Uncertainty Quantification Research Articles

Inferring Surface NO2 Over Western Europe: A Machine Learning Approach With Uncertainty Quantification

AbstractNitrogen oxides (NOx = NO + NO2) are of great concern due to their impact on human health and the environment. In recent years, machine learning (ML) techniques have been widely used for surface NO2 estimation with rapid developments in computational power and big data. However, the uncertainties inherent to such retrievals are rarely studied. In this study, a novel ML framework has been developed, enhanced with uncertainty quantification techniques, to estimate surface NO2 and provide corresponding data‐induced uncertainty. We apply the Boosting Ensemble Conformal Quantile Estimator (BEnCQE) model to infer surface NO2 concentrations over Western Europe at the daily scale and 1 km spatial resolution from May 2018 to December 2021. High NO2 mainly appears in urban areas, industrial areas, and roads. The space‐based cross‐validation shows that our model achieves accurate point estimates (r = 0.8, R2 = 0.64, root mean square error = 8.08 μg/m3) and reliable prediction intervals (coverage probability, PI‐50%: 51.0%, PI‐90%: 90.5%). Also, the model result agrees with the Copernicus Atmosphere Monitoring Service (CAMS) model. The quantile regression in our model enables us to understand the importance of predictors for different NO2 level estimations. Additionally, the uncertainty information reveals the extra potential exceedance of the World Health Organization (WHO) 2021 limit in some locations, which is undetectable by only point estimates. Meanwhile, the uncertainty quantification allows assessment of the model's robustness outside existing in‐situ station measurements. It reveals challenges of NO2 estimation over urban and mountainous areas where NO2 is highly variable and heterogeneously distributed.

Bayesian Domain-Adversarial Regression Adaptation: A New Self-Driven Remaining Useful Life Prediction Method Across Different Machines With Uncertainty Quantification

Bayesian Domain-Adversarial Regression Adaptation: A New Self-Driven Remaining Useful Life Prediction Method Across Different Machines With Uncertainty Quantification

Research on Stock Price Prediction Model Based on Sentiment Factor and Multi-Core Bagging Algorithm

Stock price prediction model is one of the key research points in the quantitative financial field. With the rapid development of data acquisition and storage technology, the data of emotional factors based on nonlinear structure is increasing. How to combine this part of information with common European technology factors to increase the ability of the model is a problem that needs to be solved. Based on this, this paper proposes a method of uncertainty quantification that combines European-and non-European data. Specifically, on the one hand, the Gaussian process regression model is used to capture the unknown relationship between predictive variables and price; on the other hand, the multi-kernel learning technology based on European and non- European kernel functions is used to combine the effective information of European and non- European predictive variables. Moreover, the proposed method can weigh the bias of the prediction model against the variance by using the Bagging algorithm. The simulated data analysis shows that the proposed method not only improves the prediction performance of the European Gaussian process, but also works in the presence of irrelevant predictive variables. Finally, the actual data analysis shows that the proposed method has achieved good prediction results in the task of predicting the rise and fall of stock prices.

Groundwater modelling for decision-support in practice: Insights from Sweden.

Groundwater is an essential resource for drinking water, food production, and industrial applications worldwide. Over-exploitation and pollution pose significant risks to groundwater sustainability. Groundwater models can be powerful tools for optimizing use, managing risks, and aiding decision-making. For this purpose, models should assimilate pertinent data and quantify uncertainties in outcomes. We examine applied modelling for characterization and decision support in Sweden from 2010 to 2023. We also review syllabi of water-related courses in Swedish higher education to assess the inclusion and extent of groundwater modelling education. We find that important academic advances in groundwater modelling over the past two decades have not translated into practical application within Sweden's industry, that uncertainty quantification is rarely undertaken, and that groundwater modelling remains a low priority in higher education. Based on these findings, we offer recommendations that, while informed by the Swedish context, hold relevance for educational institutions, industry, and decision-makers internationally.

