Reliable Estimates Research Articles

Mechanism and Data-Driven Dual Estimation of Coupling Hydraulic-Thermal States for Steam Heating Networks Considering Multi-Time-Scale Characteristics.

For a steam heating network (SHN), which is one of the most important parts of the integrated energy systems in an industrial park, it is essential to provide accurate and reliable estimation of hydraulic and thermal states, to ensure its operational safety and economy. Considering two different time-scale characteristics of the hydraulic and thermal processes in the SHN, this article proposes a mechanism and data-driven dual estimation method for the coupling hydraulic-thermal dynamic states. Due to the fact that the existing coupled estimation methods with one time scale may suffer from heavy computational burden, a data-driven dual sequential acrlong DSE method of the SHN is proposed based on the two-time scales, in which the dynamics of slow thermal states can also be captured when performing the acrlong SE of the fast hydraulic process. Furthermore, to improve the computational and communicational efficiency, a distributed interaction strategy based on the nodal transformation matrix is designed for large-scale steam systems. To verify the effectiveness of the proposed method, a single pipeline system and two real-world industrial superheated steam networks are employed. Compared to other state-of-the-art methods, the proposed method achieves the best tradeoff between the estimation accuracy and computational efficiency.

An Optimized Uncertainty-Aware Training Framework for Neural Networks.

Uncertainty quantification (UQ) for predictions generated by neural networks (NNs) is of vital importance in safety-critical applications. An ideal model is supposed to generate low uncertainty for correct predictions and high uncertainty for incorrect predictions. The main focus of state-of-the-art training algorithms is to optimize the NN parameters to improve the accuracy-related metrics. Training based on uncertainty metrics has been fully ignored or overlooked in the literature. This article introduces a novel uncertainty-aware training algorithm for classification tasks. A novel predictive uncertainty estimate-based objective function is defined and optimized using the stochastic gradient descent method. This new multiobjective loss function covers both accuracy and uncertainty accuracy (UA) simultaneously during training. The performance of the proposed training framework is compared from different aspects with other UQ techniques for different benchmarks. The obtained results demonstrate the effectiveness of the proposed framework for developing the NN models capable of generating reliable uncertainty estimates.

Reliability estimation in multicomponent stress-strength model using weighted exponential-Lindley distribution

This research investigates the reliability estimation in multicomponent stress-strength model when both the stress and strengths are drawn from Weighted Exponential-Lindley distribution. Reliability assessment is carried out using classical and Bayesian approaches. The Bayes estimates of the reliability in the multicomponent stress-strength model are derived under a squared error loss function using informative and non-informative priors for the parameters. Further, Lindley's approximation and Gibbs sampling method are used to develop Bayes estimators for the system's reliability due to the lack of explicit forms. Additionally, an asymptotic confidence interval and the highest probability density credible interval are constructed to gauge system performance. A simulation study is conducted to assess the performance of reliability estimators. Finally, a real data set is analysed for illustrative purposes.

The accuracy of reliability coefficients: A reanalysis of existing simulations.

Controversy over which reliability estimators should be used persists due to a lack of knowledge about their accuracy. Simulation is an effective tool to obtain an answer, but existing simulation studies yield contradictory results regarding which reliability estimators are the best. The causes of these inconsistent conclusions have yet to be discussed. This study reanalyzes existing studies to understand these contradictions. The most important reason is that previous studies consider only a few reliability estimators. This study examines approximately 30 reliability estimators and finds that there is no single, most accurate reliability estimator across all data types. Instead, several reliability estimators are accurate to comparable levels for unidimensional data (congeneric reliability, Guttman's lambda2, and ten Berge-Zegers's mu). Likewise, multiple reliability estimators perform similarly for multidimensional data (multidimensional parallel reliability, correlated factors reliability, and second-order factor reliability). Whereas many recent studies support factor analysis (FA) reliability estimators, this study shows that not all FA reliability estimators are accurate and that some cause severe overestimation. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Attenuation proxy hidden in surface brightness – colour diagrams

