Uncertainty Quantification Research Articles

Optimal planning for hybrid renewable energy systems under limited information based on uncertainty quantification

Developing hybrid renewable energy systems (HRES) is crucial for ensuring affordable, sustainable, and reliable energy access in remote rural and island regions. Rich and detailed data play a pivotal role in the optimal design of HRES. However, remote areas often face data limitations due to inadequate metering infrastructure, which further increases uncertainties in HRES design. This paper proposes a planning optimization method that quantifies multiple uncertainties, requiring only limited information for the optimal HRES design. First, uncertainties in HRES planning are classified into different types based on intrinsic randomness, data availability, and impact level. Then, by integrating uncertainty quantification with credibility theory, knowledge-based scenario generation models are developed to leverage limited available information to generate extreme and typical operating conditions for a tailored HRES design. Finally, a fuzzy credibility-constrained stochastic-robust optimization model is proposed to optimize the design of HRES. A practical case facing significant data scarcity and gaps is used to validate the effectiveness of the proposed method. The proposed approach reduces the loss of load probability for HRES to 0.02% and lowers the levelized cost of energy to $0.16/kWh—33% lower than that of the deterministic method and 79% lower than that of the traditional stochastic method.

Quantification of contaminant mass discharge and uncertainties: Method and challenges in application at contaminated sites

Contaminant mass discharge (CMD) estimation involves combining multilevel concentration and flow measurements to quantify the contaminant mass passing through a control plane downgradient of a point source. However, geological heterogeneities and limited data introduce uncertainties that complicate CMD estimation and risk assessment. Although CMD is increasingly used in groundwater management, methods for quantifying and handling these uncertainties are still needed. This study develops and tests a CMD estimation method based on Bayesian geostatistics to quantify CMD uncertainties using data from a control plane perpendicular to the contaminant plume.By combining geostatistical conditional simulations of the spatial concentration distribution with the flow, an ensemble of CMD realizations is generated, from which a cumulative distribution function is derived. A key element of this approach is the use of a macrodispersive transport model to simulate the spatial concentration trend. This ensures that the estimated concentration reflects the expected physical behavior of the contaminant plume while also allowing the integration of site-specific conceptual information.The method is applicable to plumes with dissolved contaminants, such as chlorinated solvents, petroleum hydrocarbons, Per- and polyfluoroalkyl substances (PFAS) and pesticides. Site-specific conceptual understanding is used to inform the prior probability density functions of the structural model parameters and to define acceptable simulated concentration limits. We applied the method at three sites contaminated with chlorinated ethenes, demonstrating its robustness across varying information levels and data availability.Our results shows that strong site-specific conceptual knowledge and high sampling density constrain the CMD uncertainty (CV = 21 %) and results in estimated model parameters and a spatial concentration distribution that agrees well with the conceptual model. For a site with less data and limited conceptual knowledge, CMD and concentration distribution estimates are still feasible, though with higher uncertainty (CV = 41 %). Extending the method to account for multiple source zones and complex plume migration improved parameter identification and reduced the 95 % CMD confidence interval by 11 % ([4950–8750] to [5090–8480] g yr−1), while also providing a spatial concentration distribution in better agreement with the plume conceptualization.This study highlights the importance of integrating site-specific conceptual knowledge in CMD estimation, particularly for less-sampled sites. The method can furthermore assist in identifying remediation targets, evaluating remedial effectiveness, and optimizing sampling strategies.

Operational sensitivity analysis of flooding volume in urban areas

We focus on a probability-based approach to analyze the flooding volume during extreme rainfall events in urban areas. Our approach considers uncertainty in both non-operational and operational variables. The former are quantities that are tied to the characterization of rainfall events and key catchment features, whose uncertainties stem from incomplete characterization. The latter comprise elements of the system on which actions can be taken within a range of design values. As the non-deterministic nature of these two types of quantities differs at a fundamental level, we rely on an operational Global Sensitivity Analysis theoretical framework that explicitly recognizes this distinction. As a test bed to showcase our approach, we consider an urban catchment in Northern Italy. We assess the sensitivity of the flooding volume to a set of operational variables, such as diameter and roughness of a set of conduits of the sewer network as well as potential improvement of the infiltration capacity of the urban catchment. We show that our approach can identify the operational configuration with the highest effectiveness in mitigating instances of flooding, taking into account the uncertainties in the non-operational quantities that drive the system behavior.

