Search

Operations researchers worldwide rely extensively on quantitative simulations to model alternative aspects of the COVID-19 pandemic. Proper uncertainty quantification and sensitivity analysis are fundamental to enrich the modeling process and communicate correctly informed insights to decision-makers. We develop a methodology to obtain insights on key uncertainty drivers, trend analysis and interaction quantification through an innovative combination of probabilistic sensitivity techniques and machine learning tools. We illustrate the approach by applying it to a representative of the family of susceptible-infectious-recovered (SIR) models recently used in the context of the COVID-19 pandemic. We focus on data of the early pandemic progression in Italy and the United States (the U.S.). We perform the analysis for both cases of correlated and uncorrelated inputs. Results show that quarantine rate and intervention time are the key uncertainty drivers, have opposite effects on the number of total infected individuals and are involved in the most relevant interactions.

As an efficient tool for uncertainty quantification of wind power forecasting, prediction intervals (PIs) provide essential prognosis to power system operator. Merely improving the statistical quality of PIs with respect to calibration and sharpness cannot always contribute to the operational value for specific decision-making issue. In order to bridge the gap between forecasting and decision, this paper proposes a novel cost-oriented machine learning (COML) framework that unifies nonparametric wind power PI construction and decision-making. Formulated as a bilevel programming model, the COML minimizes the operational costs of decision-making process by adaptively adjusting the quantile proportion pair of PIs resulting from extreme learning machine based quantile regression. The hierarchical optimization model of the COML is equivalently simplified as a single level nonlinear programming problem. Then an enhanced branch-and-contract (EBC) algorithm with innovative bounds contraction strategy is devised to efficiently capture the optimum of the single level problem with bilinear nonconvexity. Numerical experiments based on actual wind farm data simulate the online forecasting and decision process for wind power offering. Comprehensive comparisons verify the substantial superiority of the proposed COML methodology in terms of forecasting quality, operational value, as well as computational efficiency for practical application.

Manufactured blades are inevitably different from their design intent, which leads to a deviation of the performance from the intended value. To quantify the associated performance uncertainty, many approaches have been developed. The traditional Monte Carlo method based on a Computational Fluid Dynamics solver (MC-CFD) for a three-dimensional compressor is prohibitively expensive. Existing alternatives to the MC-CFD, such as surrogate models and second-order derivatives based on the adjoint method, can greatly reduce the computational cost. Nevertheless, they will encounter ‘the curse of dimensionality’ except for the linear model based on the adjoint gradient (called MC-adj-linear). However, the MC-adj-linear model neglects the nonlinearity of the performance function. In this work, an improved method is proposed to circumvent the low-accuracy problem of the MC-adj-linear without incurring the high cost of other alternative models. The method is applied to the study of the aerodynamic performance of an annular transonic compressor cascade, subject to prescribed geometric variability with industrial relevance. It is found that the proposed method achieves a significant accuracy improvement over the MC-adj-linear with low computational cost, showing the great potential for fast uncertainty quantification.

Sliding-window-based low-rank matrix approximation (LRMA) is a technique widely used in hyperspectral images (HSIs) denoising or completion. However, the uncertainty quantification of the restored HSI has not been addressed to date. Accurate uncertainty quantification of the denoised HSI facilitates applications such as multisource or multiscale data fusion, data assimilation, and product uncertainty quantification since these applications require an accurate approach to describe the statistical distributions of the input data. Therefore, we propose a prior-free closed-form element-wise uncertainty quantification method for LRMA-based HSI restoration. Our closed-form algorithm overcomes the difficulty of handling uncertainty in HSI patch mixing caused by the sliding-window strategy used in the conventional LRMA process. The proposed approach only requires the uncertainty of the observed HSI and provides the uncertainty result relatively rapidly and with similar computational complexity as the LRMA technique. We conduct extensive experiments to validate the estimation accuracy of the proposed closed-form uncertainty approach. The method is robust to at least 10% random impulse noise at the cost of 10%-20% of additional processing time compared to the LRMA. The experiments indicate that the proposed closed-form uncertainty quantification method is more applicable to real-world applications than the baseline Monte Carlo test, which is computationally expensive.

AimThe global Red List (RL) from the International Union for the Conservation of Nature is the most comprehensive global quantification of extinction risk, and widely used in applied conservation as well as in biogeographic and ecological research. Yet, due to the time- consuming assessment process, the RL is biased taxonomically and geographically, which limits its application on large scales, in particular for understudied areas such as the tropics, or understudied taxa, such as most plants and invertebrates. Here we present IUCNN, an R- package implementing deep learning models to predict species RL status from publicly available geographic occurrence records (and other traits if available).InnovationWe implement a user-friendly workflow to train and validate neural network models, and subsequently use them to predict species RL status. IUCNN contains functions to address specific issues related to the RL framework, including a regression-based approach to account for the ordinal nature of RL categories and class imbalance in the training data, a Bayesian approach for improved uncertainty quantification, and a target accuracy threshold approach that limits predictions to only those species whose RL status can be predicted with high confidence. Most analyses can be run with few lines of code, without prior knowledge of neural network models. We demonstrate the use of IUCNN on an empirical dataset of ∼14,000 orchid species, for which IUCNN models can predict extinction risk within minutes, while outperforming comparable methods.Main conclusionsIUCNN harnesses innovative methodology to estimate the RL status of large numbers of species. By providing estimates of the number and identity of threatened species in custom geographic or taxonomic datasets, IUCNN enables large-scale analyses on the extinction risk of species so far not well represented on the official RL.