Multiple Closed Curve Modeling with Uncertainty Quantification for Shape Analysis

Multiple Closed Curve Modeling with Uncertainty Quantification for Shape Analysis

Nested Sampling for Uncertainty Quantification and Rare Event Estimation

Nested Sampling for Uncertainty Quantification and Rare Event Estimation

HAGMN-UQ: Hyper association graph matching network with uncertainty quantification for coronary artery semantic labeling

Coronary artery disease (CAD) is one of the leading causes of death worldwide. Accurate extraction of individual arterial branches from invasive coronary angiograms (ICA) is critical for CAD diagnosis and detection of stenosis. Generating semantic segmentation for coronary arteries through deep learning-based models presents challenges due to the morphological similarity among different types of coronary arteries, making it difficult to maintain high accuracy while keeping low computational complexity. To address this challenge, we propose an innovative approach using the hyper association graph-matching neural network with uncertainty quantification (HAGMN-UQ) for coronary artery semantic labeling on ICAs. The graph-matching procedure maps the arterial branches between two individual graphs, so that the unlabeled arterial segments are classified by the labeled segments, and the coronary artery semantic labeling is achieved. Leveraging hypergraphs not only extends representation capabilities beyond pairwise relationships, but also improves the robustness and accuracy of the graph matching by enabling the modeling of higher-order associations. In addition, employing the uncertainty quantification to determine the trustworthiness of graph matching reduces the required number of comparisons, so as to accelerate the inference speed. Consequently, our model achieved an accuracy of 0.9211 for coronary artery semantic labeling with a fast inference speed, leading to an effective and efficient prediction in real-time clinical decision-making scenarios.

A benchmark on uncertainty quantification for deep learning prognostics

Reliable uncertainty quantification on RUL prediction is crucial for informative decision-making in predictive maintenance. In this context, we assess some of the latest developments in the field of uncertainty quantification for deep learning prognostics. This includes the state-of-the-art variational inference algorithms for Bayesian neural networks (BNN) as well as popular alternatives such as Monte Carlo Dropout (MCD), deep ensembles (DE), and heteroscedastic neural networks (HNN). All the inference techniques share the same inception architecture as functional model. The performance of the methods is evaluated on a subset of the large NASA N-CMAPSS dataset for aircraft engines. The assessment includes RUL prediction accuracy, the quality of predictive uncertainty, and the possibility of breaking down the total predictive uncertainty into its aleatoric and epistemic parts. Although all methods are close in terms of accuracy, we find differences in the way they estimate uncertainty. Thus, DE and MCD generally provide more conservative predictive uncertainty than BNN. Surprisingly, HNN achieve strong results without the added complexity of BNN. None of these methods exhibited strong robustness to out-of-distribution cases, with BNN and HNN methods particularly susceptible to low accuracy and overconfidence. BNN techniques presented anomalous miscalibration issues at the later stages of the system lifetime.

Multivariate sensitivity-adaptive polynomial chaos expansion for high-dimensional surrogate modeling and uncertainty quantification

This work develops a novel basis-adaptive method for constructing anisotropic polynomial chaos expansions of multidimensional (vector-valued, multi-output) model responses. The adaptive basis selection is based on multivariate sensitivity analysis metrics that can be estimated by post-processing the polynomial chaos expansion and results in a common anisotropic polynomial basis for the vector-valued response. This allows the application of the method to problems with up to moderately high-dimensional model inputs (in the order of tens) and up to very high-dimensional model responses (in the order of thousands). The method is applied to different engineering test cases for surrogate modeling and uncertainty quantification, including use cases related to electric machine and power grid modeling and simulation, and is found to produce highly accurate results with comparatively low data and computational demand.

Uncertainty quantification of collective nuclear observables from the chiral potential parametrization

Abstract We perform an uncertainty estimate of quadrupole moments and B(E2) transition rates that inform nuclear collectivity. In particular, we study the low-lying states of 6Li and 12C using the ab initio symmetry-adapted no-core shell model. For a narrow standard deviation of approximately 1% on the low-energy constants which parametrize high-precision chiral potentials, we find output standard deviations in the collective observables ranging from approximately 3-6%. The results mark the first step towards a rigorous uncertainty quantification of collectivity in nuclei that aims to account for all sources of uncertainty in ab initio descriptions of challenging collective and clustering observables.

