Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “inversion 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Overview of IMPACT Data Acquisition System and Data Reduction Process

This report documents the development of the data acquisition system (DAS) and data reduction methodologies for the Irradiated Material Property Accelerated Characterization Test (IMPACT) experiment at the Advanced Test Reactor (ATR). The IMPACT experiment is designed to enable in-pile measurement of thermal conductivity in metallic nuclear fuels, specifically U-10Zr, using an instrumented thermal conductivity probe. The DAS supports both passive temperature monitoring and active thermal interrogation of the probe through controlled AC and DC excitation. Significant modifications to laboratory-scale systems were required to accommodate the higher resistance paths associated with the in-pile application. Custom electronics and relay-controlled measurement sequencing were developed to enable the measurement and sufficient power delivery to the sensing region. A reduced-order, axisymmetric thermal model based on the thermal quadrupoles method is presented to support data interpretation. This model enables efficient evaluation of transient heat transfer behavior and facilitates solution of the inverse problem required to extract thermal properties from measured signals. Multiple boundary condition formulations are discussed to address varying experimental time scales and geometries. Additionally, machine learning techniques are introduced to support data reduction and improve confidence in inverse solutions. Convolutional neural networks are applied to identify the presence of gas gaps and other evolving geometric features that significantly impact thermal response during irradiation. These efforts contribute to the broader integration of digital twin frameworks and real-time modeling capabilities within the Advanced Fuels Campaign.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗
DOE OSTI2023

Computationally-driven discovery of second harmonic generation in EuBa 3 (B 3 O 6 ) 3 through inversion symmetry breaking

Nonlinear optical (NLO) crystals with superior properties are significant for advancing laser technologies and applications. Introducing rare earth metals to borates is a promising and effective way to modify the electronic structure of a crystal to improve its optical properties in the visible and ultraviolet range. In this work, we computationally discover inversion symmetry breaking in EuBa 3 (B 3 O 6 ) 3 , which was previously identified as centric, and demonstrate noncentrosymmetry via synthesizing single crystals for the first time by the floating zone method. We determine the correct space group to be P 6¯. The material has a large direct bandgap of 5.56 eV and is transparent down to 250 nm. The complete anisotropic linear and nonlinear optical properties were also investigated with a d 11 of ∼0.52 pm/V for optical second harmonic generation. Further, it is Type I and Type II phase matchable. This work suggests that rare earth metal borates are an excellent crystal family for exploring future deep ultraviolet (DUV) NLO crystals. It also highlights how first principles computations combined with experiments can be used to identify noncentrosymmetric materials that have been wrongly assigned to be centrosymmetric.

He, Jingyang (ORCID:0000000238863659)↗
DOE OSTI2023

Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations

Predictive modeling typically relies on Bayesian model calibration to provide uncertainty quantification. Variational inference utilizing fully independent (“mean-field”) Gaussian distributions are often used as approximate probability density functions. This simplification is attractive since the number of variational parameters grows only linearly with the number of unknown model parameters. However, the resulting diagonal covariance structure and unimodal behavior can be too restrictive to provide useful approximations of intractable Bayesian posteriors that exhibit highly non-Gaussian behavior, including multimodality. High-fidelity surrogate posteriors for these problems can be obtained by considering the family of Gaussian mixtures. Gaussian mixtures are capable of capturing multiple modes and approximating any distribution to an arbitrary degree of accuracy, while maintaining some analytical tractability. Unfortunately, variational inference using Gaussian mixtures with full-covariance structures suffers from a quadratic growth in variational parameters with the number of model parameters. The existence of multiple local minima due to strong nonconvex trends in the loss functions often associated with variational inference present additional complications, These challenges motivate the need for robust initialization procedures to improve the performance and computational scalability of variational inference with mixture models. In this work, we propose a method for constructing an initial Gaussian mixture model approximation that can be used to warm-start the iterative solvers for variational inference. The procedure begins with a global optimization stage in model parameter space. In this step, local gradient-based optimization, globalized through multistart, is used to determine a set of local maxima, which we take to approximate the mixture component centers. Around each mode, a local Gaussian approximation is constructed via the Laplace approximation. Finally, the mixture weights are determined through constrained least squares regression. The robustness and scalability of the proposed methodology is demonstrated through application to an ensemble of synthetic tests using high-dimensional, multimodal probability density functions. Here, the practical aspects of the approach are demonstrated with inversion problems in structural dynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A scalable variational method for estimating the latent infection-rate field of an outbreak