Quantifying uncertainty in landslide susceptibility mapping due to sampling randomness

The quality of landslide and non-landslide samples plays a crucial role in the landslide susceptibility maps (LSM) generated using machine learning algorithms. However, uncertainties arising from non-landslide sample collection can significantly compromise the reliability of these maps. Current methods, such as buffer-controlled sampling (BCS), often fail to address this issue adequately. This study aims to fill that gap by employing Monte Carlo simulations combined with BCS to quantify the uncertainties associated with non-landslide sampling and improve LSM accuracy. A novel framework is proposed, integrating landslide susceptibility confidence maps (LSCMs) to address the inherent uncertainty in BCS-based LSMs. The framework evaluates inconsistencies in LSMs, showing that maps generated by the same model differ in over 30% of the area due to variations in non-landslide sample selection. The proposed approach outperforms traditional methods by correctly classifying landslide-prone areas, particularly in low and very low susceptibility zones, while providing a more reliable quantification of uncertainty. These findings underscore the limitations of traditional LSM methods and demonstrate that LSCMs offer a more robust tool for landslide hazard assessment. The framework enhances the precision of susceptibility mapping and provides critical insights for better risk mitigation and disaster preparedness.

Real-time modeling of transient crustal deformation through the quantification of uncertainty deduced from GNSS data

We propose a new method for real-time uncertainty monitoring of earthquake and volcano source models using data from the global navigation satellite system (GNSS) and explore its application concerning observation station placement. The Geospatial Information Authority of Japan operates two main types of GNSS earth observation network system (GEONET) coordinates for crustal deformation monitoring on different time scales: post-processing analysis values and real-time GEONET analysis system for rapid deformation monitoring (REGARD). REGARD uses the Markov Chain Monte Carlo (MCMC) method termed real-time automatic uncertainty estimation of a coseismic single rectangular model using GNSS data (RUNE) for single rectangular fault model estimation to handle uncertainty. Thus far, no GNSS monitoring system can automatically detect transient crustal deformation events, such as volcanic activity and earthquake swarms, on timescales of a day or less. We extended RUNE and developed a core program for a new monitoring system for earthquake and volcanic source models and their uncertainties. Our program achieved automatic and stable MCMC utilization for rectangular fault, dike, Mogi, and spheroid models by increasing the computational speed, improving search efficiency, and adjusting hyperparameters. The program automatically determines the standard deviation of the likelihood function assuming a normal distribution with weights for each observation station. The calculation time was within 15 s for 1 × 106 samples on a standard 1U server. We assessed the reliability of the developed method using synthetic and observed GNSS data from the 2015 Sakurajima volcanic event. The results were consistent with the assumed model and previous studies and indicated an advantage in automatically quantifying uncertainty in a short computation time. Based on MCMC samples, we developed a new visualization algorithm to indicate areas on a map in which the number of observation stations should be expanded. We assessed the reliability using data from the 2023 Noto Peninsula earthquake [Mj 6.5]. The results indicate that the algorithm is helpful in studying the placement of stations. The above model extensions and their application are essential to achieve a rapid quantitative understanding of disaster events near urban areas and for utilizing this information in emergency response activities.Graphical

Study on characteristics and prediction of the pressure drag of the swept strut under supersonic wide-range conditions

In this paper, the numerical simulation of the swept strut ramjet combustor was carried out under wide-range conditions (Ma3 = 1.8 ∼ 5.0), and the pressure drag characteristics of the swept strut were discussed. The results show that the pressure drag characteristics of the swept strut are related to the Mach number of the combustor inlet and the swept angle of the strut. The decreased boundary of the strut pressure drag coefficient gradually advances with the decrease of the Mach number of the combustor inlet. When Ma3 = 1.8 ∼ 2.0, the pressure drag reduction boundary is α = 15°. When Ma3 = 2.2 ∼ 2.8, the pressure drag reduction boundary is α = 45°. When Ma3 = 3.0 ∼ 4.0, the pressure drag reduction boundary is α = 60°. When Ma3 = 5.0, the pressure drag reduction boundary is α = 65°. In addition, with the decrease of the Mach number of the combustor inlet, the pressure drag reduction performance benefit brought by increasing the swept angle of the strut will gradually increase. Furthermore, a pressure drag coefficient prediction model suitable for wide-range conditions and multiple configurations of swept struts was proposed based on deep learning. The prediction model consists of two parts in series, which includes the prediction model of the surface pressure coefficient of the swept strut based on multilayer perceptron (MLP) and the prediction model of the pressure drag coefficient of the swept strut based on convolutional neural network (CNN). To improve the prediction accuracy of the MLP model, new training samples were added based on the ensemble-based uncertainty quantification, and the improved MLP model was obtained by retraining. The results show that both the two prediction models have high prediction accuracy under the effect of multiple complex flow characteristics on the strut. The results of this study are helpful to provide a reference for the aerodynamic drag reduction design of the strut in the wide-speed supersonic combustor.

