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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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Enhancing the Operational Resilience of Advanced Reactors with Digital Twins by Recurrent Neural Networks

Because of a lack of operation data during abnormal and accident scenarios, along with the existence of uncertainty in the evaluation model for transient and accident analysis, the established abnormal and emergency operating procedures can be biased in characterizing the reactor states and ensuring operational resilience. To improve state awareness and ensure operational flexibility for minimizing effects on the system due to anomaly, digital twin (DT) technology is suggested to support operator's decision-making by effectively extracting and using knowledge of the current and future plant states from the knowledge base. To demonstrate DT's capability for recovering the complete states of reactors and for predicting the future reactor behaviors, this paper develops and assesses both the diagnosis and prognosis DTs in a nearly autonomous management and control system for an Experimental Breeder Reactor-II simulator during different loss-of-flow scenarios.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Distribution Development for the RDX Regional Model at Los Alamos National Laboratory - 20385

Representing uncertainty in model inputs often means finding a balance between uncertainty and physical reality. Developing wide distributions may seem conservative in principle, but this approach may lead to unrealistic model results. Characterizing the current state of knowledge of stochastic inputs presents many challenges, especially if the data available are limited or have limited relevance to the site. Relationships among these inputs may also be important to represent but are typically complex or difficult to define. Often special adjustments must be made to account for reduced credibility in particular data. If parameters are strongly related to one another, a correlation structure may be developed for input to the model. Other techniques such as regression models may be used to incorporate relationships between the information available and the desired parameters. The process of developing distributions must consider details of the model in terms of what the distribution is meant to represent. This paper uses the example of a probabilistic fate and transport model for hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) in the regional aquifer at Los Alamos National Laboratory (LANL). For many parameters, a single draw is applied to all space and time over which the model is run, for a single iteration. This simplification is often made for many reasons, and can often be beneficial, but also adds additional complexity in the distribution development process. Defining the distributional goals as they relate to the modeling process is an important step, which should take place prior to evaluation of the data. Usually, the distributions developed are meant to characterize the average value of the parameter over the spatial and temporal domain of the model. Distribution development requires consideration of many sources of information on the parameter where available, ideally from multiple references. Examples of different sources include data from different references but also from different conditions, measurement methods, or experimental types. Depending on these conditions and the reliability or relevance of particular references, different sources of data may each contribute valuable information but have varying relevance to the site. In these cases, weighting data unequally is a useful way to incorporate this information. As an example, aqueous dispersivity data are available for a variety of rock types. Only a few values are available for the desired rock type, and this is not enough to develop a distribution. Therefore, dispersivity values from other rock types are included in distribution development but are down-weighted such that the best data have the most influence on the distribution developed. In another case, K{sub d} distributions in the model are meant to represent a known composition of multiple soil types. Data from these materials are weighted accordingly to develop a distribution for the weighted average K{sub d} across soil types. Other cases include varying reliability of different sources, and weighting data according to the confidence in these sources. In some cases, input parameters are correlated with one another. An example is advective porosity, which is positively correlated with total porosity and must be less than total porosity. Paired data with both parameters must exist to discern the relationship between the two parameters and if it is necessary to build a correlation structure into the model. In general, correlated parameters may be represented in the model by a multivariate distribution, or perhaps more desirably, capturing the correlation within the developed distributions which may be treated as independent from one another. In the example of porosity, this can be done by transforming advective porosity into a proportion of total porosity which may be drawn independently from the distribution of total porosity. This paper explores how complex data and correlations can be incorporated to meet the distributional goals of the model, using the RDX regional model as a detailed example. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
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↗
DOE OSTI2026

Measurement of muon neutrino charged-current quasielasticlike cross section using off-axis NuMI beam at ICARUS

This paper presents the first neutrino cross-section measurement from the ICARUS detector at Fermilab, using Neutrinos at the Main Injector (NuMI) beam data collected from two beam operation periods corresponding to 2.5 × 10 20 protons-on-target in neutrino beam mode. The signal is defined by events with no pions produced in the final state, a topology dominated by charged-current quasielasticlike signatures. The measurement is reported as flux-averaged differential cross sections as functions of kinematic variables that provide sensitivity to the complex nuclear effects that often dominate the systematic uncertainty budgets of neutrino oscillation measurements. Specifically, this work reports cross sections in two angular variables—the angle of the outgoing lepton and the opening angle between the lepton and leading proton—and two variables characterizing the kinematic imbalance between the muon and proton in the plane transverse to the incoming neutrino. These results are compared against predictions from a variety of neutrino event generators, with p values calculated between the extracted cross sections and each prediction. Overall, the predictions agree with the data; however, the current budget of uncertainties does not yet provide sufficient discriminating power to favor a specific model.