In this paper, we explore whether the infection-rate of a disease can serve as a robust monitoring variable in epidemiological surveillance algorithms. The infection-rate is dependent on population mixing patterns that do not vary erratically day-to-day; in contrast, daily case-counts used in contemporary surveillance algorithms are corrupted by reporting errors. The technical challenge lies in estimating the latent infection-rate from case-counts. Here we devise a Bayesian method to estimate the infection-rate across multiple adjoining areal units, and then use it, via an anomaly detector, to discern a change in epidemiological dynamics. We extend an existing model for estimating the infection-rate in an areal unit by incorporating a Markov random field model, so that we may estimate infection-rates across multiple areal units, while preserving spatial correlations observed in the epidemiological dynamics. To carry out the high-dimensional Bayesian inverse problem, we develop an implementation of mean-field variational inference specific to the infection model and integrate it with the random field model to incorporate correlations across counties. The method is tested on estimating the COVID-19 infection-rates across all 33 counties in New Mexico using data from the summer of 2020, and then employing them to detect the arrival of the Fall 2020 COVID-19 wave. We perform the detection using a temporal algorithm that is applied county-by-county. We also show how the infection-rate field can be used to cluster counties with similar epidemiological dynamics.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Analyses of internal structures and defects in materials using physics-informed neural networks

Characterizing internal structures and defects in materials is a challenging task, often requiring solutions to inverse problems with unknown topology, geometry, material properties, and nonlinear deformation. Here, we present a general framework based on physics-informed neural networks for identifying unknown geometric and material parameters. By using a mesh-free method, we parameterize the geometry of the material using a differentiable and trainable method that can identify multiple structural features. We validate this approach for materials with internal voids/inclusions using constitutive models that encompass the spectrum of linear elasticity, hyperelasticity, and plasticity. We predict the size, shape, and location of the internal void/inclusion as well as the elastic modulus of the inclusion. Our general framework can be applied to other inverse problems in different applications that involve unknown material properties and highly deformable geometries, targeting material characterization, quality assurance, and structural design.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Photovoltaic inverter-based quantification of snow conditions and power loss

Snow is a significant challenge for photovoltaic (PV) systems at northern latitudes, where the pace of deployment is rapid but snow-related power losses can exceed 30% of annual production. Accurate snow-related power loss estimation methods for utility-scale sites can support snow mitigation strategies, inform resource planning and validate predictive snow-loss models. This study builds on our previous work on inverter-based detection of snow, and its implications for utility-scale power production, by validating the accuracy of our snow-loss method across different PV sites and system designs and highlighting its value in bringing greater visibility to PV plant operations in winter. Our estimation method is both novel and scalable, requiring only standard monitoring data to correlate snow-related losses with meteorological data. As demonstrated here, our validation method involved three main steps: 1) estimation of performance losses for multiple systems by comparing measured inverter data to modeled data; 2) application of a detection framework to identify which performance losses are snow-related; and 3) comparison of snow-related losses among three utility-scale sites differing in tilt angle. Results show that utility-scale systems at higher tilt angles consistently shed snow more quickly/completely than their lower-tilt counterparts. Further, monthly and seasonal snow losses are inversely and non-linearly correlated with tilt angle when normalized for cumulative snowfall. These results are consistent with the findings of previous studies and support the broad applicability of this method to fixed-tilt utility-scale PV systems around the world that routinely experience snow-related performance losses.