Wind turbine condition monitoring dataset of Fraunhofer LBF

Fraunhofer wind turbine dataset contains monitoring data from a 750 W wind turbine, including accelerometers and tachometer, to capture structural response, bearing vibrations and rotational velocity. Additionally, temperatures, wind speed and wind direction have been measured, while weather conditions have been acquired from selected sources. Various damage scenarios, including mass imbalance, and aerodynamic imbalance as well as damages on bearings’ outer race, inner race and roller element have been implemented. The availability of time series data makes the dataset well suited for both machine learning and signal processing-based condition monitoring applications. The availability of heterogeneous sensors has created a dataset particularly suited for information fusion, data fusion, multi-sensor approaches, and holistic monitoring. Experiments were conducted in real-world conditions outside of a controlled laboratory environment, thereby introducing challenges such as variable rotor speed, noise, overloads, and other environmental factors. Consequently, the dataset is qualified for tasks involving uncertainty quantification and signal pre-processing. This document will detail the test equipment, experimental procedures, simulated damage cases and measurement parameters.

Uncertainty quantification on small angle x-ray scattering measurement using Bayesian deep learning

Small angle x-ray scattering (SAXS) is a widely recognized solution for measuring complex nanostructures. With the increasing demand for accurately assessing structural characteristics and optimizing manufacturing processes, uncertainty quantification in SAXS inverse problems has become a critical issue. However, traditional methods face challenges such as slow computation speed and inaccurate estimation of multidimensional parameters. To overcome these issues, we propose an uncertainty quantification approach suitable for SAXS measurement that approximates the posterior using Bayesian deep learning. The effectiveness and reliability of our method are illustrated by assessing structural parameters of synthetic 2D Si grating samples. The uncertainty quantification takes only about 2.3 s, thousands of times faster than the conventional Markov Chain Monte Carlo (MCMC) methods. Also, our method has superior repeatability for parameter measurement compared to the MCMC approaches. It provides the potential of efficient and reliable SAXS measurement in increasingly intricate semiconductor manufacturing.

Deep Conformal Supervision: Leveraging Intermediate Features for Robust Uncertainty Quantification.

Trustworthiness is crucial for artificial intelligence (AI) models in clinical settings, and a fundamental aspect of trustworthy AI is uncertainty quantification (UQ). Conformal prediction as a robust uncertainty quantification (UQ) framework has been receiving increasing attention as a valuable tool in improving model trustworthiness. An area of active research is the method of non-conformity score calculation for conformal prediction. We propose deep conformal supervision (DCS), which leverages the intermediate outputs of deep supervision for non-conformity score calculation, via weighted averaging based on the inverse of mean calibration error for each stage. We benchmarked our method on two publicly available datasets focused on medical image classification: a pneumonia chest radiography dataset and a preprocessed version of the 2019 RSNA Intracranial Hemorrhage dataset. Our method achieved mean coverage errors of 16e-4 (CI: 1e-4, 41e-4) and 5e-4 (CI: 1e-4, 10e-4) compared to baseline mean coverage errors of 28e-4 (CI: 2e-4, 64e-4) and 21e-4 (CI: 8e-4, 3e-4) on the two datasets, respectively (p < 0.001 on both datasets). Based on our findings, the baseline results of conformal prediction already exhibit small coverage errors. However, our method shows a significant improvement on coverage error, particularly noticeable in scenarios involving smaller datasets or when considering smaller acceptable error levels, which are crucial in developing UQ frameworks for healthcare AI applications.

Assessing the value of combined use of distributed acoustic sensing (DAS) and multicomponent vertical seismic profiling (VSP) data with network-based full waveform inversion and uncertainty quantification: A case study in Alberta, Canada

Distributed acoustic sensing (DAS) technology, deployed in a vertical seismic profiling (VSP) experimental configuration, has emerged as a candidate for non-disruptive and low-cost seismic monitoring of CO2 geostorage and plume evolution. Full waveform inversion (FWI) has likewise received significant attention because it uses relatively complete physical models of wave propagation and because of its sample-by-sample incorporation of data information. Recent artificial neural network-based FWI algorithms (built with, for instance, recursive neural networks, or RNNs) have added to FWI a range of flexible and efficient tools for gradient computation and options for uncertainty assessment and initial model proxies. An important current research area for the use of DAS data is to better understand how they change our confidence levels in models selected through FWI. In particular, we seek to understand whether either DAS data or conventional geophone data alone are optimal for FWI model selection in the CO2 problem, and if not, to what degree they complement each other. The Snowflake 4D VSP dataset, which includes multi-offset and multi-azimuth broadband sources illuminating both fiberoptic cable and densely sampled accelerometer phones in the borehole, was acquired by our group to directly address these questions. In this study, we quantify uncertainty (UQ) by sampling the posterior model covariance matrix from the inverse Hessian matrix at the end of RNN-FWI runs on the Snowflake baseline data, invoking a velocity-density parameterization, and involving mixtures of accelerometer and DAS data. In this UQ context, the complementary effect of combining accelerometer and DAS data is evident in the Vp and Vs models. Our confidence in the approach is bolstered by its independent prediction of a region of known high uncertainty. In the overall pursuit of reliable and low-cost monitoring tools, this supports continued consideration of a multicomponent sensors supported by DAS approach.