Huge uncertainty exists in time dependent effects of deflection, especially for those concrete beam bridges in long-term service stage. The uncertainty has brought about great barriers to reliable assessment or reasonable prediction for the deflection. Most studies in this field focused on qualitative analysis rather than quantitative one. In order to realize the transformation from qualitative analysis to quantitative field of the uncertainty issue for bridge structure and expend the existing research, the Bayesian inference model was employed to conduct uncertainty quantification analysis based on the open-source database provided by Northwest University. The uncertainty coefficient was introduced to measure the differences between the test results and the theoretical ones for creep and shrinkage data. In the meantime, a surrogate model was proposed on deviation between long-term deflection for numerical value and experimental one, in which the former was calculated by ANSYS software and the latter was acquired by the in-door test on a simply supported beam, namely, Faber beam. After that, the uncertainty coefficient was introduced to update the model and the simulating process was performed again in which the corrected mean value of the posterior distribution was utilized. The results show that it narrows the error zone drastically, in which the relative reduction rate range from 49.83% to 82.76% for 95% lower confidence limit and from 11.46% to 98.73% for upper one. These outcomes prove the validity for the posterior distribution and also indicate that it could be a prospective way to improve the accuracy of the model significantly by utilizing the uncertainty coefficient. Besides, the method provided in this study could inspire the researchers who study in similar field and to do further exploration in the future.

The tilted-wave interferometer is an interferometrical measurement system for the accurate optical form measurement of optical aspheres and freeform surfaces. Its evaluation procedure comprises a high-dimensional inverse problem to reconstruct the form of the surface under test from measured data. Recent work has used a deep learning hybrid approach to solve the inverse problem successfully in a simulation environment. A quantification of the model uncertainty was incorporated using ensemble techniques. In this paper, we expand the application of the deep learning approach from simulations to measured data and show that it produces results similar to those of a state-of-the-art method in a real-world environment.

Machine learning (ML) based pavement performance models have gained increasing popularity in recent years due to their strong power in modelling complex relationships. However, the insufficiency of...

This paper presents an analysis and optimization of Airborne Wind Energy Systems (AWESs), designed to maximize the Annual Energy Production (AEP) and, in the second part, the economic profit. A gradient-based optimization algorithm is used to perform the preliminary design of the main AWES sub-systems. A global sensitivity analysis is carried out to study how the design process, represented by the optimization problem, is influenced by aleatory and epistemic uncertainties. In particular, Ground-Gen and Fly-Gen AWESs are studied with a unified model to allow for a quantitative comparison. In the first part of the work, an ideal hybrid AWES design with ground and on-board power generation is considered. With this approach, the common characteristics of Ground-Gen and Fly-Gen AWES designs that maximize AEP are found. In the second part, Ground-Gen and Fly-Gen AWES optimal economic designs are analyzed individually. It is found that a fully developed AWES has strong potential to be highly competitive in the energy market, by providing cheap renewable energy. Fly-Gen AWESs are found to be slightly more profitable than Ground-Gen if the airborne unit is not replaced often. The main physical and economical characteristics of optimal designs are highlighted.

Mathematical and computational modeling have been increasingly applied in many areas of cancer research, aiming to improve the understanding of tumorigenic mechanisms and to suggest more effective therapy protocols. The mathematical description of the tumor growth dynamics is often made using the exponential, logistic, and Gompertz models. However, recent literature has suggested that the Allee effect may play an important role in the early stages of tumor dynamics, including cancer relapse and metastasis. For a model to provide reliable predictions, it is necessary to have a rigorous evaluation of the uncertainty inherent in the modeling process. In this work, our main objective is to show how a model framework that integrates sensitivity analysis, model calibration, and model selection techniques can improve and systematically characterize model and data uncertainties. We investigate five distinct models with different complexities, which encompass the exponential, logistic, Gompertz, and weak and strong Allee effects dynamics. Using tumor growth data published in the literature, we perform a global sensitivity analysis, apply a Bayesian framework for parameter inference, evaluate the associated sensitivity matrices, and use different information criteria for model selection (First- and Second-Order Akaike Information Criteria and Bayesian Information Criterion). We show that such a wider methodology allows having a more detailed picture of each model assumption and uncertainty, calibration reliability, ultimately improving tumor mathematical description. The used in vivo data suggested the existence of both a competitive effect among tumor cells and a weak Allee effect in the growth dynamics. The proposed model framework highlights the need for more detailed experimental studies on the influence of the Allee effect on the analyzed cancer scenario.

Numerical simulations of earthquake damage on buildings require the definition of a reliable and appropriate seismic input (e.g., acceleration time histories and/or response spectra) in order to validate the accuracy of structural models in reproducing the observed level of damage – or no damage – associated with a particular earthquake. However, for sites that are not located close to active seismic stations, the definition of the ground motion that would have likely been recorded during an earthquake is not a trivial task.In this paper, we present the results of a case study where the seismic input at the sites of construction of three modern unreinforced masonry buildings caused by the Emilia May 29, 2012 M6.0 earthquake has been recreated following three different methods involving natural, artificial, and deconvolved accelerograms. The differences in the results are compared and contrasted highlighting the intrinsic limitations of the three different approaches while addressing an appropriate use of the seismic input when assessing the seismic performance of the three buildings.

Automatic medical image analysis (e.g., medical image classification) is widely used in the early diagnosis of various diseases. The computer-aided diagnosis (CAD) systems enable accurate disease detection and treatment. Nowadays, deep learning (DL)-based CAD systems have been able to achieve promising results in most of the healthcare applications. Also, uncertainty quantification in the existing DL methods have not gained enough attention in the field of medical research. To fill this gap, we propose a novel, simple and effective fusion model with uncertainty-aware module for medical image classification called Binary Residual Feature fusion (BARF). To deal with uncertainty, we applied the Monte Carlo (MC) dropout during inference to obtain the mean and standard deviation of the predictions. The proposed model has two main strategies: direct and cross validated using four different medical image datasets. Our experimental results demonstrate that the proposed model is efficient for medical image classification in real clinical settings.