Abd Alrahman, F. [Houston U.]↗
DOE OSTI2026

Non -degenerate marginal-likelihood calibration with application to quantum characterization

Here, we propose a marginal likelihood strategy within the Kennedy-O’Hagan (KOH) Bayesian framework, where a Gaussian process (GP) models the discrepancy between a physical system and its simulator. Our approach introduces a novel marginalized likelihood by integrating out the degenerate eigenspace of the covariance matrix, rather than approximating the original likelihood. Unlike approximation methods that compromise accuracy for computational efficiency, our method defines an exact likelihood—distinct from the original but preserving all relevant information. This formulation achieves computational efficiency and stability, even for large datasets where the covariance matrix nears degeneracy. Applied to the characterization of a superconducting quantum device at Lawrence Livermore National Laboratory, the approach enhances the predictive accuracy of the Lindblad master equations for modeling Ramsey measurement data by effectively quantifying uncertainties consistent with the quantum data.

general physics↗
DOE OSTI2024

Characterization of Most Promising Sequestration Formations in the Rocky Mountain Region

The project Characterization of Most Promising Sequestration Formations in the Rocky Mountain Region is one of 9 site characterization projects that were implemented as part of ARRA (American Recovery and Reinvestment Act). Data from this project was used to improve resolution of data in NATCARB in the area of study. Data related to this study has already been incorporated in NATCARB Atlas. The Rocky Mountain Carbon Capture and Storage (RMCCS) project investigated multiple geologic formations and characterized a local site on the Colorado Plateau for future CCS opportunities. The RMCCS project focused on the Cretaceous Dakota, Jurassic Entrada, and Pennsylvanian Weber Sandstones, the three largest regional formations. All formations in this project are potential CO2 storage resources for future power plants, natural gas processing plants, cement plants, and oil shale development projects. The area adjacent to Craig, Colorado, (Sand Wash Basin) was the area selected for detailed geologic characterization on the RMCCS project. The basin was selected in part because the geology can be extrapolated to other sites on the Colorado Plateau. Field mapping and seismic surveys were conducted to identify and evaluate the basin's structural configuration. A 9,745-foot deep characterization well was drilled to collect 131 feet of core and a suite of geophysical well log data. Petrophysical tests on samples of core were used to calibrate geophysical log data, which can be used to obtain storage resource estimates and evaluate associated uncertainty as well as simulate the hydrologic behavior of injected CO2. A detailed analysis of the primary formations (Dakota, Entrada and Weber sandstones) yielded a more accurate CO2 storage resource assessment for these formations within the Colorado Plateau; RMCCS estimates indicate a total CO2 storage resource of more than 38,000 million metric tons. The characterization of the Sand Wash Basin (2-D seismic surveys, multiple well logs and lithological, petrophysical and geochemical analyses) allowed for a detailed 3-D model to be constructed. The model served as the framework for analyses ranging from CO2 storage resource, injectivity, and subsurface flow to uncertainty estimates to evaluation of risk.

2-D seismic↗
DOE OSTI2020

Understanding Contaminant Migration within a Dynamic River Corridor through Field Experiments and Reactive Transport Modeling

The behavior of a persistent uranium plume within an extended river corridor at the DOE Hanford site is dominantly controlled by river stage fluctuations in the adjacent Columbia River. The plume behavior is further complicated by substantial heterogeneity in physical and geochemical properties of the host aquifer sediments. Multi-scale field and laboratory experiments and reactive transport modeling were integrated to understand the complex plume behavior influenced by highly variable hydrologic and geochemical conditions in time and space. In this paper, we (1) describe multiple data sets from field-scale uranium adsorption and desorption experiments performed at our experimental well-field, (2) develop a reactive transport model that incorporates hydrologic and geochemical heterogeneities characterized from multi-scale and multi-type datasets and a surface complexation reaction network based on laboratory studies, and (3) compare the modeling and observation results to provide insights on how to refine the conceptual model and reduce prediction uncertainties. The experimental results revealed significant spatial variability in uranium adsorption/desorption behavior, while modeling demonstrated that ambient hydrologic and geochemical conditions and heterogeneities in sediment physical and chemical properties both contributed to complex plume behavior and its persistence. This research underscores the great challenges in adequately characterizing this type of site to model the reactive transport processes over scales of 10 m or more. Our analysis provides important insights into the characterization, understanding, modeling, and remediation of groundwater contaminant plumes influenced by dynamic surface water and groundwater interactions.

