOR spectra. ENDOR spectroscopy is central for determining the hyperfine coupling of nitrogen atoms of the two chlorophyll molecules comprising oxidized P 700 and the involvement of protein nitrogen atoms with reduced A 1 . While HF ENDOR of A 1 - allows identification of two nitrogen atoms, HF ENDOR of P 700 + still does not permit unique assignment of the recorded hyperfine couplings.

15N↗

NASA NTRS1974

Lunar orbit determination in the presence of unmodeled accelerations

A technique for estimating the state of an artificial satellite in the presence of unmodeled accelerations is presented. The unmodeled acceleration is approximated by a first-order Gauss-Markov sequence which can be separated into a timewise-correlated component and a purely random component. Using this approximation, a sequential procedure for estimating the position, velocity, and the unmodeled acceleration is developed. The method is evaluated by reducing range-rate observations obtained by tracking the Apollo 10 and 11 spacecraft during the lunar-orbit phase of the mission. Numerical results are presented which show that the observation residual pattern lies within the observation noise standard deviation. The values of the estimated components of the unmodeled acceleration are repeatable from orbit to orbit within a given mission and from mission to mission when the same ground track is covered. Finally, the variation in the radial component of the unmodeled acceleration shows a high correlation with the reported location of the lunar surface mascons.

Ingram, D. S.↗

DOE OSTI2026

Learning earthquake ground motions via conditional generative modeling

Predicting high-fidelity ground motions for future earthquakes is crucial for seismic hazard assessment and infrastructure resilience. Conventional empirical simulations suffer from sparse sensor distribution and geographically localized earthquake locations, while physics-based methods are computationally intensive and require accurate representations of Earth structures and earthquake sources. We propose an artificial intelligence (AI) spectrogram generator, Conditional Generative Modeling for Ground Motion (CGM-GM). CGM-GM leverages earthquake magnitudes and geographic coordinates of earthquakes and sensors as inputs, when postprocessed with phase information, capturing spatially continuous Fourier amplitude spectra (FAS) as well as properties such as P and S arrivals, and waveform durations, without explicit physics constraints. This is achieved through a probabilistic autoencoder that extracts latent distributions in the time-frequency domain and variational sequential models for prior and posterior distributions. We evaluate the performance of CGM-GM using small-magnitude earthquake records from the San Francisco Bay Area, a region with high seismic risks. Here, we report that CGM-GM demonstrates potential for complementing physics-based simulations and non-ergodic empirical ground motion models, as well as shows promise in seismology and beyond.

geophysics↗

DOE OSTI2025

A New Hybrid Quantum-Classical Algorithm for Solving the Unit Commitment Problem

Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach these problems. We develop a hybrid quantum-classical algorithm for the Unit Commitment (UC) problem in power systems which aims at minimizing the total cost while optimally allocating generating units to meet the hourly demand of the power loads. The hybrid algorithm combines a variational quantum algorithm (VQA) with a classical Benders-type heuristic. The resulting algorithm computes approximate solutions to UC in three stages: i) a collection of UC vectors capable meeting the power demand with lowest possible operating costs is generated based on VQA; ii) a classical sequential least squares programming (SLSQP) routine is leveraged to find the optimal power level corresponding to a predetermined number of candidate vectors; iii) in the last stage, the approximate solution of UC along with generating units power level combination is given. To demonstrate the effectiveness of the presented method, three different systems with 3 generating units, 10 generating units, and 26 generating units were tested for different time periods. In addition, convergence of the hybrid quantum-classical algorithm for select time periods is proven out on IonQ's Forte system.

Aboumrad, Willie [IonQ, Inc]↗

DOE OSTI2024

A numerical method for simulating variable density flows in membrane desalination systems

Here, we present a novel method for simulating unsteady, variable density, fluid flows in membrane desalination systems. By assuming the density varies only with concentration and temperature, the scheme decouples the solution of the governing equations into two sequential blocks. The first solves the governing equations for the temperature and concentration fields, which are used to compute all thermophysical properties. The second block solves the conservation of mass and momentum equations for the velocity and pressure. We show that this is computationally more efficient than schemes that iterate over the full coupled equations in one block. We verify that the method achieves second-order spatial-temporal accuracy, and we use the method to investigate buoyancy-driven convection in a desalination process called vacuum membrane distillation. Specifically, we show that with gravity properly oriented, variations in temperature and concentration can trigger a double-diffusive instability that enhances mixing and improves water recovery. We also show that the instability can be strengthened by providing external heating.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Co-orchestration of multiple instruments to uncover structure–property relationships in combinatorial libraries

The rapid growth of automated and autonomous instrumentation brings forth opportunities for the co-orchestration of multimodal tools that are equipped with multiple sequential detection methods or several characterization techniques to explore identical samples. This is exemplified by combinatorial libraries that can be explored in multiple locations via multiple tools simultaneously or downstream characterization in automated synthesis systems. In co-orchestration approaches, information gained in one modality should accelerate the discovery of other modalities. Correspondingly, an orchestrating agent should select the measurement modality based on the anticipated knowledge gain and measurement cost. Herein, we propose and implement a co-orchestration approach for conducting measurements with complex observables, such as spectra or images. The method relies on combining dimensionality reduction by variational autoencoders with representation learning for control over the latent space structure and integration into an iterative workflow via multi-task Gaussian Processes (GPs). This approach further allows for the native incorporation of the system's physics via a probabilistic model as a mean function of the GPs. We illustrate this method for different modes of piezoresponse force microscopy and micro-Raman spectroscopy on a combinatorial Sm-BiFeO3 library. However, the proposed framework is general and can be extended to multiple measurement modalities and arbitrary dimensionality of the measured signals.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Sequential spectral line analysis for accurate density and temperature diagnosis of laboratory opacity measurements

The accuracy of iron opacity calculated in stellar interiors has been questioned since the discovery of the “solar problem” and the discrepancies between the measured and modeled iron opacity reported in 2015. Experimental opacity benchmarks require accurate temperature and density measurements, which were inferred by analyzing tracer magnesium spectra in those experiments. Could the observed discrepancy be explained by insufficient accuracy in the inferred temperature, density, and their uncertainties? Previous analyses may have yielded biased results due to three limitations: (1) simultaneous multi-line fitting, (2) approximations in line-shape models, and (3) exclusion of certain spectral lines due to insufficient background characterization. Notably, the first issue is a common concern for many inversion methods, including Bayesian inferences. We present a refined analysis method that overcomes these limitations, applied to three categories of iron opacity experiments (Anchor 1, 2, and 3). In particular, the sequential fitting method yields unbiased results with more realistic uncertainties by accounting for line inconsistencies in the parameter uncertainties. The average electron temperature and density values are 162 ± 6 eV and (7.0 ± 1.9) × 10 21 cm −3 for six Anchor 1 experiments, 189 ± 7 eV and (3.4 ± 0.3) × 10 22 cm −3 for 21 Anchor 2 experiments, and 201 ± 6 eV and (4.8 ± 1.1) × 10 22 cm −3 for nine Anchor 3 experiments. These results show ∼4% temperature and ∼20% density reproducibility over a decade, which also aligns with the inferred parameter uncertainties. In conclusion, the resulting temperature and density uncertainties lead to a quasi-continuum iron opacity variation of ±4%–7% for wavelengths below 9.5 Å, which is insufficient to explain the significant model-data discrepancies reported in 2015.

Absorption spectroscopy↗