Aims. Large future sky surveys, such as the Legacy Survey of Space and Time (LSST), will provide optical photometry for billions of objects. Reliable estimation of the physical properties of galaxies requires information about dust attenuation, which is usually derived from ultraviolet (UV) and infrared (IR) data. This paper aims to construct a proxy for the far-UV (FUV) attenuation (AFUVp) from the optical data alone, enabling the rapid estimation of the star formation rate (SFR) for galaxies that lack UV or IR data. This will accelerate and improve the estimation of key physical properties of billions of LSST–like observed galaxies (observed in the optical bands only). Methods. To mimic LSST observations, we used the deep panchromatic optical coverage of the Sloan Digital Sky Survey (SDSS) Photometric Catalogue, Data Release 12, complemented by the estimated physical properties for the SDSS galaxies from the GALEX-SDSS-WISE Legacy Catalog (GSWLC) and inclination information obtained from the SDSS Data Release 7. We restricted our sample to the 0.025–0.1 spectroscopic redshift range and investigated relations among surface brightness, colours, and dust attenuation in the FUV range for star-forming galaxies obtained from the spectral energy distribution (SED). Results. Dust attenuation is best correlated with colour measured between u and r bands (u − r) and the surface brightness in the u band (μu). We provide a dust attenuation proxy for galaxies on the star-forming main sequence. This relation can be used for the LSST or any other type of broadband optical survey. The mean ratio between the catalogue values of SFRs and those estimated using optical-only SDSS data with the AFUVp prior calculated as ΔSFR = log(SFRthis work/SFRGSWLC) is found to be less than 0.1 dex, while runs without priors result in an SFR overestimation larger than 0.3 dex. The presence or absence of the AFUVp has a negligible influence on the stellar mass (Mstar) estimation (with ΔMstar in the range from 0 to −0.15 dex). Conclusions. We note that AFUVp is reliable for low-redshift main sequence galaxies. Forthcoming deep optical observations of the LSST Deep Drilling Fields, which also have multi-wavelength data, will enable one to calibrate the obtained relation for higher redshift galaxies and, possibly, extend the study towards other types of galaxies, such as early-type galaxies off the main sequence.

Accuracy and sensitivity of soil erosion estimation using 137Cs technology: A statistical perspective

Random spatial variation of the 137Cs inventory is the principal contributor to uncertainty in soil erosion estimation using 137Cs technology. A statistically sound sampling design is imperative for obtaining reliable soil erosion estimations. The objectives of this study are to: 1) characterize the effect of sample size on the estimates of mean inventories; 2) evaluate the sensitivity of the estimated soil redistribution to sample size using a new 137Cs model; 3) compare erosion detection limits among five conversion models; and 4) assess three spatial interpolation methods. Two small watersheds were sampled in an irregular grid design, and 30 samples were taken on a reference site. A moving window scheme was used to compute the 7-point and 11-point means of 137Cs inventories. The Welch’s modified t-test was used to test the mean estimates and to compute the detection limits for the replicated samples. Five models were selected to convert 137Cs inventories to soil redistribution rates. Since most single samples without replication yielded insignificant test results, the 137Cs technique cannot be used to estimate soil erosion at a single point due to random spatial variation. With 30 reference samples, 7 replicate samples on the sampling site provided reliable estimations of 137Cs inventories and soil redistribution. The spatial patterns of the estimated 137Cs inventories and soil redistribution became more regular and systematic as sample size increased, which agreed increasingly well with topography and surface hydrology. Replicate samples can be taken from each landform element or slope position where the erosion rate is expected to be uniform. Alternatively, a systematic grid sampling scheme can be used, and the nearest neighbors can be treated as replicates to calculate moving averages. The Type I and II errors with replicated samples showed that all sampling positions should be included in calculating watershed or area mean erosion rates even though the Type I errors indicated insignificant redistribution rates for some samples. Due to the lack of spatial autocorrelation, spline and inverse distance weighting methods performed better than kriging for interpolation. Detection limits and magnitudes of soil redistribution varied substantially with conversion models, depending on their sensitivities to changes in 137Cs inventories.