The seismic response of geological reservoirs is a function of the elastic properties of porous rocks, which depends on rock types, petrophysical features, and geological environments. Such rock characteristics are generally classified into geological facies. We propose to use the convolutional neural networks in a Bayesian framework to predict facies based on seismic data and quantify the uncertainty in the classification. A variational approach is adopted to approximate the posterior distribution of neural parameters that is mathematically intractable. The network is trained on labeled examples. The mean and the standard deviation of the distribution of neural parameters are randomly drawn from predefined Gaussian functions for the initialization, and are updated by minimizing the negative evidence lower bound. The facies classification is applied to seismic sections not included in the training data set. We draw multiple random samples from the trained variational posterior distribution to simulate an ensemble predictor and classify the most probable seismic facies. We implement the proposed network in the open-source library of TensorFlow Probability, for its convenience and flexibility. The applications show that the internal regions of the seismic sections are generally classified with higher confidence than their boundaries, as measured by the predictive entropy that is calculated based on a multiclass probability across the possible facies. A plain neural network is also applied for comparison, by assigning fixed values to the neural parameters using a classical backpropagation technique. The comparison shows consistent results; however, the proposed approach is able to assess the uncertainty in the predictions.

Obtaining quantitative survey responses that are both accurate and informative is crucial to a wide range of fields. Traditional and ubiquitous response formats such as Likert and Visual Analogue Scales require condensation of responses into discrete point values - but sometimes a range of options may better represent the correct answer. In this paper, we propose an efficient interval-valued response mode, whereby responses are made by marking an ellipse along a continuous scale. We discuss its potential to capture and quantify valuable information that would be lost using conventional approaches, while preserving a high degree of response-efficiency. The information captured by the response interval may represent a possible response range - i.e., a conjunctive set, such as the real numbers between three and six. Alternatively, it may reflect uncertainty in respect to a distinct response - i.e., a disjunctive set, such as a confidence interval. We then report a validation study, utilizing our recently introduced open-source software (DECSYS) to explore how interval-valued survey responses reflect experimental manipulations of several factors hypothesised to influence interval width, across multiple contexts. Results consistently indicate that respondents used interval widths effectively, and subjective participant feedback was also positive. We present this as initial empirical evidence for the efficacy and value of interval-valued response capture. Interestingly, our results also provide insight into respondents' reasoning about the different aforementioned types of intervals - we replicate a tendency towards overconfidence for those representing epistemic uncertainty (i.e., disjunctive sets), but find intervals representing inherent range (i.e., conjunctive sets) to be well-calibrated., Comment: 59 pages, 12 figures, submitted to Behavior Research Methods

Purpose The quantitative detection of failure modes is important for making deep neural networks reliable and usable at scale. We consider three examples for common failure modes in image reconstruction and demonstrate the potential of uncertainty quantification as a fine-grained alarm system. Methods We propose a deterministic, modular and lightweight approach called Interval Neural Network (INN) that produces fast and easy to interpret uncertainty scores for deep neural networks. Importantly, INNs can be constructed post hoc for already trained prediction networks. We compare it against state-of-the-art baseline methods (MCDrop, ProbOut). Results We demonstrate on controlled, synthetic inverse problems the capacity of INNs to capture uncertainty due to noise as well as directional error information. On a real-world inverse problem with human CT scans, we can show that INNs produce uncertainty scores which improve the detection of all considered failure modes compared to the baseline methods. Conclusion Interval Neural Networks offer a promising tool to expose weaknesses of deep image reconstruction models and ultimately make them more reliable. The fact that they can be applied post hoc to equip already trained deep neural network models with uncertainty scores makes them particularly interesting for deployment.

A framework for dynamically updating post-earthquake functional recovery forecasts is presented to reduce the epistemic uncertainty in the predictive model. A Bayesian Network (BN) model is used to provide estimates of the total recovery time, and a process-based discrete event simulation (PBDES) model generates forecasts of the complete recovery trajectory. Both models rely on component damage and duration-based input parameters that are dynamically updated using Bayes’ theorem, as information becomes available throughout the recovery process. The effectiveness of the proposed framework is demonstrated through an application to the pipe network of the City of Napa water distribution system. More specifically, pipe damage and repair data from the 2014 earthquake are used as a point of comparison for the dynamic forecasts. It is shown that, over time, the mean value of the total recovery duration generated by the BN-based model converges to the observed value and the dispersion is reduced. Also, despite a crude initial estimate, the median trajectory generated by the PBDES model provides a reasonable approximation of the observed recovery within 30 days following the earthquake. The proposed framework can be used by emergency managers to investigate the efficacy of post-event mitigation measures (e.g. crew allocation, resource prioritization) utilizing the most current data and knowledge.

Chemical engineers rely on models for design, research, and daily decision-making, often with potentially large financial and safety implications. Previous efforts a few decades ago to combine artificial intelligence and chemical engineering for modeling were unable to fulfill the expectations. In the last five years, the increasing availability of data and computational resources has led to a resurgence in machine learning-based research. Many recent efforts have facilitated the roll-out of machine learning techniques in the research field by developing large databases, benchmarks, and representations for chemical applications and new machine learning frameworks. Machine learning has significant advantages over traditional modeling techniques, including flexibility, accuracy, and execution speed. These strengths also come with weaknesses, such as the lack of interpretability of these black-box models. The greatest opportunities involve using machine learning in time-limited applications such as real-time optimization and planning that require high accuracy and that can build on models with a self-learning ability to recognize patterns, learn from data, and become more intelligent over time. The greatest threat in artificial intelligence research today is inappropriate use because most chemical engineers have had limited training in computer science and data analysis. Nevertheless, machine learning will definitely become a trustworthy element in the modeling toolbox of chemical engineers. (C) 2021 THE AUTHORS. Published by Elsevier LTD on behalf of Chinese Academy of Engineering and Higher Education Press Limited Company.