Cooper, Emma C. (ORCID:0000000190554098)↗
DOE OSTI2026

PyHydroGeophysX: An extensible open-source platform for integrating hydrological models with geophysical measurements

Hydrological models and geophysical measurements are widely used tools for understanding subsurface hydrological processes relevant to water resource management, yet they typically remain disconnected due to technical barriers. We present PyHydroGeophysX, an open-source Python platform bridging this gap by providing standardized interfaces between hydrological modeling software (MODFLOW, ParFlow) and geophysical simulation tools (PyGIMLi, SimPEG). The platform implements bidirectional workflows: translating hydrological outputs into simulated geophysical responses through petrophysical models, and extracting hydrological information from geophysical inversions. Key features include bidirectional workflow modules, configurable petrophysical models, time-lapse inversion with temporal regularization, parallel computing, and mesh utilities for property transfer between geophysical and hydrological grids. The modular architecture of PyHydroGeophysX enables researchers to incorporate additional models and methods, fostering broader adoption of integrated hydrogeophysical approaches. The software is freely available on GitHub and is intended for researchers and practitioners working at the intersection of hydrology and geophysics.

Hydrogeophysics↗
DOE OSTI2022

Geothermal Fault Zone and Fluid Imaging through Joint Airborne ZTEM and Ground MT Data Inversion Analysis

This project has aimed to achieve detailed electrical resistivity resolution at geothermal reservoir scales by combining airborne natural electromagnetic (EM) field surveying (ZTEM) with ground magnetotelluric (MT) measurements to approximate an airborne MT geophysical method. MT alone is relatively expensive and may have permitting challenges in sensitive areas. Airborne ZTEM field data contains only the magnetic field, requires a background assumption, and has been limited to relatively high frequencies, thus suffering uniqueness problems. Based on proto-type 2D simulations, ZTEM ambiguities may be reduced through formal incorporation with possibly sparse ground MT soundings, which we pursued in full 3D for this project. The methodology was tested at the high-temperature Roosevelt Hot Springs geothermal system, Utah, which was considered advantageous given the near total exposure of crystalline reservoir rocks across the project area. ZTEM and ground MT survey data were acquired in 2017, subcontracted to outside parties with which we have worked in the past. These included 80 remote-referenced tensor MT soundings over the Mineral Mountains and adjacent Roosevelt Hot Spring producing geothermal system. These MT stations abut later coverage of a similar number of MT stations taken for the Utah FORGE project providing excellent total data aperture to re-solve structure beneath both project areas better than either set alone. The airborne ZTEM survey covered 704 line kilometers in E-W flight lines with a 250 m line spacing. Although this survey was timed during a maintenance-related shutdown of power production at the Roosevelt Hot Springs, other noise sources difficult to identify but including two high-voltage state-scale transmission lines compromised the ZTEM survey badly leading to unusable responses. Thus, with DOE management concurrence, the project proceeded to emphasize inversion and interpretation of the joint SubTER-FORGE MT data sets with regard to the Roosevelt Hot Springs reservoir recharge and to deep heat sources for both it and the Utah FORGE EGS project area. We also investigated the joint ZTEM-MT sampling concept with data sets from the Eleven Mile Canyon prospect area donated by the U.S. Navy (A. Sabin, PoC). Inversion of the SubTER-FORGE MT data using the HexMT 3D finite element algorithm reveals a large, low-resistivity anomaly extending sub-vertically through the depth range of the crust beneath the western Mineral Mountains. The steep conductive zone connects in the lower crust to a more tabular conductor characteristic of much of the Great Basin that generally is ascribed to current mafic magmatic underplating, hybridization and fluid release. The location of the resolved anomaly relative to the recent (0.5-0.8 Ma) eruptive centers of the Mineral Mountains implicates it as remnants of the magma body which fed these centers. This structure appears to be currently feeding heat and fluids upward into the Roosevelt Hot Springs hydrothermal system, as well as heat laterally to the FORGE project area. Separate and joint inversion models were carried out for the donated Eleven Mile Canyon MT-ZTEM data set to demonstrate concept. ZTEM only inversion showed two main alteration zones in the western portion of the project area known from geological mapping. Joint inversion including an E-W profile of MT soundings sharpened these features considerably. It also resolved in much greater detail the graben related normal faulting structure of the central project area which lies at depths exceeding the sensitivity of ZTEM alone. The sparse number of MT da-ta relative to the ZTEM required upweighting the former by a factor of several, but an exact procedure awaits future research. Our final impression is that sparse MT data can improve resolution of the subsurface over that of ZTEM alone. However, well sampled MT data are to be preferred and offer the simplicity of interpreting just one data type, and possess the superior resolution capability coming with the electric field everywhere, and from their high bandwidth.

