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There have been impressive advances in the physical and mathematical modelling of complex physiological systems in the last few decades, with the potential to revolutionise personalised healthcare with patient-specific evidence-based diagnosis, risk assessment and treatment decision support using digital twins. However, practical progress and genuine clinical impact hinge on successful model calibration, parameter estimation and uncertainty quantification, which calls for novel innovative adaptions and methodological extensions of contemporary state-of-the-art inference techniques from Statistics and Machine Learning. In the present study, we focus on two computational fluid-dynamics (CFD) models of the blood systemic and pulmonary circulation. We discuss state-of-the-art emulation techniques based on deep learning and Gaussian processes, which are coupled with established inference techniques based on greedy optimisation, simulated annealing, Markov Chain Monte Carlo, History Matching and rejection sampling for computationally fast inference of unknown parameters of the CFD models from blood flow and pressure data. The inference task was set as a competitive challenge which the participants had to conduct within a limited time frame representative of clinical requirements. The performance of the methods was assessed independently and objectively by the challenge organisers, based on a ground truth that was unknown to the method developers. Our results indicate that for the systemic challenge, in which an idealised case of noise-free data was considered, the relative deviation from the ground-truth in parameter space ranges from 10−5% (highest-performing method) to 3% (lowest-performing method). For the pulmonary challenge, for which noisy data was generated, the performance ranges from 0.9% to 7% deviation for the parameter posterior mean, and from 35% to 570% deviation for the parameter posterior variance.

Methane (CH4) is globally the second most critical greenhouse gas after carbon dioxide, contributing to 16%–25% of the observed atmospheric warming. Wetlands are the primary natural source of methane emissions globally. However, wetland methane emission estimates from biogeochemistry models contain considerable uncertainty. One of the main sources of this uncertainty arises from the numerous uncertain model parameters within various physical, biological, and chemical processes that influence methane production, oxidation, and transport. Sensitivity Analysis (SA) can help identify critical parameters for methane emission and achieve reduced biases and uncertainties in future projections. This study performs SA for 19 selected parameters responsible for critical biogeochemical processes in the methane module of the Energy Exascale Earth System Model (E3SM) land model (ELM). The impact of these parameters on various CH4 fluxes is examined at 14 FLUXNET- CH4 sites with diverse vegetation types. Given the extensive number of model simulations needed for global variance-based SA, we employ a machine learning (ML) algorithm to emulate the complex behavior of ELM methane biogeochemistry. We found that parameters linked to CH4 production and diffusion generally present the highest sensitivities despite apparent seasonal variation. Comparing simulated emissions from perturbed parameter sets against FLUXNET-CH4 observations revealed that better performances can be achieved at each site compared to the default parameter values. This presents a scope for further improving simulated emissions using parameter calibration with advanced optimization techniques.

We introduce linear regression using physics-based basis functions optimized through the geometry of an inner product space. This method addresses the challenge of surrogate modeling with high-dimensional input, as the physics-based basis functions encode problem-specific information. We demonstrate the method using a proof-of-concept nonlinear random vibration example.

ObjectiveFast and accurate deformable image registration (DIR) that include DIR uncertainty estimation are essential for safe and reliable clinical deployment. While recent deep learning models have shown promise in predicting DIR with its uncertainty, challenges persist in proper uncertainty evaluation and hyperparameter optimization for these methods. This work aims to develop and evaluate a model that can perform fast DIR and predict its uncertainty in seconds.ApproachIn this study, we introduce a novel probabilistic multi-resolution image registration model utilizing convolutional neural networks (CNNs) to estimate a multivariate normal distributed dense displacement field (DDF) in a multimodal image registration problem. To assess the quality of the DDF distribution predicted by the model, we propose a new metric based on the Kullback-Leibler divergence. The performance of our approach was evaluated against three other DIR algorithms (VoxelMorph, Monte Carlo Drop-Out, and Monte Carlo B-splines) capable of predicting uncertainty. The evaluation of the models included not only the quality of the deformation but also the reliability of the estimated uncertainty. Our application investigated registration of a treatment planning computed tomography (CT) to follow-up cone beam CT for daily adaptive radiotherapy.Main resultsThe hyperparameter tuning of the models showed that there is a trade-off between the reliability of the estimated uncertainty and the accuracy of the deformation. In the optimal trade-off our model excelled in contour propagation and uncertainty estimation (p < 0.01) compared to existing uncertainty estimation models. We obtained an average dice similarity coefficient of 0.89 and a KL-divergence of 0.15.SignificanceBy addressing challenges in DIR uncertainty estimation and evaluation, our work showed that both the DIR and its uncertainty can be reliably predicted paving the way for safe deployment in clinical environment..