Recent years have witnessed the prominent advancements of deep learning (DL) in the arsenal of prognostics and health management. However, the prognostic uncertainty problem extensively existed in industrial devices is not addressed by most DL approaches. This article formulates a novel Bayesian Deep Learning (BDL) framework to characterize the prognostic uncertainties. A distinguished advantage of the framework is its capacity of capturing the comprehensive effects of two critical uncertainties: 1) epistemic uncertainty, accounting for the uncertainty in the model, and 2) aleatoric uncertainty, representing the impact of random disturbance, such as measurement errors. The former arises from the variability of the model weights, and the latter is characterized by selected lifetime distributions. We integrate both uncertainties by defining BDL as priors of lifetime parameters. A sequential Bayesian boosting algorithm is executed to improve the estimation accuracy and compress the credible intervals. The superior prediction performance of our framework is validated by a real-world dataset collected from hydraulic mechanisms of circuit breakers.

The probabilistic modelling is widely used in engineering practices, especially for assessing the safety and reliability of complex systems. Dynamic evidential network (DEN) can efficiently deal with epistemic uncertainty based on Dempster-Shafer theory. This work proposes an extended discrete-time DEN model along with an extensive review of its applications in engineering. The proposed model combines the Dempster-Shafer theory, used for handling epistemic uncertainty across a new state-space reconstruction of components, and the dynamic Bayesian network is used for multi-state system reliability. The model application is demonstrated on a real case study from the aviation field. The application quantifies reliability and availability parameters that help to prioritize maintenance activities and avoid failures of complex redundant systems. The proposed model can serve as a tool to assess the reliability and availability of industrial systems suffering from parameter uncertainty and common cause failures.

Mineral resources are typically quantified by estimating the grade–tonnage curve for different resource categories. Statutory resource assessment reports (e.g., NI-43-101), however, do not include a measure of uncertainty for the disclosed resources despite the major investments required for mining projects. Although conditional simulation can provide confidence intervals (CIs) for resource estimation, it requires a strong stationarity assumption and depends on the variogram model selected, which is often poorly defined with the available data. In order to avoid these limitations, this research proposes the use and comparison of two machine learning (ML) methods, multiple linear regression and a multilayer neural network, to generate tonnage curves and their CIs directly from the data. The classical variogram modeling step is replaced by the specification of intervals for each parameter of the selected variogram model. The learning is carried out in a perfectly controlled environment using simulations with known variograms. Numerous reference deposits are sampled, and for each one, a series of conditional realizations define the mean tonnage and CI curves. Different statistics computed for the entire data set are used as input to predict the tonnage and CI curves by the ML methods. The results indicate that there are no significant differences between the ML methods. In addition, ML resource predictions outperform those obtained with ordinary kriging, constrained kriging, uniform conditioning and indirect lognormal correction, being surpassed only by the discrete Gaussian model. Nevertheless, these predictors were favored by the use of true variogram models. Moreover, the coverage probabilities of different CIs reach the nominal levels indicating adequate resource uncertainty quantification. Finally, two case studies validate the effectiveness of the proposed approach for tonnage prediction and uncertainty quantification.

At a regional scale, the best predictor for the 3D geology of the near-subsurface is often the information contained in a geological map. One challenge we face is the difficulty in reproducibly preparing input data for 3D geological models. We present two libraries (map2loop and map2model) that automatically combine the information available in digital geological maps with conceptual information, including assumptions regarding the subsurface extent of faults and plutons to provide sufficient constraints to build a prototype 3D geological model. The information stored in a map falls into three categories of geometric data: positional data, such as the position of faults, intrusive, and stratigraphic contacts; gradient data, such as the dips of contacts or faults; and topological data, such as the age relationships of faults and stratigraphic units or their spatial adjacency relationships. This automation provides significant advantages: it reduces the time to first prototype models; it clearly separates the data, concepts, and interpretations; and provides a homogenous pathway to sensitivity analysis, uncertainty quantification, and value of information studies that require stochastic simulations, and thus the automation of the 3D modelling workflow from data extraction through to model construction. We use the example of the folded and faulted Hamersley Basin in Western Australia to demonstrate a complete workflow from data extraction to 3D modelling using two different open-source 3D modelling engines: GemPy and LoopStructural.

Machine learning (ML) plays a growing role in the design and discovery of chemicals, aiming to reduce the need to perform expensive experiments and simulations. ML for such applications is promising but difficult, as models must generalize to vast chemical spaces from small training sets and must have reliable uncertainty quantification metrics to identify and prioritize unexplored regions. Ab initio computational chemistry and chemical intuition alike often take advantage of differences between chemical conditions, rather than their absolute structure or state, to generate more reliable results. We have developed an analogous comparison-based approach for ML regression, called pairwise difference regression (PADRE), which is applicable to arbitrary underlying learning models and operates on pairs of input data points. During training, the model learns to predict differences between all possible pairs of input points. During prediction, the test points are paired with all training set points, giving rise to a set of predictions that can be treated as a distribution of which the mean is treated as a final prediction and the dispersion is treated as an uncertainty measure. Pairwise difference regression was shown to reliably improve the performance of the random forest algorithm across five chemical ML tasks. Additionally, the pair-derived dispersion is both well correlated with model error and performs well in active learning. We also show that this method is competitive with state-of-the-art neural network techniques. Thus, pairwise difference regression is a promising tool for candidate selection algorithms used in chemical discovery.

We propose a Bayesian deep learning framework for model driven online sparse channel estimation task in Multi-user MIMO systems. Tools from Bayesian neural network and stochastic variational Bayesian Inference are utilized to capture aleatoric and epistemic uncertainty estimates. We treat the network prediction as an auxiliary variable to allow inference performance to be unaffected by the stage of training of the network. In addition to providing uncertainty estimates, being Bayesian, the framework enables us the possibility to marginalize over penalty parameters and is well suited for online scenario with changing environments. Our simulations show that the framework is robust to model mismatch, and efficiently captures uncertainty in the predictions.