15 GEOTHERMAL ENERGY↗
DOE OSTI2025

Paper or Plastic? Multiscale Material Handling Properties of Two Model Municipal Solid Waste Streams

Purpose: Municipal Solid Waste (MSW) is a potentially valuable sustainable feedstock for fuel and chemical production due to its carbon-rich content and low cost. This study aims to assess the material handling properties of paperand plastic-rich MSW feedstocks to mitigate equipment failure and processing downtime. Methods: The material handling properties of crumbled MSW feedstocks were measured using apowder rheometer with mass flow hopper calculations to assess handling performance. Inverse gas chromatography was use to measure the surface energy differences between feedstocks. Electron microscopy and Raman spectroscopy was used to evaluate microscale features that may contribute to material handling differences. Results: Plastic and paper rich feedstocks crumbled to a nominal 2 mm particle size were observed to have similar flow and handling characteristics with reasonable hopper outlets. 2 mm plastic rich crumbles, with their higher bulk density, exhibited superior flow performance. By contrast, 4 mm material required significantly larger hopper outlets, indicating poor flowability. Paper rich and 4 mm plastic rich samples displayed broad particle size distributions, which contributed to particle interlocking, jamming, and other flow issues. Electron microscopy revealed that plastic rich samples were significantly smoother, enhancing their flowability compared to the rougher, paper rich materials. Conclusions: This study establishes critical material handling baselines for processing MSW as a viable feedstock for fuel and chemical production. The findings highlight the importance of optimizing particle size and feedstock composition to improve flowability and handling performance.

09 BIOMASS FUELS↗
DOE OSTI2020

Predictive Inverse Model for Advective Heat Transfer in a Short–Circuited Fracture: Dimensional Analysis, Machine Learning, and Field Demonstration

Identifying fluid flow maldistribution in planar geometries is a well–established problem in subsurface science/engineering. Of particular importance to the thermal performance of enhanced (or “engineered”) geothermal systems is identifying the existence of nonuniform (i.e., heterogeneous) permeability and subsequently predicting advective heat transfer. Here, machine learning via a genetic algorithm (GA) identifies the spatial distribution of an unknown permeability field in a two–dimensional Hele–Shaw geometry (i.e., parallel plates). The inverse problem is solved by minimizing the L2 norm between simulated residence time distribution (RTD) and measurements of an inert tracer breakthrough curve (BTC) (C–Dot nanoparticle). Principal component analysis (PCA) of spatially correlated permeability fields enabled reduction of the parameter space by more than a factor of 10 and restricted the inverse search to reservoir–scale permeability variations. Thermal experiments and tracer tests conducted at the mesoscale Altona Field Laboratory (AFL) demonstrate that the method accurately predicts the effects of extreme flow channeling on heat transfer in a single bedding–plane rock fracture. However, this is only true when the permeability distributions provide adequate matches to both tracer RTD and frictional pressure loss. Without good agreement to frictional pressure loss, it is still possible to match a simulated RTD to measurements, but subsequent predictions of heat transfer are grossly inaccurate. Here, the results of this study suggest that it is possible to anticipate the thermal effects of flow maldistribution, but only if both simulated RTDs and frictional pressure loss between fluid inlets and outlets are in good agreement with measurements.

42 ENGINEERING↗
DOE OSTI2022

Using Multiscale Ethane/Methane Observations to Attribute Coal Mine Vent Emissions in the San Juan Basin From 2013 to 2021

