Uncertainty Quantification Research Articles

Machine-learning-driven semiauto multiscenario horizon interpretation with uncertainty quantification

Horizon interpretation is one of the most labor-intensive and interpreter-dependent processes in the reservoir characterization workflow. This issue becomes critical, particularly when the quality of a seismic reflector is poor. The uncertainty caused by inaccurate seismic horizon interpretations often misleads the volumetric analyses of subsurface reservoirs. To resolve these issues, we develop a four-step machine-learning-based semiautomated horizon interpretation workflow. In the first step, we generate multiple virtual stratigraphic labels. We then generate multiple synthetic data points to mimic the features of field data by applying a cycle-consistent generative adversarial network. In the third step, we train a U-Net augmented with feature pyramid attention and a convolutional block attention module on the synthetic data set. Finally, the probabilistic distribution results are used to obtain multiple horizon selection scenarios, yielding various possible stratigraphic results. As our method yields a probability distribution rather than a single value for a given field data and seed point, we can obtain multiple possible horizon scenarios rather than a single horizon. Through uncertainty quantification, we can select an appropriate horizon among multiple scenarios. We apply our method to the Smeaheia field data set, which is characterized by numerous and large faults, and compare the results with reference interpretation to confirm its accuracy. The field data example indicates that our method can be applied to complex geologic structures.

WISER: Multimodal variational inference for full-waveform inversion without dimensionality reduction

We develop a semiamortized variational inference (VI) framework designed for computationally feasible uncertainty quantification in full-waveform inversion to explore the multimodal posterior distribution without dimensionality reduction. The framework is called full-waveform VI via subsurface extensions with refinements (WISER). WISER builds on top of a supervised generative artificial intelligence method that performs approximate amortized inference that is low-cost albeit showing an amortization gap. This gap is closed through nonamortized refinements that make frugal use of wave physics. Case studies illustrate that WISER is capable of full-resolution, computationally feasible, and reliable uncertainty estimates of velocity models and imaged reflectivities.

Decay Heat Power Uncertainty Quantification in Studsvik’s System for Spent Fuel Analyses

Studsvik’s approach to spent nuclear fuel (SNF) analyses combines isotopic concentrations, fluxes, and cross sections, calculated by the CASMO5 neutron transport and depletion code, with irradiation history data from the SIMULATE5 reactor core simulator and tabulated isotopic decay data. These data sources are used and processed by the SNF code to compute the SNF characteristics. Recent advances in the system, including uncertainty analyses of the computed decay heat power, are presented in this paper. The decay heat power uncertainty is evaluated accounting for the uncertainties in the operating conditions and uncertainties in the nuclear and decay data. The model involves a series of stochastic perturbations combined with the linear propagation law. The uncertainty quantification complements the best estimate decay heat power.

Anisotropic resistivity estimation and uncertainty quantification from borehole triaxial electromagnetic induction measurements: Gradient-based inversion and physics-informed neural network

Rapid and accurate petrophysical reservoir description and quantification is important for subsurface energy resource modeling and engineering. Triaxial borehole resistivity measurements enable the estimation of key in-situ rock properties, such as the volumetric concentration of shale and sandstone resistivity. However, traditional approaches for estimating these properties from triaxial, or anisotropic, borehole resistivity measurements rely on analytical solutions that solve a system of equations simultaneously, which can lead to numerical instability and inefficiency. By reformulating the system of anisotropic resistivity equations as an inverse problem, we can achieve a more stable, accurate, and efficient estimation of key petrophysical properties. We propose two methods, namely nonlinear gradient-based and physics-informed neural network (PINN) inversion, to estimate the volumetric concentration of shale and sandstone resistivity from the parallel- and perpendicular-to-bedding-plane resistivity logs, posed as the solution of an inverse problem. Furthermore, we compare the PINN, nonlinear gradient-based inversion and analytical solution methods in terms of accuracy, computational efficiency, and uncertainty quantification using four different datasets of anisotropic resistivity logs, i.e., two synthetic and two field cases. The PINN inversion technique estimates the petrophysical properties within 0.5 CPU milliseconds with an accuracy between 91% and 99%, while nonlinear gradient-based inversion can estimate the petrophysical properties with an accuracy between 98% and 99% but requires several CPU minutes depending on the size of the dataset. The proposed PINN technique is therefore capable of providing fast and accurate estimation and uncertainty quantification of key petrophysical properties from triaxial resistivity logs, with comparable accuracy and approximately 106 speedup compared to nonlinear gradient-based inversion, and can be used for real-time applications such as automatic shale properties estimation, logging-while-drilling measurement interpretation, automated well geosteering, and time-lapse reservoir monitoring.

