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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Variational Information Planning for Sequential Decision Making

We consider the setting of sequential decision making where, at each stage, potential actions are evaluated based on expected reduction in posterior uncertainty, given by mutual information (MI). As MI typically lacks a closed form, we propose an approach which maintains variational approximations of, both, the posterior and MI utility. Our planning objective extends an established variational bound on MI to the setting of sequential planning. The result, variational information planning (VIP), is an efficient method for sequential decision making. We further establish convexity of the variational planning objective and, under conditional exponential family approximations, we show that the optimal MI bound arises from a relaxation of the well-known exponential family moment matching property. Here, we demonstrate VIP for sensor selection, experiment design, and active learning, where it meets or exceeds methods requiring more computation, or those specialized to the task.

Pacheco, Jason↗
DOE OSTI2020

PyDA: A Hands-On Introduction to Dynamical Data Assimilation with Python

Dynamic data assimilation offers a suite of algorithms that merge measurement data with numerical simulations to predict accurate state trajectories. Meteorological centers rely heavily on data assimilation to achieve trustworthy weather forecast. With the advance in measurement systems, as well as the reduction in sensor prices, data assimilation (DA) techniques are applicable to various fields, other than meteorology. However, beginners usually face hardships digesting the core ideas from the available sophisticated resources requiring a steep learning curve. In this tutorial, we lay out the mathematical principles behind DA with easy-to-follow Python module implementations so that this group of newcomers can quickly feel the essence of DA algorithms. We explore a series of common variational, and sequential techniques, and highlight major differences and potential extensions. We demonstrate the presented approaches using an array of fluid flow applications with varying levels of complexity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Sequential Image Recovery Using Joint Hierarchical Bayesian Learning

Abstract Recovering temporal image sequences (videos) based on indirect, noisy, or incomplete data is an essential yet challenging task. We specifically consider the case where each data set is missing vital information, which prevents the accurate recovery of the individual images. Although some recent (variational) methods have demonstrated high-resolution image recovery based on jointly recovering sequential images, there remain robustness issues due to parameter tuning and restrictions on the type of sequential images. Here, we present a method based on hierarchical Bayesian learning for the joint recovery of sequential images that incorporates prior intra- and inter-image information. Our method restores the missing information in each image by “borrowing” it from the other images. More precisely, we couple sequential images by penalizing their pixel-wise difference. The corresponding penalty terms (one for each pixel and pair of subsequent images) are treated as weakly-informative random variables that favor small pixel-wise differences but allow occasional outliers. As a result, all of the individual reconstructions yield improved accuracy. Our method can be used for various data acquisitions and allows for uncertainty quantification. Some preliminary results indicate its potential use for sequential deblurring and magnetic resonance imaging.

Xiao, Yao↗
DOE OSTI2022

Sequential linear integer programming for integer optimal control with total variation regularization

We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty implies that the considered integer control problems admit minimizers. We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective. In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality. We demonstrate the theoretical findings on a computational example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Seismic Monitoring at the Farnsworth CO2-EOR Field Using Time-Lapse Elastic-Waveform Inversion of 3D-3C VSP Data

During the Development Phase of the U.S. Southwest Regional Partnership on Carbon Sequestration, supercritical CO2 was continuously injected into the deep oil-bearing Morrow B formation of the Farnsworth Unit in Texas for Enhanced Oil Recovery (EOR). The project injected approximately 94 kilotons of CO2 to study geologic carbon storage during CO2-EOR. A three-dimensional (3D) surface seismic dataset was acquired in 2013 to characterize the subsurface structures of the Farnsworth site. Following this data acquisition, the baseline and three time-lapse three-dimensional three-component (3D-3C) vertical seismic profiling (VSP) data were acquired at a narrower surface area surrounding the CO2 injection and oil/gas production wells between 2014 and 2017 for monitoring CO2 injection and migration. With these VSP datasets, we inverted for subsurface velocity models to quantitatively monitor the CO2 plume within the Morrow B formation. We first built 1D initial P-wave (Vp) and S-wave (Vs) velocity models by upscaling the sonic logs. We improved the deep region of the Vp and Vs models by incorporating the deep part of a migration velocity model derived from the 3D surface seismic data. We improved the shallow region of 3D Vp and Vs models using 3D traveltime tomography of first arrivals of VSP downgoing waves. We further improved the 3D baseline velocity models using elastic-waveform inversion (EWI) of the 3D baseline VSP upgoing data. Our advanced EWI method employs alternative tomographic and conventional gradients and total-variation-based regularization to ensure the high-fidelity updates of the 3D baseline Vp and Vs models. We then sequentially applied our 3D EWI method to the three time-lapse datasets to invert for spatiotemporal changes of Vp and Vs in the reservoir. Our inversion results reveal the volumetric changes of the time-lapse Vp and Vs models and show the evolution of the CO2 plume from the CO2 injection well to the oil/gas production wells.