Abstract Source attribution of natural gas emissions from fossil fuels in New Mexico's San Juan Basin (SJB) is challenging due to source heterogeneity and emissions transience. We demonstrate that ethane (C 2 H 6 ) to methane (CH 4 ) mixing ratios can identify and separate sources over different scales using various measurement techniques. We report simultaneous CH 4 and C 2 H 6 observations near a coal mine vent and oil and gas (O&G) emission sources using ground‐based in situ measurements in 2020/2021. During these campaigns, we observed a stable coal vent C 2 H 6 :CH 4 ratio of 1.28% ± 0.11%, discernibly different than nearby O&G source ratios ranging from 0.9% to 16.8%. We analyze airborne observations of the SJB taken in 2014/2015 that exhibit similar coal vent ratios and further show the region's heterogeneity. We identify episodic O&G sources, including a gas plant source detected in 2014/2015 that is absent in our 2020/2021 data. We examine total column observations of C 2 H 6 and CH 4 made in 2013 with a solar spectrometer and find a C 2 H 6 :CH 4 ratio of 1.3% ± 0.4% for the coal vent. The stable and unique coal vent ratio relative to other O&G sources in the region is used to demonstrate that consistent attribution is possible using various measurement methods at multiple scales across many years. Finally, we demonstrate that using C 2 H 6 as a proxy for fossil CH 4 inversions can inform detailed basin‐scale inversions, provided we understand source specific changes in the C 2 H 6 :CH 4 ratio like we report in the SJB.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Quasiprobabilistic Readout Correction of Midcircuit Measurements for Adaptive Feedback via Measurement Randomized Compiling

Quantum measurements are a fundamental component of quantum computing. However, on present-day quantum computers, measurements can be more error prone than quantum gates and are susceptible to nonunital errors as well as nonlocal correlations due to measurement crosstalk. While readout errors can be mitigated in postprocessing, this is inefficient in the number of qubits due to a combinatorially large number of possible states that need to be characterized. In this work, we show that measurement errors can be tailored into a simple stochastic error model using randomized compiling, enabling the efficient mitigation of readout errors via quasiprobability distributions reconstructed from the measurement of a single preparation state in an exponentially large confusion matrix. We demonstrate the scalability and power of this approach by correcting readout errors without matrix inversion on a large number of different preparation states applied to a register of eight superconducting transmon qubits. Moreover, we show that this method can be extended to midcircuit measurements used for active feedback via quasiprobabilistic error cancellation, and we demonstrate the correction of measurement errors on an ancilla qubit used to detect and actively correct bit-flip errors on an entangled memory qubit. Our approach enables the correction of readout errors on large numbers of qubits and offers a strategy for correcting readout errors in adaptive circuits in which the results of midcircuit measurements are used to perform conditional operations on nonlocal qubits in real time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Anomaly Attribution with Likelihood Compensation

This paper addresses the task of explaining anomalous predictions of a black-box regression model. When using a black-box model, such as one to predict building energy consumption from many sensor measurements, we often have a situation where some observed samples may significantly deviate from their prediction. It may be due to a sub-optimal black-box model, or simply because those samples are outliers. In either case, one would ideally want to compute a responsibility score indicative of the extent to which an input variable is responsible for the anomalous output. In this work, we formalize this task as a statistical inverse problem: Given model deviation from the expected value, infer the responsibility score of each of the input variables. We propose a new method called likelihood compensation (LC), which is founded on the likelihood principle and computes a correction to each input variable. To the best of our knowledge, this is the first principled framework that computes a responsibility score for real valued anomalous model deviations. We apply our approach to a real-world building energy prediction task and confirm its utility based on expert feedback.

Idé, Tsuyoshi↗
DOE OSTI2020

Time-Resolved Spectroscopy of Insulator-Metal Transitions: Exploring Low-Energy Dynamics in Strongly Correlated Systems. Final Report