Chen, Xingyuan↗
DOE OSTI2022

Improved quantitation of SIMS depth profile measurements of niobium via sample holder design improvements and characterization of grain orientation effects

The importance of SIMS analyses for “N-doped” impurity alloyed niobium and other surface-alloyed materials continues to increase. A major hurdle is the uncertainty of instrument calibration due to changes in sample height either from sample surface topography or from the sample holder itself. The CAMECA sample holder design allows for many types of samples to be analyzed. However, a drawback is that the holder faceplate can bend, contributing an uncertainty in the relative sensitivity factor (RSF) used to quantify the SIMS results. Here, we describe an improved sample holder having a reinforced faceplate, which prevents deflection and reduces uncertainty. Simulations show that the new design significantly reduces deflection from 10 μm to 5 nm. Sample measurements show a reduction of RSF uncertainty from this source from 4.1% to 0.95%. Grain orientation has long been suspected to affect RSF measurement as well. A bicrystal implant standard, consisting of randomly oriented and [001] grains, was successively rotated 15° between analyses. It was observed that 20% of the analyses performed on the randomly oriented grain exhibited anomalously high RSF values as well as slow sputter rates. These features were associated with the changing grain normal orientation with respect to the primary Cs + beam. The grain orientation associated with the rise in RSF was simulated and determined to be the [101] crystallographic plane, thus indicating that ion channeling was responsible for the significantly increased RSF. Focused ion beam analysis confirmed slower sputter rates for the cardinal crystallographic orientations, indicating that ion channeling occurred for each.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Milestone Report for MS8: Extend Quantitative Brine and CO 2 Leakage Calculations

This report summarizes results of the risk analysis and characterization of CO 2 and brine leakage potential of Farnsworth Unit (FWU) wells. U.S. DOE’s National Risk Assessment Partnership (NRAP) program works on quantitatively assess long-term environmental risks amidst significant geologic uncertainty and variability. NRAP risk assessment and computational tools are developed to quantify uncertainties and calculate risk associated with geologic sequestration of carbon dioxide (CO 2 ). For this study, we have developed a workflow from University of Utah’s physics-based reservoir simulators to performing leakage calculations using NRAP Tools. NRAP tools (NRAP-IAM-CS, RROM-Gen) are used to conduct leakage risk analysis based on Eclipse simulation results, and characterize wellbore leakage at the Farnworth Site. This report summarizes results of the risk analysis and characterization of CO 2 and brine leakage potential of Farnsworth Unit (FWU) wells.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Calibration and Uncertainty Estimation Using the Ensemble Kalman Filter with a Large Subsurface Flow and Transport Model - 20321

At routinely monitored groundwater contamination sites, periodically measured environmental conditions such as groundwater levels and contaminant concentrations are used to inform and confirm a conceptual site model (CSM) and guide the development and calibration of a numerical groundwater flow and transport model. The calibration of groundwater flow and transport models after each measurement (sampling) event can illuminate deficiencies in a CSM, identify areas where additional monitoring is warranted, and predict the behavior of the system to guide decision making. However, manual and automated (e.g. PEST) model calibration tools can be time-consuming and computationally expensive to implement after each sampling event. Perhaps as a result, such calibration tools generally utilize all available monitoring data simultaneously rather than sequentially assimilating monitoring data one sampling event at a time as the results from sampling become available. A more real-time data assimilation approach may reduce parameter uncertainty, quantify the value of additional monitoring data, and produce a usable model more quickly and with less effort. To mitigate the potential time-consuming aspects of manual and widely applied automated calibration techniques, a data assimilation algorithm called the ensemble Kalman filter (EnKF) was evaluated as a relatively efficient method of model calibration and uncertainty assessment via the sequential integration of monitoring data into a model. The EnKF was able to successfully and efficiently assimilate monitoring and modeling data to calibrate a complex flow and transport model at a real-world site with significant subsurface heterogeneity, uncertainty, and 12 years of monitoring data (over 4,000 individual measurements of groundwater levels and over 2,500 measurements of contaminant concentrations). Starting with an uncalibrated model data from annual sampling events were sequentially assimilated, and the resultant predication errors and estimated parameter uncertainties were tracked. After all monitoring data were assimilated, both flow and transport residuals at the end of the EnKF process were comparable to those produced via a concurrent PEST calibration effort but required fewer model simulations. Both uncertainty and prediction errors decreased over time. In a real-time application, the adequacy of the model could be assessed after each sampling event. The benefits of such a real-time approach to utilizing monitoring data include reduced costs (in the form of model updates or site characterization efforts), early flagging of possible errors in the CSM, and a reduced risk of overfitting and corresponding increased confidence in model predictions. This tool may be particularly useful compared to other calibration techniques (e.g. manual, PEST) when model runtimes are long, calibration parameters are many, or parameter uncertainty is large. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Quantifying the drivers of ecosystem fluxes and water potential across the soil-plant-atmosphere continuum in an arid woodland