Uncertainty quantification in sequential hybrid deep transfer learning for solar irradiation predictions

Uncertainty quantification in sequential hybrid deep transfer learning for solar irradiation predictions

An Optimal Dual Data-Driven Framework for RUL Prediction With Uncertainty Quantification

An Optimal Dual Data-Driven Framework for RUL Prediction With Uncertainty Quantification

Permittivity measurement with uncertainty quantification in cement-based composites using ENNreg-ANet and high-frequency electromagnetic waves

Permittivity measurement with uncertainty quantification in cement-based composites using ENNreg-ANet and high-frequency electromagnetic waves

A novel approach to seismic fragility evaluation of underground structures considering hybrid epistemic uncertainties of both seismic demand and capacity

Precise seismic fragility analysis holds significant importance in the evaluation of seismic resilience for underground structures. However, the conventional seismic fragility analysis of underground structures usually ignores the hybrid epistemic uncertainties caused by the limited samples of both seismic demand and thresholds and deterministic boundaries between different limit states, which can inevitably cause errors in the seismic resilience evaluation of underground structures. Thus, focusing on the quantification of epistemic uncertainties, this paper aims to propose an approach to seismic fragility evaluation of underground structures considering hybrid epistemic uncertainties of both seismic demand and capacity. In this approach, the analytical formulation of seismic fragility considering the fuzziness of limit states is firstly derived via adopting the entropy equivalence method. Then, the non-parametric Bootstrap method and maximum entropy principle, as well as the Copula theory are combined to establish a probability model characterizing the statistical uncertainties of both seismic demand and capacity. On this basis, the variability of failure probability of underground structures is quantified, and the envelope fuzzy seismic fragility is obtained. Moreover, the influences of the coupling effect of statistical uncertainty and fuzziness on the seismic fragility of underground structures are also analyzed in this paper. The results show that the seismic fragility of underground structures based on limited samples of both seismic demand and thresholds and deterministic boundaries between different limit states has significant variability, and the variability degree of fragility is various under different ground motion intensities. Besides, the envelope fuzzy seismic fragility curves can effectively reflect the coupling effect of statistical uncertainty and fuzziness and adequately characterize the variability of estimated seismic fragility, which can provide a more accurate basis for seismic resilience evaluation of underground structures.

Unknown input uncertainty calculation using virtual input shaping and interval analysis

A triaxial accelerometer has been developed to measure and determine the uncertainty associated with unknown vibrations disturbing a small force metrology experiment. However, methodological shortcomings remain regarding the calculation of uncertainty for dynamic measurements. Therefore, this paper proposes an alternative framework to estimate the uncertainty of specific dynamic quantities of interest with a nonlinear and uncertain measuring system. The novelty of the proposed methodology lies in the use of an accurate and equivalent representation of the physical system based on a linear model, combined with an additive virtual input describing all the unknown unmodeled dynamics. Measurement models are defined considering measurement biases, and uncertainty is calculated using interval analysis tools. Such tools allow determining the feasible values of the quantities of interest to be estimated. The innovative aspects of the proposed approach are fully illustrated in simulation on the triaxial accelerometer, comparing linear and nonlinear measurement models in passive mode.