Transition metal oxides (TMOs) have attracted much attention in recent years. The strong coupling between charge, spin, and orbital degrees of freedom creates novel functional properties. The research at the interplay between ferromagnetism, ferroelectricity and conductivity provides a promising way to the development of future spintronic devices. The interface characterization of multifunctional oxide heterostructures is crucial to understand deeply the magnetic response, spin injection and spin transport. In year one, we characterized optically the magnetic property with the method of magnetization-induced second-harmonic generation (MSHG), which is a sensitive technique to selectively probe the interface where the spatial inversion symmetry is broken. The interface of n-type BaTiO 3 (BTO)/La 0.67 Sr 0.33 MnO 3 (LSMO) forms a Schottky barrier and displays a good diode effect. By applying an external electric field across the sample, we observe the magnetoelectric (ME) coupling effect to modulate the interface magnetization. The voltage dependent magnetic contrast sharply vanishes at positive voltage (applied to LSMO contact) and reveals a ferromagnetic (FM)-to- antiferromagnetic (AFM) transition occurring at the interface, while the magneto-optic Kerr effect (MOKE) indicates that the bulk property is not affected. The strain mediated mechanism and ferroelectric (FE) polarization induced charge medicated mechanism are both discussed, but they do not play an important role in the observed magnetization transition. A new mechanism is proposed - the injected minority spins through strong Hund's interaction with the local magnetic moments at positive voltage weaken the double-exchange interaction of nearby Mn e g electrons, thereby reducing the ferromagnetic (FM) ordering. The dominant superexchange interaction of localized t 2g electrons finally leads to the AFM configuration. By reducing the electron carrier concentration of BTO, a positive voltage shift of the transition is observed. The oxygen richer sample with lower carrier concentration requires a higher voltage to increase the hole doping level of LSMO to induce the interfacial AFM phase. By inserting a thin (1nm) La 0.5 Ca 0.5 MnO 3 layer between BTO and LSMO, the interface magnetic response from LSMO is enhanced. In year two, a non-multiferroic heterostructure SrTiO 3 (STO)/ La 0.5 Ca 0.5 MnO 3 (LCMO)/La 0.67 Sr 0.33 MnO 3 (LSMO) was studied. In this system, the interface FM-AFM transition is observed at negative voltage. The STO layer may act as a hole-donating layer, which induces the hole transfer to LSMO making it overdoped, while the LCMO interlayer at the 0.5 hole doping level displays complicated CE type AFM phase. Thus the AFM phase is dominant at the interface and electron accumulation is required to induce the FM phase by applying a negative voltage. For oxygen rich sample, the magnetic MSHG loop reappears at high positive voltage (around +2.5 V). At high doping level (x > 0.5), LSMO exhibits A-type AFM order, consisting of AFM superexchange coupling between adjacent layers and intralayer FM double-exchange coupling. The less tensile strain of STO and LSMO due to a smaller lattice mismatch as compared to BTO would result in a weaker interlayer coupling . Thus, interfacial A-type AFM order can occur in STO/LCMO/LSMO heterostructure at high hole doping concentration. The study of ME coupling of multifunctional oxide heterostructures is definitely important to the development and performance of future spintronic devices. The results presented here regarding the interfacial magnetic transition controlled by an external electric field offer some new perspective to study the spin transport of magnetic tunnel junctions.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Direct reactions with the AT-TPC

Direct reactions are crucial tools for accessing properties of the atomic nucleus. Fundamental and exotic phenomena such as collective modes, pairing, weakbinding effects and evolution of single-particles energies can be investigated in peripheral collisions between a heavy nucleus and a light target. The necessity of using inverse kinematics to reveal how these structural properties change with isospin imbalance renders direct reactions a challenging technique when using the missing mass method. In this scenario, Active Target Time Projection Chambers (AT-TPC) have demonstrated an outstanding performance in enabling these types of reactions even under conditions of very low beam intensities. The AT-TPC of the Facility for Rare Isotope Beams (FRIB) is a next generation multipurpose Active Target. When operated inside a solenoidal magnet, direct reactions benefit from the measurement of the magnetic rigidity that enables particle identification and the determination of the excitation energy with high resolution without the need of auxiliary detectors. Additionally, the AT-TPC can be coupled to a magnetic spectrometer improving even further its spectroscopic investigation capability. In this contribution, we discuss inelastic scattering and transfer reaction data obtained via the AT-TPC and compare them to theory. In particular, we present the results for the 14 C(p,p′) and 12 Be (p,d) 11 Be reactions. For 14 C, we compare the experimental excitation energy of the first 1 – excited state with coupled-cluster calculationsbased on nuclear interactions from chiral effective field theory and with available shell-model predictions. For 12 Be, we determine the theoretical spectroscopic factors of the 12 Be (p,d) 11 Be transfer reaction in the shell modeland compare them to the experimental excitation spectrum from a qualitative standpoint.