Comparing psychopathological symptoms, life satisfaction, and personality traits between the WHO and APA frameworks of gaming disorder symptoms: A psychometric investigation.

The inclusion of Internet Gaming Disorder (IGD) in the fifth revision of the Diagnostic and Statistical Manual of Mental Disorders (DSM-5) by the American Psychiatric Association and Gaming Disorder in the 11th revision of the International Classification of Diseases (ICD-11) by the World Health Organization requires consistent psychological measures for reliable estimates. The current study aimed to investigate the psychometric properties of the Gaming Disorder Test (GDT), the Ten-Item Internet Gaming Disorder Test (IGDT-10), and the Five-Item Gaming Disorder Test (GDT-5) and to compare the WHO and the APA frameworks of gaming disorder symptoms in terms of psychopathological symptoms, life satisfaction, and personality traits. A sample of 723 Swedish gamers was recruited (29.8% women, 68.3% men, 1.9% other, Mage = 29.50 years, SD = 8.91). The results indicated notable differences regarding the estimated possible risk groups between the two frameworks. However, the association between gaming disorder symptoms and personality traits, life satisfaction, and psychopathological symptoms appeared consistent across the two frameworks. The results showed excellent psychometric properties in support of the one-factor model of the GDT, IGDT-10, and GDT-5, including good reliability estimates (McDonald's omega) and evidence of construct validity. Additionally, the results demonstrated full gender and age measurement invariance of the GDT, IGDT-10, and GDT-5, indicating that gaming disorder symptoms are measured equally across the subgroups. These findings demonstrate that the IGDT-10, GDT-5, and GDT are appropriate measures for assessing gaming disorder symptoms and facilitating future research in Sweden.

Single microparticle characterization using multi-wavelength lens-free imaging

Holographic imaging captures an interference pattern, effectively encoding an object‘s properties such as size, shape and refractive index in the hologram. Lens-free holographic imaging offers a scalable solution with large field of view to analyze microparticles or cells in high-throughput biological imaging applications. We studied characterization of single particles based on their holographic fingerprint using multi-wavelength illumination based lens-free holography. Deciphering this information directly in the hologram domain with our multi-wavelength approach allows for reliable estimation of object refractive index along with its size without ambiguity. This work provides a path forward for lens-free imaging-based microparticle characterization that can prove useful in biological studies such as cell analysis and characterization.

County-Level Poverty Evaluation Using Machine Learning, Nighttime Light, and Geospatial Data

The accurate and timely acquisition of poverty information within a specific region is crucial for formulating effective development policies. Nighttime light (NL) remote sensing data and geospatial information provide the means for conducting precise and timely evaluations of poverty levels. However, current assessment methods predominantly rely on NL data, and the potential of combining multi-source geospatial data for poverty identification remains underexplored. Therefore, we propose an approach that assesses poverty based on both NL and geospatial data using machine learning models. This study uses the multidimensional poverty index (MPI), derived from county-level statistical data with social, economic, and environmental dimensions, as an indicator to assess poverty levels. We extracted a total of 17 independent variables from NL and geospatial data. Machine learning models (random forest (RF), support vector machine (SVM), adaptive boosting (AdaBoost), extreme gradient boosting (XGBoost), and light gradient boosting machine (LightGBM)) and traditional linear regression (LR) were used to model the relationship between the MPI and independent variables. The results indicate that the RF model achieved significantly higher accuracy, with a coefficient of determination (R2) of 0.928, a mean absolute error (MAE) of 0.030, and a root mean square error (RMSE) of 0.037. The top five most important variables comprise two (NL_MAX and NL_MIN) from the NL data and three (POI_Ed, POI_Me, and POI_Ca) from the geographical spatial data, highlighting the significant roles of NL data and geographical data in MPI modeling. The MPI map that was generated by the RF model depicted the detailed spatial distribution of poverty in Fujian province. This study presents an approach to county-level poverty evaluation that integrates NL and geospatial data using a machine learning model, which can contribute to a more reliable and efficient estimate of poverty.