A Comparative Analysis of Fractal and Fractionalized Thermal Non-Equilibrium Model for Chaotic Convection Saturated by Porous Medium

The convective heat transfer is one of the most important mechanism of heat transference for controlling the chaotic characteristics in porous media. A comparative study of thermal non-equilibrium model is proposed for fractal porous under the consideration of chaotic convection. A novel chaos control is focused between fractal porous and fractional porous by means of newly proposed differential and integral techniques. The sensitivity analysis for chaos expansion and uncertainty quantification for the flow in heterogeneous media have been perceived to the problem of chaotic convection through numerical simulations. In order to approximate the propagation of chaos, two types of simulations have been carried out in terms of chaotic attractors through fractal and fractional approaches. For examining a variety of chaos under the numerical simulations in which fractal domain is varied and fractional domain is fixed, fractal domain is fixed and fractional domain is varied, and both fractal as well as fractional domain are varied. Finally, it is observed that the fractional and fractal memory effects have caused by interactions between uncertain parameters and disclosed the microstructures on the permeability of porous media.

Probabilistic Machine Learning: New Frontiers for Modeling Consumers and their Choices

Making sense of massive, individual-level data is challenging: marketing researchers and analysts need flexible models that can accommodate rich patterns of heterogeneity and dynamics, work with and link diverse data types, and scale to modern data sizes. Practitioners also need tools that can quantify uncertainty in models and predictions of consumer behavior to inform optimal decision-making. In this paper, we demonstrate the promise of probabilistic machine learning (PML), which refers to the pairing of probabilistic modeling and machine learning methods, in pushing the frontier of combining flexibility, scalability, interpretability, and uncertainty quantification for building better models of consumers and their choices. Specifically, we overview both PML models and inference methods, and highlight their utility for addressing four common classes of marketing problems: (1) uncovering heterogeneity, (2) flexibly modeling nonlinearities and dynamics, (3) handling high-dimensional and unstructured data, and (4) addressing missingness, often via data fusion. We also discuss promising directions in enriching marketing models, reflecting recent developments in representation learning, causal inference, experimentation and decision-making, and theory-based behavioral modeling.

A generic random field approach for stratification uncertainty quantification

A generic random field approach for stratification uncertainty quantification

Trustworthy Bayesian Deep Learning Framework for Uncertainty Quantification and Confidence Calibration: Application in Machinery Fault Diagnosis

Trustworthy Bayesian Deep Learning Framework for Uncertainty Quantification and Confidence Calibration: Application in Machinery Fault Diagnosis

Quantification of Uncertainty in PV Generation Prediction through Machine Learning Regularization Techniques

Quantification of Uncertainty in PV Generation Prediction through Machine Learning Regularization Techniques

An asymmetric pinching damaged hysteresis model for glubam members: Parameter identification and model comparison

The performance of glue laminated bamboo (glubam) members is governed by the nonlinear response at their joints, where high deformation levels and stress concentrations are developed. Numerous phenomenological models are presently employed to describe the hysteresis behavior of these joints, while these models always have an excessive number of parameters, and the physical interpretation of these parameters is often challenging. Moreover, some hysteresis models cannot capture all hysteresis features such as asymmetry, pinching, and damage. Consequently, this paper introduces a novel phenomenological-based hysteretic model named Asymmetric Pinching Damaged (APD) model, and implemented it in Abaqus by combining connector and spring elements in series or parallel. This model encompasses asymmetry, pinching, and strength degradation for bamboo joint components, with parameters that possess clear physical meanings and are readily comprehensible. This study also presented a parameter identification framework coupling the Parallel Genetic Algorithm (PGA) and Bayesian Neural Network (BNN). By merging the FE modeling and optimizing algorithms with the interactive application of ABAQUS and Python software platforms, the integrated identification framework is capable of performing multi-threaded parallel computation of finite element models considering the BNN-based uncertainty quantification, thus greatly improving the efficiency of parameter identification.