Currently available uncertainty quantification (UQ) neural networks (NNs) are trained through the statistical error minimization. Therefore, NNs perform poorly for critical input patterns. Some input patterns have lower coverage probabilities than others. Such input dependent performance is evident in electricity price prediction where different input features are coming from heterogeneous monitoring sources. This paper proposes a prediction interval (PI) based UQ of the electricity price with the proposed partial adversarial training to achieve the input-domain independent performance. The proposed training consists of initial training, adversarial sample generations from critical samples and a final training with the combined datasets of critical samples and initial training samples. Critical situations are situations where prediction systems struggle to predict and make higher statistical errors. Multiple NNs are first trained with different initializations. Each uncovered sample to the NN pair in the training set generates an adversarial sample. The adversarial dataset is concatenated with the initial samples. The final NN training is performed with the combined dataset. The technique is visualized with rough sketches in both time and input domain. The feasibility and performance are examined on experimental electricity market price datasets.

Purpose There is recent emphasis on designing new materials and alloys specifically for metal additive manufacturing (AM) processes, in contrast to AM of existing alloys that were developed for other traditional manufacturing methods involving considerably different physics. Process optimization to determine processing recipes for newly developed materials is expensive and time-consuming. The purpose of the current work is to use a systematic printability assessment framework developed by the co-authors to determine windows of processing parameters to print defect-free parts from a binary nickel-niobium alloy (NiNb5) using laser powder bed fusion (LPBF) metal AM. Design/methodology/approach The printability assessment framework integrates analytical thermal modeling, uncertainty quantification and experimental characterization to determine processing windows for NiNb5 in an accelerated fashion. Test coupons and mechanical test samples were fabricated on a ProX 200 commercial LPBF system. A series of density, microstructure and mechanical property characterization was conducted to validate the proposed framework. Findings Near fully-dense parts with more than 99% density were successfully printed using the proposed framework. Furthermore, the mechanical properties of as-printed parts showed low variability, good tensile strength of up to 662 MPa and tensile ductility 51% higher than what has been reported in the literature. Originality/value Although many literature studies investigate process optimization for metal AM, there is a lack of a systematic printability assessment framework to determine manufacturing process parameters for newly designed AM materials in an accelerated fashion. Moreover, the majority of existing process optimization approaches involve either time- and cost-intensive experimental campaigns or require the use of proprietary computational materials codes. Through the use of a readily accessible analytical thermal model coupled with statistical calibration and uncertainty quantification techniques, the proposed framework achieves both efficiency and accessibility to the user. Furthermore, this study demonstrates that following this framework results in printed parts with low degrees of variability in their mechanical properties.

Due to uncertainties in the deterioration process of long service-life assets, assessing reliability and planning maintenance and inspection activities are often difficult tasks. Most of the methods developed use operational or historical data from the manufacturer to predict the deterioration of the asset and estimate its reliability. However, in practice, such failure data is often scarce (e.g. very rare events) and the reliability prediction models might not be adapted to the operation of the user. In addition, available data gathered from maintenance or inspection tasks might only inform about a short period of time, and it might be difficult to obtain the corresponding reliability predictions as the associated uncertainty is still significant. Hence, this paper introduces a reliability assessment method that quantifies uncertainties regarding the failure of long service-life components. It combines Cooke’s classical method (also known as Structured Expert Judgement) with a histogram technique, creating a performance-based method to assess uncertainty in components lifetime distributions. A case study on railway wheelsets is analysed to illustrate the effectiveness of such approach. The results show that the presented method is able to assess failure rates, which can support decisions in reliability-based maintenance of engineering systems.

While neural networks achieve state-of-the-art performance for many molecular modeling and structure–property prediction tasks, these models can struggle with generalization to out-of-domain examples, exhibit poor sample efficiency, and produce uncalibrated predictions. In this paper, we leverage advances in evidential deep learning to demonstrate a new approach to uncertainty quantification for neural network-based molecular structure–property prediction at no additional computational cost. We develop both evidential 2D message passing neural networks and evidential 3D atomistic neural networks and apply these networks across a range of different tasks. We demonstrate that evidential uncertainties enable (1) calibrated predictions where uncertainty correlates with error, (2) sample-efficient training through uncertainty-guided active learning, and (3) improved experimental validation rates in a retrospective virtual screening campaign. Our results suggest that evidential deep learning can provide an efficient means of uncertainty quantification useful for molecular property prediction, discovery, and design tasks in the chemical and physical sciences., A fast, scalable approach for uncertainty quantification in neural networks enables uncertainty-aware molecular property prediction, accelerated property optimization, and guided virtual screening.

Quantifying predictive uncertainty in deep neural networks is a challenging and yet unsolved problem. Existing quantification approaches can be categorized into two lines. Bayesian methods provide a complete uncertainty quantification theory but are often not scalable to large-scale models. Along another line, non-Bayesian methods have good scalability and can quantify uncertainty with high quality. The most remarkable idea in this line is Deep Ensemble, but it is limited in practice due to its expensive computational cost. Thus, we propose HatchEnsemble to improve the efficiency and practicality of Deep Ensemble. The main idea is to use function-preserving transformations, ensuring HatchNets to inherit the knowledge learned by a single model called SeedNet. This process is called hatching, and HatchNet can be obtained by continuously widening the SeedNet. Based on our method, two different hatches are proposed, respectively, for ensembling the same and different architecture networks. To ensure the diversity of models, we also add random noises to parameters during hatching. Experiments on both clean and corrupted datasets show that HatchEnsemble can give a competitive prediction performance and better-calibrated uncertainty quantification in a shorter time compared with baselines.

International audience; Tasks such as analysis, design optimization, and uncertainty quantification can be computationally expensive. Surrogate modeling is often the tool of choice for reducing the burden associated with such data-intensive tasks. However, even after years of intensive research, surrogate modeling still involves a struggle to achieve maximum accuracy within limited resources. This work summarizes various advanced, yet often straightforward, statistical tools that help. We focus on four techniques with increasing popularity in the surrogate modeling community: (i) variable screening and dimensionality reduction in both the input and the output spaces, (ii) data sampling techniques or design of experiments, (iii) simultaneous use of multiple surrogates, and (iv) sequential sampling. We close the paper with some suggestions for future research.