The characterization of the subsurface profile properties that are susceptible to liquefaction during earthquakes is of great importance in accident prevention. Field data can be used in a stochastic inverse problem to estimate the material properties using Markov chain Monte Carlo Methods (McMC) that incorporates prior knowledge about the unknown parameters as well as the data available. Here, we numerically study the Random Walk (RW) and Differential Evolution (DE) variations of the Metropolis algorithm in the context of seismic modeling considering the viscoelastic wave equation. The algorithms are tested with data from the 1987 Superstition Hills earthquake recorded at the Wildlife Site. The results show the effectiveness and accuracy of these algorithms, with emphasis to DE which reached convergence earlier compared to RW. [ABSTRACT FROM AUTHOR]

Hydrometric data poverty compounds the challenge of accounting for uncertainties in non-stationary stage–discharge relationships. This paper builds on three methods to explore the integration of a dynamic approach to rating curve assessment and a physically based Bayesian framework for quantifying discharge amid geomorphologically induced rating shifts in a sparsely gauged alluvial river. The Modified GesDyn–FlowAM–BaRatin method entails sequentially segmenting gaugings according to residual indicators of riverbed instability and channel conveyance variability, leveraging cross-sectional surveys to augment calibration data, and eliciting hydraulic priors for probabilistic rating curve estimation. This method is applied to a Philippine watershed, where quarrying near the gauging station has ostensibly caused morphodynamic adjustments. Time-variable credible intervals for discharge are computed. The optimal estimates root mean square error (RMSE = 2.96 m3/s) from maximum a posteriori rating curves outperform the hydrographer's benchmark (RMSE = 5.00 m3/s), whose systematic errors from the gauged flows arise from lapses in shift detection. [ABSTRACT FROM AUTHOR]

This tutorial examines the failure theories of Tresca and von Mises, both of which are crucial for designing metallic structures. Conventionally, Tresca is regarded as more conservative than von Mises from a deterministic perspective. This tutorial, however, introduces a different viewpoint, presenting a scenario where von Mises' theory may appear more conservative when variability in the mechanical system parameters is considered. This often-overlooked aspect is not extensively addressed in standard textbooks on solid mechanics and the strength of materials. The tutorial aims to shed light on the non-negligible probability where von Mises' criterion yields a smaller equivalent stress than Tresca, thus being more conservative. It underscores the importance of integrating probabilistic considerations into stress analyses of solids, offering valuable insights for the education of structural mechanics. [ABSTRACT FROM AUTHOR]

An open problem in diabetes clinical practice is determining where and how much insulin should be administered to a person with diabetes (PwD) and how many carbohydrates they should eat to maintain blood glucose levels at healthy safe levels. Here, we propose the use of a minimal model describing the glucose dynamics of PwD. Using glucose Pwd's data, we calibrate the minimal model considering the uncertainty due to errors in glucose measurement, finding the model parameter values that best reproduce the current glucose levels. Then, all the possible combinations of insulin administration and carbohydrate intake are analysed with the aim of maintaining the glucose at safe levels during the following hours. The resulting procedure is tested with data from two real persons with scenarios of the most typical situations. We expect to apply this procedure in more complex models to help the physicians to give suitable recommendations to PwD. [ABSTRACT FROM AUTHOR]

To enhance the decision-making process and reduce economic losses caused by future flooding, it is critical to quantify uncertainty in each step of flood risk analysis. To address the often-missing uncertainty quantification, we propose a new methodology that combines damage functions and probability bounds analysis. We estimate the likely direct tangible damage to 375,973 residential buildings along the Fraser River through Metro Vancouver, Canada, for a range of climate change driven flood scenarios, while transparently representing the associated uncertainties caused by sampling error, imprecise measurement, and uncertainty in building height and basement conditions. Furthermore, for the purposes of developing effective management strategies, uncertainties in this study are classified into two categories, namely aleatory and epistemic. According to our findings and absent significant action, we should expect an enormous increase in flood damage to the four categories of residential buildings considered in this study by the year 2100. Moreover, the results show that second-order Monte Carlo simulation cannot adequately represent epistemic uncertainty for small sample sizes. In such a case, we recommend employing a probability box to delineate the epistemic uncertainty. [ABSTRACT FROM AUTHOR]