Computation of prediction intervals for forest aboveground biomass predictions using generalized linear models in a large-extent boreal forest region

Abstract Remotely sensed data have an important application for estimation of forest variables, e.g. height, volume, and aboveground biomass (AGB). The increased use of remotely sensed data implemented along with model-based inference has shown improved efficiency in prediction and mapping of such forest variables. In this study, plot-level airborne laser scanning data and Swedish National Forest Inventory field reference data were used to predict AGB using generalized linear models (GLMs) assuming Gamma and Tweedie distributions for the field observed AGB. The GLMs were selected considering the convenience of not correcting transformation bias as it is required in other regression models with transformed response variable. To overcome the challenge in providing reliable uncertainty estimates for the estimated forest variable map products at individual pixel-scale, we focused on computing 95% prediction intervals (PIs) for Gamma and Tweedie GLMs with a square root link function. The relative uncertainties were computed as the ratio between the half-width of the PIs and the predicted AGBs. The AGB-airborne laser scanning models were developed with root mean square error values of 22.6 Mgha−1 (26%) and 21.7 Mgha−1 (25%), respectively, for the Gamma and Tweedie GLMs. Two methods were applied to compute PIs for the Gamma GLM, one using the R package ‘ciTools’ and another derived through asymptotic theory. It was found that the 95% PIs computed using ‘ciTools’ had the most accurate coverage probability in comparison to the other method. An extended version of these PIs was also utilized for the Tweedie GLMs. The range of PIs associated with the prediction of AGB were narrower for lower predicted AGB values compared with the length of higher predicted AGB values. Comparing the two fitted models, the Gamma GLM showed lower relative uncertainties for the lower range of predicted AGBs, whereas the Tweedie GLM showed lower relative uncertainties for the higher range of predicted AGBs. Overall, the Tweedie GLM provided a better model fit for AGB predictions.

Estimation of Reliability under Conditional Stress - Strength Setup based on Weibull Distribution

The Weibull distribution has been extensively studied and applied across various fields due to its versatility in modeling a wide range of phenomena, especially in reliability engineering, survival analysis, and lifetime modeling. The concept of Rl a,b , which represents a system's reliability in a conditional stress-strength setup, was proposed by Sabre and Khorshidian (2021). In this research, the problem of estimating reliability of the component is considered when strength variable X and stress variable Y follow independent Weibull distributions with common shapes and different scale parameters under conditional stress-strength setup. The maximum likelihood estimator, asymptotic confidence interval, Bootstrap estimators, Boot-p estimators, and Bayes estimator under-squared error loss function with associated highest posterior density interval are constructed for conditional stress-strength reliability. Simulation study is conducted to estimate mean square error (MSE) of estimator of conditional stress-strength reliability. The real data analysis is also carried out.

Pain in the Context of Sensory Deafferentation.

Pain that accompanies deafferentation is one of the most mysterious and misunderstood medical conditions. Prevalence rates for the assorted conditions vary considerably but the most reliable estimates are greater than 50% for strokes involving the somatosensory system, brachial plexus avulsions, spinal cord injury, and limb amputation, with controversy surrounding the mechanistic contributions of deafferentation to ensuing neuropathic pain syndromes. Deafferentation pain has also been described for loss of other body parts (e.g., eyes and breasts) and may contribute to between 10% and upwards of 30% of neuropathic symptoms in peripheral neuropathies. There is no pathognomonic test or sign to identify deafferentation pain, and part of the controversy surrounding it stems from the prodigious challenges in differentiating cause and effect. For example, it is unknown whether cortical reorganization causes pain or is a byproduct of pathoanatomical changes accompanying injury, including pain. Similarly, ascertaining whether deafferentation contributes to neuropathic pain, or whether concomitant injury to nerve fibers transmitting pain and touch sensation leads to a deafferentation-like phenotype can be clinically difficult, although a detailed neurologic examination, functional imaging, and psychophysical tests may provide clues. Due in part to the concurrent morbidities, the physical, psychologic, and by extension socioeconomic costs of disorders associated with deafferentation are higher than for other chronic pain conditions. Treatment is symptom-based, with evidence supporting first-line antineuropathic medications such as gabapentinoids and antidepressants. Studies examining noninvasive neuromodulation and virtual reality have yielded mixed results.