Deep learning has emerged as a technique of choice for rapid feature extraction across imaging disciplines, allowing rapid conversion of the data streams to spatial or spatiotemporal arrays of features of interest. However, applications of deep learning in experimental domains are often limited by the out-of-distribution drift between the experiments, where the network trained for one set of imaging conditions becomes sub-optimal for different ones. This limitation is particularly stringent in the quest to have an automated experiment setting, where retraining or transfer learning becomes impractical due to the need for human intervention and associated latencies. Here we explore the reproducibility of deep learning for feature extraction in atom-resolved electron microscopy and introduce workflows based on ensemble learning and iterative training to greatly improve feature detection. This approach allows incorporating uncertainty quantification into the deep learning analysis and also enables rapid automated experimental workflows where retraining of the network to compensate for out-of-distribution drift due to subtle change in imaging conditions is substituted for human operator or programmatic selection of networks from the ensemble. This methodology can be further applied to machine learning workflows in other imaging areas including optical and chemical imaging.

We propose a method to analyze the performance variability caused by fabrication uncertainty in photonic circuits with a large number of correlated parameters. By combining a sparse polynomial chaos expansion model with dimensionality reduction in the form of Karhunen-Loeve transform and principal component analysis, we demonstrate the stochastic analysis of the transfer function of cascaded Mach-Zehnder interferometers with up to 38 correlated uncertain parameters.

We propose a fuzzy-robust multi-objective optimization model for blood supply chain network design in disaster relief. The problem aims to minimize (1) the expected total cost of the system, (2) the implicit cost associated with patients’ waiting in hospitals, and (3) the unsatisfied demands. To model patients’ waiting and to improve the effectiveness of relief activities by decreasing congestion in hospitals, a queuing framework is utilized. A robust possibilistic programming approach is applied to capture the epistemic uncertainty of parameters and provide risk-averse solutions for policymakers. Given the conflicting objectives sought, we use multi-objective decision-making techniques, including the Torabi and Hasini approach and $$\varepsilon$$ -constrained method. Experimentation on a real-life case study confirms that the proposed framework can help decision-makers adopt suitable strategies for planning blood collection and delivery in emergencies. The results obtained show that substantial improvements in the service quality could be achieved at modest increases in the network cost by properly locating facilities using our model. We also observed that both the service level and the service quality remain relatively stable over a wide range of model parameter values, highlighting the robust nature of the proposed approach. Based on our findings, we recommend implementing risk-pooling strategies, setting realistic service level targets, and incorporating service equity as an objective. Although our model accounts for many realistic considerations, it overlooks some relevant issues like network disruptions to remain tractable, which is worthy of further investigation in future research.

The ability to identify erroneous depth estimates is of fundamental interest. Information regarding the aleatoric uncertainty of depth estimates can be, for example, used to support the process of depth reconstruction itself. Consequently, various methods for the estimation of aleatoric uncertainty in the context of dense stereo matching have been presented in recent years, with deep learning-based approaches being particularly popular. Among these deep learning-based methods, probabilistic strategies are increasingly attracting interest, because the estimated uncertainty can be quantified in pixels or in metric units due to the consideration of real error distributions. However, existing probabilistic methods usually assume a unimodal distribution to describe the error distribution while simply neglecting cases in real-world scenarios that could violate this assumption. To overcome this limitation, we propose two novel mixed probability models consisting of Laplacian and Uniform distributions for the task of aleatoric uncertainty estimation. In this way, we explicitly address commonly challenging regions in the context of dense stereo matching and outlier measurements, respectively. To allow a fair comparison, we adapt a common neural network architecture to investigate the effects of the different uncertainty models. In an extensive evaluation using two datasets and two common dense stereo matching methods, the proposed methods demonstrate state-of-the-art accuracy.

Expressions and propagations of uncertainties have been the core topics in the development of risk science in last decades, whose purpose is to provide decision-makers with clear information about the uncertainty of system's risk. Uncertainty theory is an emerging theory that has great advantages in the expression of epistemic uncertainty, compared to the theories such as subjective probability, evidence theory, and possibility theory. A new framework of uncertainty expression is proposed in this article to properly express different uncertainty sources that exist in the system, where the uncertainty theory is used to express epistemic uncertainties and frequentist probability is used to express aleatory uncertainties. A general propagation method is further developed to address the joint calculations of proposed uncertainty expressions, which can be degenerated into pure probabilistic approach and pure uncertainty -based approach. A case study is conducted to show the effectiveness of proposed method, whose results indicate that the application of proposed method will lead to a result which is easier to be understood than results of theories such as evidence theory and possibility theory, and is more robust than results of Bayesian approach.

Recently, tremendous progress has been achieved in applying deep learning schemes (DLSs) to solve inverse scattering problems (ISPs), where state-of-the-art performance has been attained. However, little attention has been paid to the uncertainty quantification of these deep-learning methods in solving ISPs. In other words, the error of the prediction is not known since the ground truth is not available in practice. In this article, a Bayesian convolutional neural network (BCNN) is used to quantify the uncertainties in solving ISPs. With Monte Carlo dropout, the proposed BCNN is able to directly predict the pixel-based uncertainties of the widely used DLSs in ISPs. To quantitatively evaluate the performance of uncertainty predictions, both correlation coefficient and nonlinear correlation distribution between the predicted uncertainty and true absolute error are calculated. The tests on both synthetic and experimental data show that the predictive uncertainty is highly correlated with true absolute error calculated from the ground truth. Besides, when DLSs fail to solve an ISP, the predicted uncertainty increases significantly, which offers a pixel-based “confidence level” in solving ISPs.