Pulmonary hypertension (PH) is a debilitating disease that alters the structure and function of both the proximal and distal pulmonary vasculature. This alters pressure-flow relationships in the pulmonary arterial and venous trees, though there is a critical knowledge gap in the relationships between proximal and distal hemodynamics in disease. Multiscale computational models enable simulations in both the proximal and distal vasculature. However, model inputs and measured data are inherently uncertain, requiring a full analysis of the sensitivity and uncertainty of the model. Thus, this study quantifies model sensitivity and output uncertainty in a spatially multiscale, pulse-wave propagation model of pulmonary hemodynamics. The model includes fifteen proximal arteries and twelve proximal veins, connected by a two-sided, structured tree model of the distal vasculature. We use polynomial chaos expansions to expedite sensitivity and uncertainty quantification analyses and provide results for both the proximal and distal vasculature. We quantify uncertainty in blood pressure, blood flow rate, wave intensity, wall shear stress, and cyclic stretch. The latter two are important stimuli for endothelial cell mechanotransduction. We conclude that, while nearly all the parameters in our system have some influence on model predictions, the parameters describing the density of the microvascular beds have the largest effects on all simulated quantities in both the proximal and distal arterial and venous circulations. [ABSTRACT FROM AUTHOR]

The timely and accurate identification of incidents, such as human factor error, is important to restore nuclear power plants (NPPs) to a stable state. However, the identification of abnormal operating conditions is difficult because of the existence of multiple scenarios. In addition, to implement mitigation actions rapidly after an incident occurs, operators must accurately identify an incident by monitoring the trends of many variables. The mental burden posed by this can increase human error and cause failure in identifying incidents. Failure to identify incidents directly results in erroneous mitigation measures, which are detrimental to NPPs. In this study, we leverage uncertainty-aware models to identify such errors and thereby increase the chances of mitigating them. We use the data collected from a physical test bed. The goal is to identify both certain and accurate models. For this, the two main aspects of focus in this study are explainable artificial intelligence (XAI) and uncertainty quantification (UQ). While XAI elucidates the decision pathway, UQ evaluates decision reliability. Their integration paints a comprehensive picture, signifying that understanding decisions and their confidence should be interlinked. Thus, in this study we leverage UQ measures (e.g. entropy and mutual information) along with Shapley additive explanations to gain insights into the features contributing to both accuracy and uncertainty in error identification. Our results show that uncertainty-aware models combined with XAI tools can explain the artificial intelligence–prescribed decisions, with the potential of better explaining errors for the operators. [ABSTRACT FROM AUTHOR]

We present a flexible method for computing Bayesian optimal experimental designs (BOEDs) for inverse problems with intractable posteriors. The approach is applicable to a wide range of BOED problems and can accommodate various optimality criteria, prior distributions and noise models. The key to our approach is the construction of a transport-map-based surrogate to the joint probability law of the design, observational and inference random variables. This order-preserving transport map is constructed using tensor trains and can be used to efficiently sample from (and evaluate approximate densities of) conditional distributions that are required in the evaluation of many commonly-used optimality criteria. The algorithm is also extended to sequential data acquisition problems, where experiments can be performed in sequence to update the state of knowledge about the unknown parameters. The sequential BOED problem is made computationally feasible by preconditioning the approximation of the joint density at the current stage using transport maps constructed at previous stages. The flexibility of our approach in finding optimal designs is illustrated with some numerical examples inspired by disease modeling and the reconstruction of subsurface structures in aquifers. [ABSTRACT FROM AUTHOR]

Solid Oxide Fuel Cell (SOFC) integrated with a Gas Turbine (GT) is a highly efficient way to convert chemical energy of hydro carbon fuel into electrical energy. SOFC-GT is a high temperature, high pressure system and features a fuel flexibility, which makes it easier to retrofit into the existing power plants. A lot of research had already taken place to make SOFC-GT more fuel efficient and cost effective as well. SOFC-GT is a complex thermodynamic electro-chemical system that has numerous input variables that affect the overall efficiency of the system. In order to further develop the SOFC-GT technology and future research, clear understanding is required to analyze relationship between the input and output parameters. One way to analyze the input/output relationship over the range of parameter variations is to conduct a probabilistic sensitivity analysis. A probabilistic sensitivity analysis of 19 input variables has been conducted to understand how each variable would affect the net power output and overall efficiency of a SOFC-GT system. [ABSTRACT FROM AUTHOR]