42 ENGINEERING↗
DOE OSTI2024

Sequential Monte Carlo for Cut-Bayesian Posterior Computation

We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We prove finite sample concentration bounds for estimators derived from the proposed method along with a linear tempering extension and apply these results to a realistic setting where a computer model is misspecified. We then illustrate the SMC method for inference in a modular chemical reactor example that includes submodels for reaction kinetics, turbulence, mass transfer, and diffusion. The samples obtained are commensurate with a direct-sampling approach that consists of running multiple Markov chains, with computational efficiency gains using the SMC method. Overall, the SMC method presented yields a novel, rigorous approach to computing with cut-Bayesian posterior distributions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A circuit-generated quantum subspace algorithm for the variational quantum eigensolver

Recent research has shown that wavefunction evolution in real and imaginary time can generate quantum subspaces with significant utility for obtaining accurate ground state energies. Inspired by these methods, we propose combining quantum subspace techniques with the variational quantum eigensolver (VQE). In our approach, the parameterized quantum circuit is divided into a series of smaller subcircuits. The sequential application of these subcircuits to an initial state generates a set of wavefunctions that we use as a quantum subspace to obtain high-accuracy groundstate energies. We call this technique the circuit subspace variational quantum eigensolver (CSVQE) algorithm. By benchmarking CSVQE on a range of quantum chemistry problems, we show that it can achieve significant error reduction in the best case compared to conventional VQE, particularly for poorly optimized circuits, greatly improving convergence rates. Furthermore, we demonstrate that when applied to circuits trapped at local minima, CSVQE can produce energies close to the global minimum of the energy landscape, making it a potentially powerful tool for diagnosing local minima.

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

Describing the Influence of Ball-milling on the Amorphization of Flubendazole Using the PDF and RMC Methods with X-ray Powder Diffraction Data

Flubendazole (FBZ) is a poorly water-soluble drug, and different methodologies have been proposed to improve its oral bioavailability. Obtaining the amorphous drug phase is an alternative to improve its water solubility. Several techniques for drug amorphization, such as spray drying, lyophilization, melt quenching, solvent-evaporation, and ball milling, can yield various types of structural disorder and possibly render variations in physicochemical properties. Herein, we focus on evaluating the influence of the ball-milling process on the amorphization of FBZ. The characterization of the average global and local structures before, during, and after the milling process is described by sequential Rietveld refinements, pair distribution function analysis, and the Reverse Monte Carlo method. In conclusion, we show that preserving the local structure (nearest molecules) can be responsible for avoiding the fast structure recrystallization commonly observed when using the solvent-evaporation process for the studied drug.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Effect of pattern transfer process on roughness of block copolymer patterns from directed self-assembly

Block copolymer-directed self-assembly (DSA) remains promising for improving pattern quality and reducing the stochastic variations that challenge high numerical aperture extreme ultraviolet lithography. Equally critical is refining pattern transfer methods for accurately transferring the rectified DSA features to the underlying substrate. We compare two atomic layer deposition (ALD)-based techniques: sequential infiltration synthesis (SIS) and dry liftoff, applied to polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) DSA patterns. Both methods utilize aluminum oxide hard masks, with one synthesized through infiltration into the PMMA domains and the other through conformal ALD coating. High-resolution scanning electron micrographs were analyzed to measure line edge, width, and placement roughness for both the line (PMMA) and space (PS) features. Although both methods yielded similar overall 3σ rms roughness, they differed significantly in the frequency-dependent power spectral density (PSD) profiles. SIS reduced line placement roughness at length scales associated with the polymer pitch, but increased space width roughness at low frequencies, whereas dry liftoff mimicked the frequency content of the original guiding pattern. This study underscores the importance of PSD evaluation in selecting optimal pattern transfer strategies for specific applications.

Block copolymers↗
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↗
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↗
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↗