Dryland ecosystems occupy a vast swath of the terrestrial land surface and exert a sizeable impact on the cycling of carbon and water globally. These biomes are characterized by tightly coupled carbon and water cycles that respond rapidly to transient pulses in water availability. However, there exist many mechanistic uncertainties regarding the environmental drivers of, and linkages between, plant and ecosystem processes. Thus, drylands are often poorly represented in many vegetation and land surface models. An enhanced understanding of dryland ecosystem function is limited by the lack of long-term, co-located, and frequent measurements of plant and ecosystem processes. At a piñon-juniper woodland in southeastern Utah, USA, we collected a continuous dataset of meteorological conditions, soil water potential from surface to bedrock, tree water potential, and ecosystem carbon and water fluxes from eddy covariance. We found that predawn and midday tree water potential and daily ecosystem fluxes were highly sensitive to fluctuations in soil water availability, particularly in shallower layers, and that daytime variability in atmospheric drivers only loosely controlled these processes. The strong connections between shallow soil water potential, tree water potential, and ecosystem fluxes occurred because of the dominant role of precipitation pulses in driving vegetation activity, as even small pulses of moisture stimulated shallow soil water potential, tree water potential, and evapotranspiration for between 1 and 2 weeks. Carbon fluxes (net ecosystem exchange and gross primary productivity) were sensitive to precipitation pulses for longer, up to 3 weeks. Our results highlight that improved monitoring and sensing of shallow soil moisture can greatly enhance our understanding of dryland ecosystem function. Here, a better mechanistic understanding of the impacts of precipitation pulses is also needed to improve vegetation modeling of dryland ecosystems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Uranium Holdup Monitoring with Compton Imaging as Function of Depth and Mass

Material Control and Accountability (MC&A) programs track masses of materials flowing through production processes, where some material remains in process equipment as holdup. Quantification of these masses using gamma emissions typically involves usage of a well characterized radiation detector and assumptions of geometric configuration to constrain detection efficiencies, where the Generalized Geometry Holdup (GGH) method is often used. Uncertainties on the order of ±50% are observed, where the difficulties arise based on the asymmetric and gradient distributions of material that do not fall within the bounds of GGH. Gamma imagers provide a possible means to improve this geometric knowledge. This work describes the process used in creating a series of mass standards to aid the development of imaging algorithms for quantification.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

2024 Milestone Report: Site 300 mPDV Optical Fiducials

In the early 2000s Photon Doppler Velocimetry (PDV) replaced the Fabry-Perot many beam system1 and has since become ubiquitous across dynamic experimental platforms to measure velocity and event times such as shock breakout, key variables for high pressure physics research. The advent of optically multiplexed oscilloscope channels to create multiplexed PDV (mPDV) increased portability and reduced price per data point. However, these advantages came with the cost of additional fielding complexity and thermally induced timing drift, which directly affects the ability to use PDV for high precision time measurement. Controlling the temperature or incorporating optical fiducials allows researchers to characterize, reduce, and correct this thermal drift in analysis. Our implemented optical fiducial or “timing marker” allows us to reduce thermal drift uncertainty from the 10s of nanoseconds down to the 100s of picoseconds with minimal added complexity to existing systems. The implementation of this timing marker normalizes uncertainty across optical delays, brings our facility cross timing into the sub nanosecond regime and lets us identify/study anomalies in our data. This improvement increases experiment reliability and quality enabling a new class of high precision experiments at S300.