Surrogate modeling is of great practical significance for parametric differential equation systems. In contrast to classical numerical methods, using physics-informed deep learning-based methods to construct simulators for such systems is a promising direction due to its potential to handle high dimensionality, which requires minimizing a loss over a training set of random samples. However, the random samples introduce statistical errors, which may become the dominant errors for the approximation of low-regularity and high-dimensional problems. In this work, we present a deep adaptive sampling method for surrogate modeling of low-regularity parametric differential equations and illustrate the necessity of adaptive sampling for constructing surrogate models. In the parametric setting, the residual loss function can be regarded as an unnormalized probability density function (PDF) of the spatial and parametric variables. In contrast to the non-parametric setting, factorized joint density models can be employed to alleviate the difficulties induced by the parametric space. The PDF is approximated by a deep generative model, from which new samples are generated and added to the training set. Since the new samples match the residual-induced distribution, the refined training set can further reduce the statistical error in the current approximate solution through variance reduction. We demonstrate the effectiveness of the proposed method with a series of numerical experiments, including the physics-informed operator learning problem, the parametric optimal control problem with geometrical parametrization, and the parametric lid-driven 2D cavity flow problem with a continuous range of Reynolds numbers from 100 to 3200. [ABSTRACT FROM AUTHOR]

In the framework of process safety studies, consequence assessment of accidental scenarios is a crucial step affecting the eventual risk profile associated with the facilities under analysis. Conventional models used for consequence assessment are based on integral models, and may not be adequate to cope with the dynamic evolution of accidental scenarios and their three‐dimensional features. On the other hand, consequence assessment models based on computational fluid dynamics (CFD) approaches are promising to cope with complex scenarios and environments, but setting the simulation introduces relevant uncertainties associated with both the input data, assumptions, and with the modelling of physical effects involved. In the present study, uncertainty quantification (UQ) techniques are applied to support advanced safety studies based on CFD simulations of hazardous gas dispersion. Firstly, the accidental scenarios are characterized by defining release scenarios and conditions and quantifying source terms using integral models. At the same time, input meteorological data are gathered. This enables the development of high‐fidelity CFD simulations of gas dispersion based on different input sets and eventually the implementation of UQ techniques. The generalized polynomial chaos (gPC) expansion is employed to obtain hazardous gas concentration based on the variation of wind direction and speed. The present method is applied for the analysis of a real plant featuring a complex layout. The results show the advantages of the present approach by quantifying the influence of meteorological conditions and providing indications for supporting the development of protection systems and emergency measures. [ABSTRACT FROM AUTHOR]

This paper introduces a methodology to build mathematical models based on evidence and data sets, considering data and model uncertainty. We study the evolution of obesity in the population, being obesity a consequence of the transmission of unhealthy lifestyle habits and behavioral patterns influenced by social networks (family, friends, peers, etc.).We propose a three-step methodology. First, we create a synthetic data set based on a previous model with real data. Then, we search for dynamic models based on difference equations that best fit the dynamics described by the dataset and their uncertainty (uncertainty-aware). To do this, we use a dynamic structured grammatical evolution algorithm (an algorithm that builds possible models) on which we have defined a grammar (set of possible expressions that can be part of the model). The definition of appropriate grammar is crucial because it allows us to build models that do not contradict the knowledge of the phenomenon studied. However, the data may suggest introducing new terms that indicate the influence of unknown factors. Finally, from among all the models obtained, we will algorithmically search for a selection of them that best describes the uncertainty of the data. This methodology can be applied to various scenarios with available datasets and a limited understanding of the phenomenon. It aims to generate models that not only achieve precision but also incorporate terms that correspond to identifiable processes, which can be explained within the context of the study problem. [ABSTRACT FROM AUTHOR]

This work presents the use of artificial neural networks (ANNs) with deep evidential regression to model the tensile stress response of a thermoplastic elastomer (TPE) considering uncertainty. Three Gaussian noise scenarios were added to a previous dataset of a TPE to simulate noise in the stress response. The trained ANN models were able to address stress–strain data that were not used for their training or validation, even in the presence of noise. The uncertainty in all tested ANN scenarios comprised, within ± 3 σ , the noisy data of the TPE stress response. The method was extended to other grades of Hytrel material with ANN architectures that obtained results with a coefficient of determination of about 0.9. These results suggest that shallow neural networks, equipped and trained using evidential output layers and an evidential regression loss, can predict, generalize, and simulate noisy tensile stress responses in TPE materials. [ABSTRACT FROM AUTHOR]