Bias-corrected high-resolution temperature and precipitation projections for Canada

High-resolution precipitation and temperature projections are indispensable for informed decision-making, risk assessment, and planning. Here, we have developed an extensive database (SPQM-CMIP6-CAN) of high-resolution (0.1°) precipitation and temperature projections extending till 2100 at a daily scale for Canada. We employed a novel Semi-Parametric Quantile Mapping (SPQM) methodology to bias-correct the Coupled Model Intercomparison Project, Phase-6 (CMIP6) projections for four Shared Socio-economic Pathways. SPQM is simple, yet robust, in reproducing the observed marginal properties, trends, and variability according to future scenarios, while maintaining a smooth transition from observations to projected simulations. The SPQM-CMIP6-CAN database encompasses 693 simulations derived from 34 diverse climate models for precipitation. Similarly, for temperature projections, our database comprises 581 simulations from 27 climate models. These projections are valuable for hydrological, environmental, and ecological studies, offering a comprehensive resource for analyses within these domains. Furthermore, these projections serve as a vital tool for the quantification of uncertainties arising from climate models, their variant configurations, and future scenarios.

Parameter estimation and uncertainty quantification of rainfall-runoff models using data assimilation methods based on deep learning and local ensemble updates

Parameter estimation and uncertainty quantification of rainfall-runoff models using data assimilation methods based on deep learning and local ensemble updates

Deep-neural-network-based framework for the accelerating uncertainty quantification of a structural–acoustic fully coupled system in a shallow sea

Deep-neural-network-based framework for the accelerating uncertainty quantification of a structural–acoustic fully coupled system in a shallow sea

Uncertainty quantification for DeepONets with ensemble Kalman inversion

Uncertainty quantification for DeepONets with ensemble Kalman inversion

A priori uncertainty quantification of reacting turbulence closure models using Bayesian neural networks

a priori uncertainty quantification of reacting turbulence closure models using Bayesian neural networks

Data-driven prediction and uncertainty quantification of PWR crud-induced power shift using convolutional neural networks

Data-driven prediction and uncertainty quantification of PWR crud-induced power shift using convolutional neural networks

Nonlinear time-dependent mapping model for shm data utilizing gan-based imputation and LSTM for uncertainty quantification

Nonlinear time-dependent mapping model for shm data utilizing gan-based imputation and LSTM for uncertainty quantification

Integrating high-resolution data and species-level traits for enhanced ecosystem projections using a dynamic vegetation model: Case study in Wallonia, Belgium.

Accurate quantification of carbon dynamics is critical for developing effective climate mitigation strategies. In this study, we employed the CARAIB dynamic vegetation model (DVM) to analyze carbon fluxes and stocks (biomass and total soil carbon) in Wallonia, Belgium (1980-2070), integrating species-level traits, high-resolution land use/land cover (LULC) data, climate data, and type-1 fuzzy logic for uncertainty quantification. We provide insights into ecosystem resilience and carbon sequestration under Representative Concentration Pathways (RCPs) 2.6 and 8.5. Historical results (1980-2020) demonstrated strong model performance, with gross primary production (GPP) validation achieving R2>0.85 against MODIS and GOSIF datasets, and aboveground biomass correlating well with GEDI (R2=0.77) and ESA-CCI (R2=0.91) datasets. Grasslands emerged as critical carbon sinks, exhibiting the highest mean GPP (2480gC m-2 yr-1), surpassing forests due to rapid growth and belowground carbon storage. Future projections (2021-2070) identified afforestation as a robust mitigation strategy, increasing forest GPP by 18% and total biomass by 60-110MtC under RCP 8.5. Under RCP 2.6, total biomass was more stable due to the milder emissions trajectory, emphasizing its potential for long-term ecosystem resilience. Interestingly, total soil carbon showed similar levels across both RCPs, indicating belowground carbon resilience despite emissions differences. Sensitivity analyses of LULC scenarios highlighted grassland resilience, with grasslands sustaining a high GPP (2604-2728gC m-2 yr-1) and contributing significantly to soil carbon storage, while deforestation caused substantial carbon losses. These findings underscore the need for nuanced land management, integrating afforestation and grassland conservation, to enhance resilience and sustainable carbon sequestration under climate change.