Uncertainty-Aware Time Series Anomaly Detection

Traditional anomaly detection methods in time series data often struggle with inherent uncertainties like noise and missing values. Indeed, current approaches mostly focus on quantifying epistemic uncertainty and ignore data-dependent uncertainty. However, consideration of noise in data is important as it may have the potential to lead to more robust detection of anomalies and a better capability of distinguishing between real anomalies and anomalous patterns provoked by noise. In this paper, we propose LSTMAE-UQ (Long Short-Term Memory Autoencoder with Aleatoric and Epistemic Uncertainty Quantification), a novel approach that incorporates both aleatoric (data noise) and epistemic (model uncertainty) uncertainties for more robust anomaly detection. The model combines the strengths of LSTM networks for capturing complex time series relationships and autoencoders for unsupervised anomaly detection and quantifies uncertainties based on the Bayesian posterior approximation method Monte Carlo (MC) Dropout, enabling a deeper understanding of noise recognition. Our experimental results across different real-world datasets show that consideration of uncertainty effectively increases the robustness to noise and point outliers, making predictions more reliable for longer periodic sequential data.

Democratizing uncertainty quantification

Uncertainty Quantification (UQ) is vital to safety-critical model-based analyses, but the widespread adoption of sophisticated UQ methods is limited by technical complexity. In this paper, we introduce UM-Bridge (the UQ and Modeling Bridge), a high-level abstraction and software protocol that facilitates universal interoperability of UQ software with simulation codes. It breaks down the technical complexity of advanced UQ applications and enables separation of concerns between experts. UM-Bridge democratizes UQ by allowing effective interdisciplinary collaboration, accelerating the development of advanced UQ methods, and making it easy to perform UQ analyses from prototype to High Performance Computing (HPC) scale.In addition, we present a library of ready-to-run UQ benchmark problems, all easily accessible through UM-Bridge. These benchmarks support UQ methodology research, enabling reproducible performance comparisons. We demonstrate UM-Bridge with several scientific applications, harnessing HPC resources even using UQ codes not designed with HPC support.

Probabilistic geophysical inversion of complex resistivity measurements using the Hamiltonian Monte Carlo method

Summary In this work, we introduce the probabilistic inversion of tomographic complex resistivity (CR) measurements using the Hamiltonian Monte Carlo (HMC) method. The posterior model distribution on which our approach operates accounts for the underlying complex-valued nature of the CR imaging problem accurately by including the individual errors of the measured impedance magnitude and phase, allowing for the application of independent regularization on the inferred subsurface conductivity magnitude and phase, and incorporating the effects of cross-sensitivities. As the tomographic CR inverse problem is non-linear, of high dimension and features strong correlations between model parameters, efficiently sampling from the posterior model distribution is challenging. To meet this challenge we use HMC, a Markov-chain Monte Carlo method that incorporates gradient information to achieve efficient model updates. To maximize the benefit of a given number of forward calculations, we use the No-U-Turn sampler (NUTS) as a variant of HMC. We demonstrate the probabilistic inversion approach on a synthetic CR tomography measurement. The NUTS succeeds in creating a sample of the posterior model distribution that provides us with the ability to analyze correlations between model parameters and to calculate statistical estimators of interest, such as the mean model and the covariance matrix. Our results provide a strong basis for the characterization of the posterior model distribution and uncertainty quantification in the context of the tomographic CR inverse problem.

Yet Another Discriminant Analysis (YADA): A Probabilistic Model for Machine Learning Applications

This paper presents a probabilistic model for various machine learning (ML) applications. While deep learning (DL) has produced state-of-the-art results in many domains, DL models are complex and over-parameterized, which leads to high uncertainty about what the model has learned, as well as its decision process. Further, DL models are not probabilistic, making reasoning about their output challenging. In contrast, the proposed model, referred to as Yet Another Discriminate Analysis(YADA), is less complex than other methods, is based on a mathematically rigorous foundation, and can be utilized for a wide variety of ML tasks including classification, explainability, and uncertainty quantification. YADA is thus competitive in most cases with many state-of-the-art DL models. Ideally, a probabilistic model would represent the full joint probability distribution of its features, but doing so is often computationally expensive and intractable. Hence, many probabilistic models assume that the features are either normally distributed, mutually independent, or both, which can severely limit their performance. YADA is an intermediate model that (1) captures the marginal distributions of each variable and the pairwise correlations between variables and (2) explicitly maps features to the space of multivariate Gaussian variables. Numerous mathematical properties of the YADA model can be derived, thereby improving the theoretic underpinnings of ML. Validation of the model can be statistically verified on new or held-out data using native properties of YADA. However, there are some engineering and practical challenges that we enumerate to make YADA more useful.