We tackle the problem of building a prediction interval in heteroscedastic Gaussian regression. We focus on prediction intervals with constrained expected length in order to guarantee interpretability of the output. In this framework, we derive a closed-form expression of the optimal prediction interval that allows for the development of a data-driven prediction interval based on plug-in. The construction of the proposed algorithm is based on two samples, one labelled and another unlabelled. Under mild conditions, we show that our procedure is asymptotically as good as the optimal prediction interval both in terms of expected length and error rate. In particular, the control of the expected length is distribution-free. We also derive rates of convergence under smoothness and the Tsybakov noise conditions. We conduct a numerical analysis that exhibits the good performance of our method. It also indicates that even with a few amount of unlabelled data, our method is very effective in enforcing the length constraint. [ABSTRACT FROM AUTHOR]

ABSTRACT The COVID‐19 infection fatality rate (IFR) is the proportion of individuals infected with SARS‐CoV‐2 who subsequently die. As COVID‐19 disproportionately affects older individuals, age‐specific IFR estimates are imperative to facilitate comparisons of the impact of COVID‐19 between locations and prioritize distribution of scarce resources. However, there lacks a coherent method to synthesize available data to create estimates of IFR and seroprevalence that vary continuously with age and adequately reflect uncertainties inherent in the underlying data. In this article, we introduce a novel Bayesian hierarchical model to estimate IFR as a continuous function of age that acknowledges heterogeneity in population age structure across locations and accounts for uncertainty in the estimates due to seroprevalence sampling variability and the imperfect serology test assays. Our approach simultaneously models test assay characteristics, serology, and death data, where the serology and death data are often available only for binned age groups. Information is shared across locations through hierarchical modeling to improve estimation of the parameters with limited data. Modeling data from 26 developing country locations during the first year of the COVID‐19 pandemic, we found seroprevalence did not change dramatically with age, and the IFR at age 60 was above the high‐income country estimate for most locations. [ABSTRACT FROM AUTHOR]

Reservoir-level forecasting, while being crucial for optimal operation, is challenged by complex physical processes and changing climate conditions. Machine learning approaches offer deterministic predictions but often neglect system physics and uncertainty. This article presents a probabilistic data-driven approach combining long short-term memory (LSTM) and Gaussian process regression (GPR) to provide both point forecasts and uncertainty estimates. The hybrid model leverages LSTM’s fitting capabilities with GPR’s robust Bayesian frameworks for uncertainty estimation in non-linear problems, offering accurate predictions without extensive high-fidelity modelling, and avoiding frequent training and parameter optimization. Evaluation with real reservoir data from India shows the model’s superiority over the vanilla LSTM for both univariate and multivariate scenarios. The proposed model achieved a Nash-Sutcliffe efficiency of 0.97 to 0.98, a mean biased error of −0.5634 to −1.0314 for 10-day forecasts, and a continuous ranked probability score of 5.80 and 1.87 for the Bhakra and Pong reservoirs, respectively. [ABSTRACT FROM AUTHOR]

The structural integrity of buried pipelines is threatened by the effects of Permanent Ground Deformation (PGD), resulting from seismic-induced landslides and lateral spreading due to liquefaction, requiring accurate analysis of the system performance. Analytical fragility functions allow us to estimate the likelihood of seismic damage along the pipeline, supporting design engineers and network operators in prioritizing resource allocation for mitigative or remedial measures in spatially distributed lifeline systems. To efficiently and accurately evaluate the seismic fragility of a buried operating steel pipeline under longitudinal PGD, this study develops a new analytical model, accounting for the asymmetric pipeline behavior in tension and compression under varying operational loads. This validated model is further implemented within a fragility function calculation framework based on the Monte Carlo Simulation (MCS), allowing us to efficiently assess the probability of the pipeline exceeding the performance limit states, conditioned to the PGD demand. The evaluated fragility surfaces showed that the probability of the pipeline exceeding the performance criteria increases for larger soil displacements and lengths, as well as cover depths, because of the greater mobilized soil reaction counteracting the pipeline deformation. The performed Global Sensitivity Analysis (GSA) highlighted the influence of the PGD and soil–pipeline interaction parameters, as well as the effect of the service loads on structural performance, requiring proper consideration in pipeline system modeling and design. Overall, the proposed analytical fragility function calculation framework provides a useful methodology for effectively assessing the performance of operating pipelines under longitudinal PGD, quantifying the effect of the uncertain parameters impacting system response. [ABSTRACT FROM AUTHOR]