The remaining useful life (RUL) estimation of bearings is critical for ensuring the reliability of mechanical systems. Owing to the rapid development of deep learning methods, a multitude of data-driven RUL estimation approaches have been proposed recently. However, the following problems remain in existing methods: 1) Most network models use raw data or statistical features as input, which renders it difficult to extract complex fault-related information hidden in signals; 2) for current observations, the dependence between current states is emphasized, but their complex dependence on previous states is often disregarded; 3) the output of neural networks is directly used as the estimated RUL in most studies, resulting in extremely volatile prediction results that lack robustness. Hence, a novel prognostics approach is proposed based on a time–frequency representation (TFR) subsequence, three-dimensional convolutional neural network (3DCNN), and Gaussian process regression (GPR). The approach primarily comprises two aspects: construction of a health indicator (HI) using the TFR-subsequence–3DCNN model, and RUL estimation based on the GPR model. The raw signals of the bearings are converted into TFR-subsequences by continuous wavelet transform and a dislocated overlapping strategy. Subsequently, the 3DCNN is applied to extract the hidden spatiotemporal features from the TFR-subsequences and construct HIs. Finally, the RUL of the bearings is estimated using the GPR model, which can also define the probability distribution of the potential function and prediction confidence. Experiments on the PRONOSTIA platform demonstrate the superiority of the proposed TFR-subsequence–3DCNN–GPR approach. The use of degradation-related spatiotemporal features in signals is proposed herein to achieve a highly accurate bearing RUL prediction with uncertainty quantification.

A significant role for a future nuclear carbon-free energy production is attributed to fast reactors, mostly employing a liquid metal as a coolant. This paper summarizes the efforts that have been undertaken in collaborative projects sponsored by the European Commission in the past 20 years in the fields of liquid-metal heat transfer modeling, fuel assembly and core thermal hydraulics, pool and system thermal hydraulics, and establishment of best practice guidelines and verification, validation, and uncertainty quantification (UQ). The achievements in these fields will be presented along with the prospects on topics which will be studied collaboratively in Europe in the years to come. These prospects include further development of heat transfer models for applied computational fluid dynamics (CFD), further analysis of the consequences of fuel assembly blockages on coolant flow and temperature, analysis of the thermal hydraulic effects in deformed fuel assemblies, extended validation of three-dimensional pool thermal hydraulic CFD models, and further development and validation of multi-scale system thermal hydraulic methods.

This study aims to estimate the value and quantify the uncertainty of the compressive strength of circular concrete-filled steel tube (CCFST) columns under eccentric loading using a hybrid machine learning model, namely PANN, which is a combination of particle swarm optimization (PSO) and artificial neural networks (ANNs). A dataset of 241 experiments is collected and used to construct such a hybrid model. The PANN performance is then compared with other data-mining techniques such as, multiple linear regression (MLR) and multiple adaptive regression spline (MARS), and benchmarked against four design codes, including EC4, ACI, AISC, and AIJ. The obtained results in terms of R of 0.995, RMSE of 11.2, and MAPE of 0.154 demonstrate that PANN is the best model serving as an efficient alternative approach to predict the compressive strength of the CCFST column under eccentric loading. The CCFST ultimate strength is also quantified uncertainty with configuration randomness (e.g., geometry, material, and loading configurations) based on Monte Carlo simulation. The simulation findings indicate the column diameter is the most sensitive to the output, the short columns are less sensitive than the long ones, and the sensitivity of CCFST columns towards uncertainty decreases when the eccentricity increasing.

The heliocentric orbital dynamics of a spacecraft propelled by a solar sail is affected by some uncertainty sources, including possible inaccuracies in the measurement of the sail film optical properties. Moreover, the solar radiation pressure, which is responsible for the solar sail propulsive acceleration generation, is not time-constant and is subject to fluctuations that are basically unpredictable and superimposed to the well-known 11-year solar activity cycle. In this context, this work aims at investigating the effects of such uncertainties on the actual heliocentric trajectory of a solar sail by means of stochastic simulations performed with a generalized polynomial chaos procedure. The numerical results give an estimation of their impact on the actual heliocentric trajectory and identify whether some of the uncertainty sources are more relevant than others. This is a fundamental information for directing more accurate theoretical and experimental efforts toward the most important parameters, in order to obtain an accurate knowledge of the solar sail thrust vector characteristics and, eventually, of the spacecraft heliocentric position.

In spite of the advent of Machine Learning (ML) and its successful deployment in measurement systems, little information can be found in the literature about uncertainty quantification in these systems [1]. Uncertainty is crucial for the adoption of ML in commercial products and services. Designers are now being encouraged to be upfront about the uncertainty in their ML systems, because products that specify their uncertainty can have a significant competitive advantage and can unlock new value, reduce risk, and improve usability [2]. In this article, we will describe uncertainty quantification in ML. Because there isn't enough room in one article to explain all ML methods, we concentrate on Deep Learning (DL), which is one of the most popular and effective ML methods in I&M [3]. Please note that this article follows and uses concepts from Part 1 [4], so readers are highly encouraged to first read that part. In addition, we assume the reader has a basic understanding of both DL and uncertainty. Readers for whom this assumption is false are encouraged to first read the brief introduction to DL and its applications in I&M presented in [3] as well as the uncertainty tutorial in [5].

Observing system uncertainty experiments (OSUEs) have been recently proposed as a cost-effective way to perform probabilistic assessment of retrievals for NASA’s Orbiting Carbon Observatory-2 (OCO-...