Uncertainty Quantification in Shear Wave Velocity Predictions: Integrating Explainable Machine Learning and Bayesian Inference

The accurate prediction of shear wave velocity (Vs) is critical for earthquake engineering applications. However, the prediction is inevitably influenced by geotechnical variability and various sources of uncertainty. This paper investigates the effectiveness of integrating explainable machine learning (ML) model and Bayesian generalized linear model (GLM) to enhance both predictive accuracy and uncertainty quantification in Vs prediction. The study utilizes an Extreme Gradient Boosting (XGBoost) algorithm coupled with Shapley Additive Explanations (SHAPs) and partial dependency analysis to identify key geotechnical parameters influencing Vs predictions. Additionally, a Bayesian GLM is developed to explicitly account for uncertainties arising from geotechnical variability. The effectiveness and predictive performance of the proposed models were validated through comparison with real case scenarios. The results highlight the unique advantages of each model. The XGBoost model demonstrates good predictive performance, achieving high coefficient of determination (R2), index of agreement (IA), Kling–Gupta efficiency (KGE) values, and low error values while effectively explaining the impact of input parameters on Vs. In contrast, the Bayesian GLM provides probabilistic predictions with 95% credible intervals, capturing the uncertainty associated with the predictions. The integration of these two approaches creates a comprehensive framework that combines the strengths of high-accuracy ML predictions with the uncertainty quantification of Bayesian inference. This hybrid methodology offers a powerful and interpretable tool for Vs prediction, providing engineers with the confidence to make informed decisions.

Learning PDFs through interpretable latent representations in Mellin space

Representing the parton distribution functions (PDFs) of the proton and other hadrons through flexible, high-fidelity parametrizations has been a long-standing goal of particle physics phenomenology. This is particularly true since the chosen parametrization methodology can play an influential role in the ultimate PDF uncertainties as extracted in QCD global analyses; these, in turn, are often determinative of the reach of experiments at the LHC and other facilities to nonstandard physics, including at large x, where parametrization effects can be significant. In this study, we explore a series of encoder-decoder machine-learning (ML) models with various neural-network topologies as efficient means of reconstructing PDFs from meaningful information stored in an interpretable latent space. Given recent effort to pioneer synergies between QCD analyses and lattice-gauge calculations, we formulate a latent representation based on the behavior of PDFs in Mellin space, i.e., their integrated moments, and test the ability of various models to decode PDFs from this information faithfully. We introduce a numerical package, , which implements several encoder-decoder models to reconstruct PDFs with high fidelity and use this end-to-end tool to explore how such neural-network-based models might connect PDF parametrizations to underlying properties like their Mellin moments. We additionally dissect patterns of learned correlations between encoded Mellin moments and reconstructed PDFs that suggest opportunities for further improvements to ML-based approaches to PDF parametrizations and uncertainty quantification. Published by the American Physical Society 2025

Neural Bayes Estimators for Irregular Spatial Data Using Graph Neural Networks

Neural Bayes estimators are neural networks that approximate Bayes estimators in a fast and likelihood-free manner. Although they are appealing to use with spatial models, where estimation is often a computational bottleneck, neural Bayes estimators in spatial applications have, to date, been restricted to data collected over a regular grid. These estimators are also currently dependent on a prescribed set of spatial locations, which means that the neural network needs to be retrained for new datasets; this renders them impractical in many applications and impedes their widespread adoption. In this work, we employ graph neural networks (GNNs) to tackle the important problem of parameter point estimation from data collected over arbitrary spatial locations. In addition to extending neural Bayes estimation to irregular spatial data, the use of GNNs leads to substantial computational benefits, since the estimator can be used with any configuration or number of locations and independent replicates, thus, amortizing the cost of training for a given spatial model. We also facilitate fast uncertainty quantification by training an accompanying neural Bayes estimator that approximates a set of marginal posterior quantiles. We illustrate our methodology on Gaussian and max-stable processes. Finally, we showcase our methodology on a dataset of global sea-surface temperature, where we estimate the parameters of a Gaussian process model in 2161 spatial regions, each containing thousands of irregularly-spaced data points, in just a few minutes with a single graphics processing unit. Supplementary materials for this article are available online.