The transient stability control for disturbances in microgrids based on a lithium-ion battery–supercapacitor hybrid energy storage system (HESS) is a challenging problem, which not only involves needing to maintain stability under a dynamic load and changing external conditions but also involves dealing with the energy exchange between the battery and the supercapacitor, the dynamic change of the charging and discharging process and other factors. This paper focuses on the bus voltage control of HESS under load mutations and system uncertainty disturbances. A BP Neural Network-based Active Disturbance Rejection Controller (BP-ADRC) is proposed within the traditional voltage-current dual-loop control framework, leveraging uncertainty quantification. Firstly, system uncertainties are quantified using system-identification tools based on measurable information. Subsequently, an Extended State Observer (ESO) is designed to estimate the total system disturbance based on the quantified information. Thirdly, an adaptive BP Neural Network-based Active Disturbance Rejection Controller is studied to achieve transient stability control of disturbances. Robust controllers, PID controllers and second-order linear Active Disturbance Rejection Controllers are employed as benchmark strategies to design simulation experiments. Simulation results indicate that, compared to other benchmark strategies, the BP-ADRC controller based on uncertainty quantification exhibits superior tracking and disturbance-rejection performance in transient stability control within microgrids of hybrid energy storage systems. [ABSTRACT FROM AUTHOR]

Uncertainty in the evolution of opponent behavior creates a non-stationary environment for the agent, reducing the reliability of value estimation and strategy selection while compromising security during the exploration process. Previous studies have developed various uncertainty quantification techniques and designed uncertainty-aware exploration methods for multi-agent reinforcement learning (MARL). However, existing methods have gaps in theoretical research and experimental verification of decoupling uncertainty between opponents and environment, which can decrease learning efficiency and lead to an unstable training process. Due to inaccurate opponent modeling, the agent is vulnerable to harm from opponents, which is undesirable in real-world tasks. To address these issues, this study proposes a novel uncertainty-guided safe exploration strategy for MARL that decouples the two types of uncertainty originating from the environment and opponents. Specifically, we introduce an uncertainty decoupling quantification technique based on a novel variance decomposition method for action-value functions. Furthermore, we present an uncertainty-aware policy optimization mechanism to facilitate safe exploration in MARL. Finally, we propose a new adaptive parameter scaling method to ensure efficient exploration by the agents. Theoretical analysis establishes the proposed approach's convergence rate, and its effectiveness is demonstrated empirically. Extensive experiments on benchmark tasks spanning differential games, multi-agent particle environments, and RoboSumo validate the proposed uncertainty-guided method's significant advantages in attaining higher scores and facilitating safe agent exploration. [ABSTRACT FROM AUTHOR]

Performing reliability analysis for reinforced concrete structures is a tedious and challenging task because it requires conducting a four-nested loop calculation procedure involving millions of data samples to account for the complex behaviours of the structures and multiple random variables. Therefore, the study proposes a novel, practical, and accurate reliability framework that is applicable for multi-component RC frame structures exhibiting different behaviours ranging from linear elastic and non-linear elastic to non-linear plastic. For this purpose, this study first employs a tree-based boosting ensemble model combined with quantile regression, dubbed as QR-LightGBM to calculate the structures' limit state function and the associated uncertainty estimation at the same time. Next, an active learning process is implemented to improve the computed reliability results progressively. During each active learning step, relevant data samples with potentially high impacts on the model accuracy are determined based on their uncertainty, and then QR-LightGBM is retrained utilizing these samples. By doing so, the prediction performance of the surrogate model is enhanced with a minimized number of actual data samples, thus significantly reducing overall computational resources. The viability and effectiveness of the proposed framework are validated through three case studies involving a simple 1D reinforced concrete beam, a 2D three-story frame, and a 3D five-story building structure. Furthermore, its performance is quantitatively demonstrated via comparison studies with competing methods such as Monte Carlo simulation, Kriging-based models, and an original LightGBM without active learning. [ABSTRACT FROM AUTHOR]

To obtain the posterior distribution of parameters for expensive numerical models with complex dynamic responses that require substantial computational resources, a model updating method utilizing the Wasserstein distance as uncertainty quantification (UQ) metric and variational Bayesian Monte Carlo (VBMC) for parameter posterior identification is proposed. Combined with MATLAB, Nastran and Adams software for secondary development, the traditional finite element model updating technology is extended to the rigid-flexible coupling model. The application results in the composite plate, satellite rigid-flexible model, and solar wing deployment model demonstrate that the updated models exhibit high precision. Compared to existing UQ methods, the Wasserstein distance can more robustly measure the discrepancy between two samples and significantly reduce model structure and parameter uncertainty. The VBMC method converges to the true parameter values after a few number of iterations, and the updating efficiency is markedly higher than that of the random-sampling-based Markov chain Monte Carlo (MCMC) method. [ABSTRACT FROM AUTHOR]