42 ENGINEERING↗
DOE OSTI2021

Kilonovae Across the Nuclear Physics Landscape: The Impact of Nuclear Physics Uncertainties on r-process-powered Emission

Merging neutron stars produce “kilonovae”—electromagnetic transients powered by the decay of unstable nuclei synthesized via rapid neutron capture (the r-process) in material that is gravitationally unbound during inspiral and coalescence. Kilonova emission, if accurately interpreted, can be used to characterize the masses and compositions of merger-driven outflows, helping to resolve a long-standing debate about the origins of r-process material in the Universe. We explore how the uncertain properties of nuclei involved in the r-process complicate the inference of outflow properties from kilonova observations. Using r-process simulations, we show how nuclear physics uncertainties impact predictions of radioactive heating and element synthesis. For a set of models that span a large range in both predicted heating and final abundances, we carry out detailed numerical calculations of decay product thermalization and radiation transport in a kilonova ejecta with a fixed mass and density profile. The light curves associated with our models exhibit great diversity in their luminosities, with peak brightness varying by more than an order of magnitude. We also find variability in the shape of the kilonova light curves and their color, which in some cases runs counter to the expectation that increasing levels of lanthanide and/or actinide enrichment will be correlated with longer, dimmer, redder emission.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Maxar Initial Satellite Characterization

This documents reports on the initial Assessment Specification and Validation (ASV) of Maxar satellite imagery as a geolocation system. Validation is a prerequisite for using geolocation for applications that require quantified uncertainty. A Variance Component Estimation (VCE) calibration of the provider’s co- variance matrices concluded that they were exaggerated. However, we currently lack enough independent validation data to quantify the improvement from the VCE. The current ASV process is slow and expensive. It will not be able to keep up with growing numbers of satellite systems. We proposed a method to automate ASV using controlled imagery. The proposed method will allow us to keep up with new sensors and generate unbounded amounts of calibration data, leading to unprecedented accuracy.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Discrete-Direct Model Calibration and Uncertainty Propagation Method Confirmed on Multi-Parameter Plasticity Model Calibrated to Sparse Random Field Data

A discrete direct (DD) model calibration and uncertainty propagation approach is explained and demonstrated on a 4-parameter Johnson-Cook (J-C) strain-rate dependent material strength model for an aluminum alloy. The methodology's performance is characterized in many trials involving four random realizations of strain-rate dependent material-test data curves per trial, drawn from a large synthetic population. The J-C model is calibrated to particular combinations of the data curves to obtain calibration parameter sets which are then propagated to “Can Crush” structural model predictions to produce samples of predicted response variability. These are processed with appropriate sparse-sample uncertainty quantification (UQ) methods to estimate various statistics of response with an appropriate level of conservatism. This is tested on 16 output quantities (von Mises stresses and equivalent plastic strains) and it is shown that important statistics of the true variabilities of the 16 quantities are bounded with a high success rate that is reasonably predictable and controllable. The DD approach has several advantages over other calibration-UQ approaches like Bayesian inference for capturing and utilizing the information obtained from typically small numbers of replicate experiments in model calibration situations—especially when sparse replicate functional data are involved like force–displacement curves from material tests. The DD methodology is straightforward and efficient for calibration and propagation problems involving aleatory and epistemic uncertainties in calibration experiments, models, and procedures.

42 ENGINEERING↗
DOE OSTI2024

Uncertainty quantification and propagation in lithium-ion battery electrodes using bayesian convolutional neural networks

The complex nature of manufacturing processes stipulates electrodes to possess high variability with increased heterogeneity during production. X-ray computed tomography imaging has proved to be critical in visualizing the complicated stochastic particle distribution of as-manufactured electrodes in lithium-ion batteries. However, accurate prediction of their electrochemical performance necessitates precise evaluation of kinetic and transport properties from real electrodes. Image segmentation that characterizes voxels to particle/pore phase is often meticulous and fraught with subjectivity owing to a myriad of unconstrained choices and filter algorithms. Here we utilize a Bayesian convolutional neural network to tackle segmentation subjectivity and quantify its pertinent uncertainties. Otsu inter-variance and Blind/Referenceless Imaging Spatial Quality Evaluator are used to assess the relative image quality of grayscale tomograms, thus evaluating the uncertainty in the derived microstructural attributes. We analyze how image uncertainty is correlated with the uncertainties and magnitude of kinetic and transport properties of an electrode, further identifying pathways of uncertainty propagation within microstructural attributes. The coupled effect of spatial heterogeneity and microstructural anisotropy on the uncertainty quantification of transport parameters is also understood. This work demonstrates a novel methodology to extract microstructural descriptors from real electrode images through quantification of associated uncertainties and discerning the relative strength of their propagation, thus facilitating feedback to manufacturing processes from accurate image based electrochemical simulations.

25 ENERGY STORAGE↗
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↗