Selection of best wavelet functions and decomposition levels for coupling with soft computing methods in estimating ETo in coastal and island regions

ABSTRACT Mass transfer-based models are among the extensively applied reference evapotranspiration (ET o ) estimation approaches that have been proven to provide reliable estimates under certain climatic and geographical conditions. A major issue with such approaches is the high variations in wind speed time series, which is a governing meteorological parameter in mass transfer-based models. few studies have focused on applying wavelet transform as a robust pre-processing technique for ETo estimation. A major question with coupling wavelet transforms with soft computing methods would be the proper choice of the wavelet function, vanishing moments and the decomposition levels. The present study aims at assessing different wavelet functions coupled with boosted regression tree (BT) models, i.e. wavelet-BT (WBT), in estimating ET o values (through mass transfer parameters) in both coastal and island regions, where it is supposed that wind speed variations are affected by sea–inland interactions and so has the sharp variations (unlike ET o ). The obtained results showed that the coupled WBT model could improve the single BT model results to a great extent, and meanwhile, the Daubechies wavelet function with six vanishing moments provided the most accurate results in all the locations. Further, the best simulation outcomes with each wavelet function were obtained when the maximum possible decomposition level was used with each function.

Integrated CFD-FEM approach for external gear pump vibroacoustic field prediction

In this work, a three-dimensional fluid-structural and vibro-acoustics coupled model of a gear pump is presented. Gear pumps represent the majority of the positive displacement machines used for flow generation in fluid power systems. Typically, the dynamics of gear pumps are dependent on the characteristics of the fluid dynamics inside the pump, which translates into vibrations to the housing. These vibrations then propagate to the surrounding medium and emit sound. The purpose of this study is to propose a three-dimensional fully integrated computational model to simulate the complete gear pump behaviour from the fluid dynamics to the structural vibrations, up to the vibroacoustic response. In this hybrid configuration, a transient CFD (Computational Fluid Dynamics) model is first developed to simulate the 3D flow field with a deforming and re-meshing approach to take into account the variation of the volume between the gears. Second, the internal pressure field calculated at each time step is then used as a loading into a structural FEM (Finite Element Method) model of the gear pump to compute the actual stresses and deformations of the housing. Third, the results of the structural response are used as excitation in a vibroacoustic sub-model to simulate the radiated noise using a high-order FEM technique. The comparison between the numerical and experimental flow curves validates the CFD model. The sound power calculations from the vibroacoustic model show good comparison with the sound intensity measurements around the pump casing, confirming the validity of the proposed coupled model. The described CFD-FEM approach proves to be a powerful gear pump design tool: it provides a reliable estimate of gear pump working parameters such as fluid power and vibroacoustic characteristics, starting from the CAD (Computer-Aided Design) geometry of the components. Furthermore, being one of the first multi-domain simulation models of a gear pump, this work can be useful to researchers as a starting point to correlate the noise emitted with the internal flow in full 3D conditions.