A common strategy to handle simulation-based uncertainty quantification problems is adopting a metamodel to replace time-demanding calculations such as computational fluid dynamics simulation or finite element analysis within Monte Carlo simulation process. However, most of the so far metamodel-assisted uncertainty quantification methods suffer from the ‘curse of dimensionality.’ The required number of evaluations, which determines the computational cost, increases exponentially as the dimensionality of the input uncertainty increases, resulting in unaffordable computational cost for high-dimensional problems. Another challenge emerges when the output uncertainties are a spatially varying field accommodating a huge number of spatial nodes. To solve these issues, here we propose a dimension-reduction metamodeling approach, in which active subspace method is utilized to reduce the input dimensionality and proper orthogonal decomposition method is utilized to reduce the output dimensionality of the spatially varying field. The relationship between the two methods is established by using the support vector regression model. Through uncertainty quantification of seven stochastic analytical functions and one stochastic convection-diffusion equation, the proposed approach was verified to be fairly accurate in propagating high-dimensional input uncertainties to either a scalar value or a spatially varying output. The accuracy and efficiency of the proposed approach in dealing with even more practical simulation-based problems were then validated by uncertainty quantification of a compressor cascade with stochastic protrusions/dents distributed on the blade surface. This work provides an effective and versatile approach for simulation-based high-dimensional uncertainty quantification problems.

Deep learning is quickly becoming essential to human ecosystem. However, the opacity of certain deep learning models poses a legal barrier in its adoption for greater purposes. Explainable AI (XAI) is a recent paradigm intended to tackle this issue. It explains the prediction mechanism produced by black box AI models, making it extremely practical for safety, security or financially important decision making. In another aspect, most deep learning studies are based on point estimate prediction with no measure of uncertainty which is vital for decision making. Obviously, these works are not suitable for real world applications. This paper presents a Remaining Useful Life (RUL) estimation problem for turbofan engines equipped with prognostic explainability and uncertainty quantification. A single input, multi outputs probabilistic Long Short-Term Memory (LSTM) is employed to predict the RULs distribution of the turbofans and SHapley Additive exPlanations (SHAP) approach is applied to explain the prognostic made. The explainable probabilistic LSTM is thus able to express its confidence in predicting and explains the produced estimation. The performance of the proposed method is comparable to several other published works

The generic model of a cable with small bending stiffness and anchored to flexible supports in rotation and translation is considered. An asymptotic analysis of the natural frequencies of this generic model is derived and shows that, for small bending stiffness, the first few natural frequencies can be expressed as a function of the cable axial force, the small bending stiffness and a single dimensionless group collecting the information of all other problem parameters. This formulation is used to develop an identification procedure of the cable axial force. Two formulations are proposed, one numerical and one semi-analytical based on a simple linear regression model. Both methods do not attempt at separately identifying the problem parameters since the observability analysis has revealed that only the cable axial force, the bending stiffness and the dimensionless group can be identified. In particular, the second method is very simple to implement and provides estimates of the cable axial force which account for the flexibility of the support. The proposed method can therefore be seen as an extension of usual identification techniques based on linear regressions of natural frequencies vs. mode number relations, by considering at the same time the bending stiffness and the deformability of supports. Being simple and robust as shown by means of an uncertainty quantification analysis, the proposed method can be conveniently embedded in the framework of a continuous monitoring strategy.

Reliable environmental context prediction is critical for wearable robots (e.g., prostheses and exoskeletons) to assist terrain-adaptive locomotion. This article proposed a novel vision-based context prediction framework for lower limb prostheses to simultaneously predict human’s environmental context for multiple forecast windows. By leveraging the Bayesian neural networks (BNNs), our framework can quantify the uncertainty caused by different factors (e.g., observation noise, and insufficient or biased training) and produce a calibrated predicted probability for online decision-making. We compared two wearable camera locations (a pair of glasses and a lower limb device), independently and conjointly. We utilized the calibrated predicted probability for online decision-making and fusion. We demonstrated how to interpret deep neural networks with uncertainty measures and how to improve the algorithms based on the uncertainty analysis. The inference time of our framework on a portable embedded system was less than 80 ms/frame. The results in this study may lead to novel context recognition strategies in reliable decision-making, efficient sensor fusion, and improved intelligent system design in various applications. Note to Practitioners —This article was motivated by two practical problems in computer vision for wearable robots: First, the performance of deep neural networks is challenged by real-life disturbances. However, reliable confidence estimation is usually unavailable and the factors causing failures are hard to identify. Second, evaluating wearable robots by intuitive trial and error is expensive due to the need for human experiments. Our framework produces a calibrated predicted probability as well as three uncertainty measures. The calibrated probability makes it easy to customize prediction decision criteria by considering how much the corresponding application can tolerate error. This study demonstrated a practical procedure to interpret and improve the performance of deep neural networks with uncertainty quantification. We anticipate that our methodology could be extended to other applications as a general scientific and efficient procedure of evaluating and improving intelligent systems.

Modeling outdoor environmental sound levels is a challenging problem. This paper reports on a validation study of two continental-scale machine learning models using geospatial layers as inputs and the summer daytime A-weighted L50 as a validation metric. The first model was developed by the National Park Service while the second was developed by the present authors. Validation errors greater than 20 dBA are observed. Large errors are attributed to limited acoustic training data. Validation environments are geospatially dissimilar to training sites, requiring models to extrapolate beyond their training sets. Results motivate further work in optimal data collection and uncertainty quantification.

Atom probe tomography, and related methods, probe the composition and the three-dimensional architecture of materials. The software tools which microscopists use, and how these tools are connected into workflows, make a substantial contribution to the accuracy and precision of such material characterization experiments. Typically, we adapt methods from other communities like mathematics, data science, computational geometry, artificial intelligence, or scientific computing. We also realize that improving on research data management is a challenge when it comes to align with the FAIR data stewardship principles. Faced with this global challenge, we are convinced it is useful to join forces. Here, we report the results and challenges with an inter-laboratory call for developing test cases for several types of atom probe microscopy software tools. The results support why defining detailed recipes of software workflows and sharing these recipes is necessary and rewarding: Open source tools and (meta)data exchange can help to make our day-to-day data processing tasks become more efficient, the training of new users and knowledge transfer become easier, and assist us with automated quantification of uncertainties to gain access to substantiated results.