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

Heat transfer in the human eyeball, a complex organ, is significantly influenced by various pathophysiological and external parameters. Particularly, heat transfer critically affects fluid behavior within the eye and ocular drug delivery processes. Overcoming the challenges of experimental analysis, this study introduces a comprehensive three‐dimensional mathematical and computational model to simulate the heat transfer in a realistic geometry. Our work includes an extensive sensitivity analysis to address uncertainties and delineate the impact of different variables on heat distribution in ocular tissues. To manage the model's complexity, we employed a very fast model reduction technique with certified sharp error bounds, ensuring computational efficiency without compromising accuracy. Our results demonstrate remarkable consistency with experimental observations and align closely with existing numerical findings in the literature. Crucially, our findings underscore the significant role of blood flow and environmental conditions, particularly in the eye's internal tissues. Clinically, this model offers a promising tool for examining the temperature‐related effects of various therapeutic interventions on the eye. Such insights are invaluable for optimizing treatment strategies in ophthalmology. [ABSTRACT FROM AUTHOR]

The solution of inverse problems is of fundamental interest in medical and astronomical imaging, geophysics as well as engineering and life sciences. Recent advances were made by using methods from machine learning, in particular deep neural networks. Most of these methods require a huge amount of data and computer capacity to train the networks, which often may not be available. Our paper addresses the issue of learning from small data sets by taking patches of very few images into account. We focus on the combination of model‐based and data‐driven methods by approximating just the image prior, also known as regularizer in the variational model. We review two methodically different approaches, namely optimizing the maximum log‐likelihood of the patch distribution, and penalizing Wasserstein‐like discrepancies of whole empirical patch distributions. From the point of view of Bayesian inverse problems, we show how we can achieve uncertainty quantification by approximating the posterior using Langevin Monte Carlo methods. We demonstrate the power of the methods in computed tomography, image super‐resolution, and inpainting. Indeed, the approach provides also high‐quality results in zero‐shot super‐resolution, where only a low‐resolution image is available. The article is accompanied by a GitHub repository containing implementations of all methods as well as data examples so that the reader can get their own insight into the performance. [ABSTRACT FROM AUTHOR]

In the fused filament fabrication (FFF) additive manufacturing process, a part is manufactured by layer-by-layer deposition of thermoplastic filaments extruded from a nozzle. This process results in microscopic voids that are stochastic in size and randomly distributed in space. Also, the elastic properties of the extruded filaments show variation. These uncertainties in the FFF process and the resulting microstructure cause a variation in the structural response (load–displacement curve) of the final printed part. A multiscale uncertainty propagation framework was developed in this study to examine the effect of microscopic inhomogeneity on the variations in the macroscopic structural behavior. Experimental data was used to quantify uncertainty at the micro-scale, while Monte Carlo simulation was used to quantify uncertainty at the meso- and macroscales. A hook model was considered as a case study for uncertainty propagation in the FFF process. [ABSTRACT FROM AUTHOR]

Traffic flow uncertainty quantification is important for making reliable decisions in transportation operations. Compared with well-studied level prediction or point prediction models, the study of uncertainty quantification that can capture the second-order fluctuations of traffic observations is still in its infancy. Current traffic flow uncertainty quantification approaches can be classified in general into distribution- or nondistribution-based. For the former, generalized autoregressive conditional heteroscedasticity (GARCH) model and stochastic volatility (SV) have been widely applied to quantify traffic flow uncertainty in terms of prediction interval, usually under a parametric Gaussian distribution assumption. However, a parametric model relies on a prespecified model structure and cannot meet the requirement raised by the time-varying traffic condition patterns. Therefore, this paper proposed a real-time traffic condition uncertainty quantification approach based on a nonparametric probability density function (PDF) estimation. For this approach, the real-time nonparametric kernel density estimation method is applied to capture the time-varying probability density of traffic flow data based on which prediction intervals are constructed in real time using the quantiles computed from the estimated time-varying nonparametric PDF. Real-world traffic flow data are applied to validate the proposed approach. The results show that the proposed approach outperforms the comparative models of an online GARCH filter and three lower and upper bound estimation (LUBE) models based on multilayer perceptron (MLP), spiking neural network (SNN), and long short-term memory networks (LSTM). The findings indicate that the quantification of traffic condition uncertainty is complementary to the conventional traffic condition level modeling, and combined, traffic level modeling and traffic uncertainty quantification can support the development of proactive and reliable transportation applications. [ABSTRACT FROM AUTHOR]