Exploring the dependability of Combined Ratio Estimators in Stratified Ranked Set Sampling: Insights from COVID-19 data

In this study, we introduce a novel combined ratio type estimator within the framework of Stratified Ranked Set Sampling to estimate the population mean of the study variable by incorporating bivariate auxiliary information. We conduct a comprehensive comparative analysis, including traditional combined ratio, combined regression, Shabbir and Khan [13], and Bhushan and Kumar [37] estimators. We assess the bias and mean squared error of the proposed estimator under the initial degree of approximation. The data source consists of COVID-19 data up to July 2023. Through empirical investigation and simulation studies, our proposed estimator consistently demonstrates superior performance compared to its counterparts, exhibiting the highest relative efficiency. These findings underscore the practical significance of our research in public health and decision-making, emphasizing the potential of this estimator to provide more accurate and reliable estimates in various applications involving ranked set sampling and auxiliary information.

Validating Synthetic Usage Data in Living Lab Environments

Evaluating retrieval performance without editorial relevance judgments is challenging, but instead, user interactions can be used as relevance signals. Living labs offer a way for small-scale platforms to validate information retrieval systems with real users. If enough user interaction data are available, then click models can be parameterized from historical sessions to evaluate systems before exposing users to experimental rankings. However, interaction data are sparse in living labs, and little is studied about how click models can be validated for reliable user simulations when click data are available in moderate amounts. This work introduces an evaluation approach for validating synthetic usage data generated by click models in data-sparse human-in-the-loop environments like living labs. We ground our methodology on the click model’s estimates about a system ranking compared to a reference ranking for which the relative performance is known. Our experiments compare different click models and their reliability and robustness as more session log data become available. In our setup, simple click models can reliably determine the relative system performance with already 20 logged sessions for 50 queries. In contrast, more complex click models require more session data for reliable estimates, but they are a better choice in simulated interleaving experiments when enough session data are available. While it is easier for click models to distinguish between more diverse systems, it is harder to reproduce the system ranking based on the same retrieval algorithm with different interpolation weights. Our setup is entirely open, and we share the code to reproduce the experiments.

Taking advantage of sampling designs in spatial small-area survey studies

Spatial small area estimation models have become very popular in some contexts, such as disease mapping. Data in disease mapping studies are exhaustive, that is, the available data are supposed to be a complete register of all the observable events. In contrast, some other small area studies do not use exhaustive data, such as survey based studies, where a particular sampling design is typically followed and inferences are later extrapolated to the entire population. In this article we propose a spatial model for small area survey studies, taking advantage of spatial dependence between units, which is the key assumption used for yielding reliable estimates in exhaustive data based studies. In addition, and in contrast to most survey-based spatial studies, we also take into account information on the sampling design and additional supplementary variables to obtain estimates in small areas. This makes it possible to merge spatial and sampling models into a common proposal.

1 Use of the GreenFeed bait system to assist in measuring fecal output and digesta kinetics

Abstract With increased use of automated feeders, like the bait dispenser on an automated head chamber system (AHCS; GreenFeed; C-Lock Inc., Rapid City, SD), more scientists are investigating ways to use this equipment. Scientist with the Agricultural Research Service initially conducted an experiment to determine if dosing titanium dioxide (TiO2) through an AHCS is an alternative to the traditional hand-fed dosing method for estimating fecal output (FO). The AHCS used had a 2-hopper bait dispensing system, where one hopper contained alfalfa pellets marked with 1% TiO2 and the other contained alfalfa pellets. During the morning (0800), hand-fed heifers received 32 g of TiO2-marked pellets, whereas AHCS-dosed heifers also received 32 g of marked pellets during their first visit each day. A two one-sided t-test indicated the FO estimates were similar (P = 0.04), but the AHCS dosed heifers had greater (P < 0.01) variability; this difference in FO variability is probably due to the increased variability in dosing time (0615 ± 6.2 h). This research has highlighted the potential for dosing cattle with a marker through the AHCS, but conventional fecal marker methods assume steady-state concentration. Our research has shown that errors associated with external marker methods are not highly associated with analytical techniques but are most influenced by dose size and sampling inaccuracy. Hence, ad libitum use of an AHCS results in non-steady-state fecal concentrations. To determine whether reliable FO estimates could be obtained under conditions of irregular but known dose times, we designed 2 experiments where the steady-state assumptions were relaxed, and fit known time measured fecal concentrations to multi-dose digesta kinetics models to estimate FO. In these experiments we used individually penned, rumen fistulated Dexter steers and limit-fed a diet of hay and protein supplement. First, after a 7-d dietary acclimation, steers were given a dose of TiO2 through the rumen fistula and again on d 14, and over 120 h after each dose, 14 spaced fecal samples were collected. In Exp. 2, steers received the first of 6 daily doses, then on d 7 no dose, and on days 8 to 12 daily dosing resumed. Beginning on d 7, when dosing was skipped, fecal sampling began and over a 120-h period 14 fecal samples were collected. For Exp. 1, marker concentration data were fit to a G2 digesta kinetics model and for Exp. 2, concentration data were fit to a multi-dose G2 digesta kinetics model assuming identical digesta kinetics for each dose and the concentration over time as the sum of each pulse. Measured FO in Exp. 2 was 11% greater than the estimates obtained from fitting measured concentrations to multi-dose digesta kinetics models.