Sequential binary classification of lithofacies from well-log data and their uncertainty quantification

Understanding and identifying the composition of various lithofacies in the subsurface is essential for successful reservoir characterization in hydrocarbon exploration. However, conventional methods such as core sampling and manual well-log interpretation are labor-intensive. As a result, many scientists are conducting research to use machine learning to study lithofacies more effectively and efficiently. However, as researchers are becoming more dependent on machine learning, an uncertainty analysis of machine-learning models is crucial to determine the reliability of the prediction results. Machine-learning algorithms that use ensemble methods provide an easy method for an uncertainty analysis but algorithms that do not use ensemble methods have difficulty in quantifying the level of uncertainty. In our research, we introduce a method known as sequential binary classification (SBC), which helps not only classify lithofacies but also to quantify and visualize the regions of uncertainty of the machine-learning models. SBC provides a method for using any classification algorithm of the user’s choice to construct an ensemble, which allows the user to quantify uncertainty readily. Our research uses the SBC algorithm to classify and quantify the uncertainty from the well-log data obtained from the North Sea near Norway. The results show that most of the lithofacies that exist in the region of interest share similar characteristics, which results in high uncertainty among the various lithofacies, and SBC helps to visualize these high uncertainties. We additionally demonstrate how SBC alleviates the class imbalance issue among the various lithofacies in the area, which is a very common problem in well-log data analytics.

Theoretical and Methodological Foundations of Uncertainty Modeling in Real Estate Markets

Motivation: The need to improve the accuracy and reliability of market valuation and risk assessment in real estate markets, especially under conditions of uncertainty.Aim: To integrate theoretical foundations and methodological approaches for modeling aleatoric and epistemic uncertainties in real estate markets using credal networks and confidence boxes (c-boxes).Approach: This paper presents a comprehensive theoretical and methodological framework for uncertainty modeling in real estate markets, focusing on the application of credal networks and confidence boxes. It does not include empirical validation or practical case studies, instead providing a detailed conceptual and methodological discussion.Results: The proposed method demonstrates significant improvements in uncertainty quantification and market analysis accuracy in theoretical terms, offering valuable insights for investors, urban planners, and policymakers. However, empirical validation is suggested for future research to confirm practical applicability.

A robust approach to Gaussian process implementation

Abstract. Gaussian process (GP) regression is a flexible modeling technique used to predict outputs and to capture uncertainty in the predictions. However, the GP regression process becomes computationally intensive when the training spatial dataset has a large number of observations. To address this challenge, we introduce a scalable GP algorithm, termed MuyGPs, which incorporates nearest-neighbor and leave-one-out cross-validation during training. This approach enables the evaluation of large spatial datasets with state-of-the-art accuracy and speed in certain spatial problems. Despite these advantages, conventional quadratic loss functions used in the MuyGPs optimization, such as root mean squared error (RMSE), are highly influenced by outliers. We explore the behavior of MuyGPs in cases involving outlying observations and, subsequently, develop a robust approach to handle and mitigate their impact. Specifically, we introduce a novel leave-one-out loss function based on the pseudo-Huber function (LOOPH) that effectively accounts for outliers in large spatial datasets within the MuyGPs framework. Our simulation study shows that the LOOPH loss method maintains accuracy despite outlying observations, establishing MuyGPs as a powerful tool for mitigating unusual observation impacts in the large data regime. In the analysis of US ozone data, MuyGPs provides accurate predictions and uncertainty quantification, demonstrating its utility in managing data anomalies. Through these efforts, we advance the understanding of GP regression in spatial contexts.

Modeling Groundwater Levels in California's Central Valley by Hierarchical Gaussian Process and Neural Network Regression

AbstractModeling groundwater levels continuously across California's Central Valley (CV) hydrological system is challenging due to low‐quality well data which is sparsely and noisily sampled across time and space. The lack of consistent well data makes it difficult to evaluate the impact of 2017 and 2019 wet years on CV groundwater following a severe drought during 2012–2015. A novel machine learning method is formulated for modeling groundwater levels by learning from a 3D lithological texture model of the CV aquifer. The proposed formulation performs multivariate regression by combining Gaussian processes (GP) and deep neural networks (DNN). The hierarchical modeling approach constitutes training the DNN to learn a lithologically informed latent space where non‐parametric regression with GP is performed. We demonstrate the efficacy of GP‐DNN regression for modeling non‐stationary features in the well data with fast and reliable uncertainty quantification, as validated to be statistically consistent with the empirical data distribution from 90 blind wells across CV. We show how the model predictions may be used to supplement hydrological understanding of aquifer responses in basins with irregular well data. Our results indicate that on average the 2017 and 2019 wet years in California were largely ineffective in replenishing the groundwater loss caused during previous drought years.