Efficient Uncertainty Quantification for Mechanical Properties of Randomly Perturbed Elastic Rods

Efficient Uncertainty Quantification for Mechanical Properties of Randomly Perturbed Elastic Rods

Stabilized weighted reduced order methods for parametrized advection-dominated optimal control problems governed by partial differential equations with random inputs

Abstract In this work, we analyze Parametrized Advection-Dominated distributed Optimal Control Problems with random inputs in a Reduced Order Model (ROM) context. All the simulations are initially based on a finite element method (FEM) discretization; moreover, a space-time approach is considered when dealing with unsteady cases. To overcome numerical instabilities that can occur in the optimality system for high values of the Péclet number, we consider a Streamline Upwind Petrov–Galerkin technique applied in an optimize-then-discretize approach. We combine this method with the ROM framework in order to consider two possibilities of stabilization: Offline-Only stabilization and Offline-Online stabilization. Moreover we consider random parameters and we use a weighted Proper Orthogonal Decomposition algorithm in a partitioned approach to deal with the issue of uncertainty quantification. Several quadrature techniques are used to derive weighted ROMs: tensor rules, isotropic sparse grids, Monte-Carlo and quasi Monte-Carlo methods. We compare all the approaches analyzing relative errors between the FEM and ROM solutions and the computational efficiency based on the speedup-index.

Toward widespread use of virtual trials in medical imaging innovation and regulatory science.

The rapid advancement in the field of medical imaging presents a challenge in keeping up to date with the necessary objective evaluations and optimizations for safe and effective use in clinical settings. These evaluations are traditionally done using clinical imaging trials, which while effective, pose several limitations including high costs, ethical considerations for repetitive experiments, time constraints, and lack of ground truth. To tackle these issues, virtual trials (aka in silico trials) have emerged as a promising alternative, using computational models of human subjects and imaging devices, and observer models/analysis to carry out experiments. To facilitate the widespread use of virtual trials within the medical imaging research community, a major need is to establish a common consensus framework that all can use. Based on the ongoing efforts of an AAPM Task Group (TG387), this article provides a comprehensive overview of the requirements for establishing virtual imaging trial frameworks, paving the way toward their widespread use within the medical imaging research community. These requirements include credibility, reproducibility, and accessibility. Credibility assessment involves verification, validation, uncertainty quantification, and sensitivity analysis, ensuring the accuracy and realism of computational models. A proper credibility assessment requires a clear context of use and the questions that the study is intended to objectively answer. For reproducibility and accessibility, this article highlights the need for detailed documentation, user-friendly software packages, and standard input/output formats. Challenges in data and software sharing, including proprietary data and inconsistent file formats, are discussed. Recommended solutions to enhance accessibility include containerized environments and data-sharing hubs, along with following standards such as CDISC (Clinical Data Interchange Standards Consortium). By addressing challenges associated with credibility, reproducibility, and accessibility, virtual imaging trials can be positioned as a powerful and inclusive resource, advancing medical imaging innovation and regulatory science.

Prediction of pathological complete response to chemotherapy for breast cancer using deep neural network with uncertainty quantification.