Analysis of Relatively Short Variable Rate “Noisy” Well Test Data Using Non-Linear Deconvolution

Short well test data are pressure-rate-time data that are not long enough to be used to infer the reservoir boundary model and are very common in the oil and gas industry. Short rate well test data may occur when companies try to cut costs of well test jobs or mostly due to improper well test design. Nevertheless, one may wish to extract the most amount of information from this limited data because the de-convolve response can allow the reservoir engineer to make the best use of the available data in selecting a suitable interpretation model by narrowing down the possible boundary models and also providing a reliable estimates of model parameters. The aim of this study is to demonstrate the usefulness and significance of pressure-rate deconvolution in analyzing relatively short variable rate data using a hypothetical case study. The simulation was carried out using Sapphire’s test design module by assuming the presence of an exploratory well in an oil reservoir above bubble point pressure. Further assumption is that the reservoir is homogenous, therefore the possibility of a changing wellbore model was neglected from the analysis. The computer codes for the simulation were inputted using python programming language. We observed from the study that although pressure and flow rate relationship can be nonlinear, the problem can be formulated as a linear problem and the nonlinearity is expressed in the features of the reservoir. The simulation results were satisfactory using the test case and deviations between model parameters and actual reservoir parameters used in simulation was shown to have an absolute value less than 8% which is within acceptable engineering limits.

Bayesian Proper Orthogonal Decomposition for Learnable Reduced-Order Models With Uncertainty Quantification

Designing and/or controlling complex systems in science and engineering relies on appropriate mathematical modeling of systems dynamics. Classical differential equation based solutions in applied and computational mathematics are often computationally demanding. Recently, the connection between reduced-order models of high-dimensional differential equation systems and surrogate machine learning models has been explored. However, the focus of both existing reduced-order and machine learning models for complex systems has been how to best approximate the high fidelity model of choice. Due to high complexity and often limited training data to derive reduced-order or machine learning surrogate models, it is critical for derived reduced-order models to have reliable uncertainty quantification at the same time. In this paper, we propose such a novel framework of Bayesian reduced-order models naturally equipped with uncertainty quantification as it learns the distributions of the parameters of the reduced-order models instead of their point estimates. In particular, we develop <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">learnable Bayesian proper orthogonal decomposition</i> (BayPOD) that learns the distributions of both the POD projection bases and the mapping from the system input parameters to the projected scores/coefficients so that the learned BayPOD can help predict high-dimensional systems dynamics/fields as quantities of interest in different setups with reliable uncertainty estimates. The developed learnable BayPOD inherits the capability of embedding physics constraints when learning the POD-based surrogate reduced-order models, a desirable feature when studying complex systems in science and engineering applications where the available training data are limited. Furthermore, the proposed BayPOD method is an end-to-end solution, which unlike other surrogate-based methods, does not require separate POD and machine learning steps. The results from a real-world case study of the pressure field around an airfoil have shown the potential of learnable BayPOD as a new family of reduced-order models with reliable uncertainty estimates.