This study addresses the estimation of material properties at a mesoscopic level using the PuMA software from an uncertainty quantification perspective. Stochastic simulation with PuMA is primarily related to the random distribution of fibers, which is an intrinsic source of uncertainty. Additionally, the selection of certain physical parameters, such as the fiber's thermal conductivity, introduces further uncertainties. The first contribution of this study is to propose a low-cost surrogate-based methodology with an unequal allocation scheme, applied for the first time to the stochastic mesoscale characterization of ablative materials. The second contribution is a study on uncertainty propagation and sensitivity analysis of material properties, providing a systematic assessment of the choice of voxel resolution for both the fibers and the domain. Specifically, the convergence of quantities of interest can be monitored, thus identifying the minimal reference elementary volume. • Building surrogate to compute statistics of material properties of a stochastic solver. • First-ever assessment of material properties at mesoscopic level using PuMA under Uncertainty Quantification. • Assessment of the choice of the voxel resolution surveying convergence, identifying minimal reference elementary volume. • Thermal conductivity variance explained by uncertainty on porosity for in-plane conductivity. [ABSTRACT FROM AUTHOR]

Streambed grain sizes control river hydro‐biogeochemical (HBGC) processes and functions. However, measuring their quantities, distributions, and uncertainties is challenging due to the diversity and heterogeneity of natural streams. This work presents a photo‐driven, artificial intelligence (AI)‐enabled, and theory‐based workflow for extracting the quantities, distributions, and uncertainties of streambed grain sizes from photos. Specifically, we first trained You Only Look Once, an object detection AI, using 11,977 grain labels from 36 photos collected from nine different stream environments. We demonstrated its accuracy with a coefficient of determination of 0.98, a Nash–Sutcliffe efficiency of 0.98, and a mean absolute relative error of 6.65% in predicting the median grain size of 20 ground‐truth photos representing nine typical stream environments. The AI is then used to extract the grain size distributions and determine their characteristic grain sizes, including the 10th, 50th, 60th, and 84th percentiles, for 1,999 photos taken at 66 sites within a watershed in the Northwest US. The results indicate that the 10th, median, 60th, and 84th percentiles of the grain sizes follow log‐normal distributions, with most likely values of 2.49, 6.62, 7.68, and 10.78 cm, respectively. The average uncertainties associated with these values are 9.70%, 7.33%, 9.27%, and 11.11%, respectively. These data allow for the computation of the quantities, distributions, and uncertainties of streambed HBGC parameters, including Manning's coefficient, Darcy‐Weisbach friction factor, top layer interstitial velocity magnitude, and nitrate uptake velocity. Additionally, major sources of uncertainty in grain sizes and their impact on HBGC parameters are examined. Plain Language Summary: Streambed grain sizes control river hydro‐biogeochemical function by modulating the resistance, speed of water exchange, and nutrient transport at water‐sediment interface. Consequently, quantifying grain sizes and size‐dependent hydro‐biogeochemical parameters is critical for predicting river's function. In natural streams, measuring these sizes and parameters, however, is challenging because grain sizes vary from millimeters to a few meters, change from small creeks to big streams, and could be concealed by complex non‐grain materials such as water, ice, mud, and grasses. All these factors make the size measurements a time‐consuming and high‐uncertain task. We address these challenges by demonstrating a workflow that combines computer vision artificial intelligence (AI), smartphone photos, and new uncertainty quantification theories. The AI performs well across various sizes, locations, and stream environments as indicated by an accuracy metric of 0.98. We apply the AI to extract the grain sizes and their characteristic percentiles for 1,999 photos. These characteristic grain sizes are then input into existing and our new theories to derive the quantities, distributions, and uncertainties of hydrobiogeochemical parameters. The high accuracy of the AI and the success of extracting grain sizes and hydro‐biogeochemical parameters demonstrate the potential to advance river science with computer vision AI and mobile devices. Key Points: Stream sediments bigger than 44 microns can be detected from smartphone photos by You Only Look Once with a Nash–Sutcliffe efficiency of 0.98Quantities, distributions, and uncertainties of streambed grain sizes can be determined from photosImpact of grain size uncertainty on hydrobiogeochemical parameters is examined [ABSTRACT FROM AUTHOR]