The I-SPY 2 trial is a national-wide, multi-institutional clinical trial designed to evaluate multiple new therapeutic drugs for high-risk breast cancer. Previous studies suggest that pathological complete response (pCR) is a viable indicator of long-term outcomes of neoadjuvant chemotherapy for high-risk breast cancer. While pCR can be assessed during surgery after the chemotherapy, early prediction of pCR before the completion of the chemotherapy may facilitate personalized treatment management to achieve an improved outcome. Notably, the acquisition of dynamic contrast-enhanced magnetic resonance (DCEMR) images at multiple time points during the I-SPY 2 trial opens up the possibility of achieving early pCR prediction. In this study, we investigated the feasibility of the early prediction of pCR to neoadjuvant chemotherapy using multi-time point DCEMR images and clinical data acquired in the I-SPY2 trial. The prediction uncertainty was also quantified to allow physicians to make patient-specific decisions on treatment plans based on the level of associated uncertainty. The dataset used in our study included 624 patients with DCEMR images acquired at 3 time points before the completion of the chemotherapy: pretreatment (T0), after 3 cycles of treatment (T1), and after 12 cycles of treatment (T2). A convolutional long short-term memory (LSTM) network-based deep learning model, which integrated multi-time point deep image representations with clinical data, including tumor subtypes, was developed to predict pCR. The performance of the model was evaluated via the method of nested 5-fold cross validation. Moreover, we also quantified prediction uncertainty for each patient through test-time augmentation. To investigate the relationship between predictive performance and uncertainty, the area under the receiver operating characteristic curve (AUROC) was assessed on subgroups of patients stratified by the uncertainty score. By integrating clinical data and DCEMR images obtained at three-time points before treatment completion, the AUROC reached 0.833 with a sensitivity of 0.723 and specificity of 0.800. This performance was significantly superior (p<0.01) to models using only images (AUROC=0.706) or only clinical data (AUROC=0.746). After stratifying the patients into eight subgroups based on the uncertainty score, we found that group #1, with the lowest uncertainty, had a superior AUROC of 0.873. The AUROC decreased to 0.637 for group #8, which had the highest uncertainty. The results indicate that our convolutional LSTM network-based deep learning model can be used to predict pCR earlier before the completion of chemotherapy. By combining clinical data and multi-time point deep image representations, our model outperforms models built solely on clinical or image data. Estimating prediction uncertainty may enable physicians to prioritize or disregard predictions based on their associated uncertainties. This approach could potentially enhance the personalization of breast cancer therapy.

Probability density estimation of polynomial chaos and its application in structural reliability analysis

Polynomial chaos expansion (PCE) is a widely used approach for establishing the surrogate model of a time-consuming performance function for the convenience of uncertainty quantification of a stochastic structure. However, it remains difficult to calculate the probability density function (PDF) of the PCE accurately for general cases, though the PDF, as a complete representation of a random variable, is often required in some uncertainty problems. To address this problem, this paper proposes a semi-analytical method to compute the PDF of a PCE. This method derives the closed-form solutions of characteristic functions (CFs) of the first- and second-order PCEs, while an equivalent parabolization technique is proposed to provide the approximate solutions of CFs of higher-order PCEs. Then, the PDF of the PCE can be obtained by the Fourier transform of the resulting CF. Three numerical examples are investigated to demonstrate the accuracy, applicability, and efficiency of the proposed method for probability density estimation of PCE in structural reliability analysis.

Efficient prediction uncertainty quantification in dam behavior monitoring with attention-based sequence-to-sequence learning

Displacement is an intuitive monitoring indicator of dam structural behavior. Conventional deterministic modeling methods frequently disregard the inherent uncertainty associated with monitoring data. This study aims to quantify such uncertainties within dam displacement predictions by augmenting a sequence-to-sequence structure with the novel recurrent unit, termed as tiny gated unit (TGU), attention mechanism, as well as quantile regression, resulting in the Att-S2STQ model. Specifically, TGU adopts only one gate to identify nonlinearity in data sequences, while Bahdanau attention mechanism dynamically assigns weights to different parts of the input sequence. The inclusion of quantile regression allows Att-S2STQ to produce prediction intervals (PIs), from which the probability density functions (PDFs) and cumulative distribution functions (CDFs) are further derived via kernel density estimation. PIs, PDFs, and CDFs jointly serve to reveal the prediction uncertainty. The effectiveness of the model is illustrated through comparative experiments using real-world dam monitoring datasets. Results indicate that the proposed model outperforms traditional methods in point, interval, and probability predictions, while also having a simpler structure and faster training. The superiority of both accuracy and efficiency makes it a valuable tool for dam management, aiding in data-driven decision-making and enhancing operational safety.