active target↗
DOE OSTI2022

Preconditioned least‐squares Petrov–Galerkin reduced order models

Abstract In this article, we introduce a methodology for improving the accuracy and efficiency of reduced order models (ROMs) constructed using the least‐squares Petrov–Galerkin (LSPG) projection method through the introduction of preconditioning. Unlike prior related work, which focuses on preconditioning the linear systems arising within the ROM numerical solution procedure to improve linear solver performance, our approach leverages a preconditioning matrix directly within the minimization problem underlying the LSPG formulation. Applying preconditioning in this way has the potential to improve ROM accuracy for several reasons. First, preconditioning the LSPG formulation changes the norm defining the residual minimization, which can improve the residual‐based stability constant bounding the ROM solution's error. The incorporation of a preconditioner into the LSPG formulation can have the additional effect of scaling the components of the residual being minimized to make them roughly of the same magnitude, which can be beneficial when applying the LSPG method to problems with disparate scales (e.g., dimensional equations, multi‐physics problems). Importantly, we demonstrate that an “ideal preconditioned” LSPG ROM (a ROM in which the preconditioner is the inverse of the Jacobian of its corresponding full order model) emulates projection of the full order model solution increment onto the reduced basis. This quantity defines a lower bound on the error of a ROM solution for a given reduced basis. By designing preconditioners that approximate the Jacobian inverse—as is common in designing preconditioners for solving linear systems—it is possible to obtain a ROM whose error approaches this lower bound. The proposed approach is evaluated on several mechanical and thermo‐mechanical problems implemented within the Albany HPC code and run in the predictive regime, with prediction across material parameter space. We demonstrate numerically that the introduction of simple Jacobi, Gauss‐Seidel, and ILU preconditioners into the proper orthogonal decomposition/LSPG formulation reduces significantly the ROM solution error, the reduced Jacobian condition number, the number of nonlinear iterations required to reach convergence, and the wall time (thereby improving efficiency). Moreover, our numerical results reveal that the introduction of preconditioning can deliver a robust and accurate solution for test cases in which the unpreconditioned LSPG method fails to converge.

Lindsay, Payton↗
DOE OSTI2022

Bayesian operator inference for data-driven reduced-order modeling

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian inverse problem with Gaussian prior and likelihood. The resulting posterior distribution characterizes the operators defining the reduced-order model, hence the predictions subsequently issued by the reduced-order model are endowed with uncertainty. The statistical moments of these predictions are estimated via a Monte Carlo sampling of the posterior distribution. Since the reduced models are fast to solve, this sampling is computationally efficient. Furthermore, the proposed Bayesian framework provides a statistical interpretation of the regularization term that is present in the deterministic operator inference problem, and the empirical Bayes approach of maximum marginal likelihood suggests a selection algorithm for the regularization hyperparameters. The proposed method is demonstrated on two examples: the compressible Euler equations with noise-corrupted observations, and a single-injector combustion process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Making Invisible Visible: Data-Driven Seismic Inversion With Spatio-Temporally Constrained Data Augmentation

Deep learning and data-driven approaches have shown great potential in scientific domains. The promise of data-driven techniques relies on the availability of a large volume of high-quality training datasets. Due to the high cost of obtaining data through expensive physical experiments, instruments, and simulations, data augmentation techniques for scientific applications have emerged as a new direction for obtaining scientific data recently. However, existing data augmentation techniques originating from computer vision yield physically unacceptable data samples that are not helpful for the domain problems that we are interested in. In this article, we develop new data augmentation techniques based on convolutional neural networks. Specifically, our generative models leverage different physics knowledge (such as governing equations, observable perception, and physics phenomena) to improve the quality of the synthetic data. To validate the effectiveness of our data augmentation techniques, we apply them to solve a subsurface seismic full-waveform inversion using simulated CO 2 leakage data. Our interest is to invert for subsurface velocity models associated with very small CO 2 leakage. We validate the performance of our methods using comprehensive numerical tests. Here via comparison and analysis, we show that data-driven seismic imaging can be significantly enhanced by using our data augmentation techniques. Particularly, the imaging quality has been improved by 15% in test scenarios of general-sized leakage and 17% in small-sized leakage when using an augmented training set obtained with our techniques.

58 GEOSCIENCES↗