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Deep neural networks (DNNs) are prominent in predictive analytics for accurately forecasting target variables. However, inherent uncertainties necessitate constructing prediction intervals for reliability. The existing literature often lacks practical methodologies for creating predictive intervals, especially for time series with trends and seasonal patterns. This paper explicitly details a practical approach integrating dual-output Monte Carlo Dropout (MCDO) with DNNs to approximate predictive means and variances within a Bayesian framework, enabling forecast interval construction. The dual-output architecture employs a custom loss function, combining mean squared error with Softplus-derived predictive variance, ensuring non-negative variance values. Hyperparameter optimization is performed through a grid search exploring activation functions, dropout rates, epochs, and batch sizes. Empirical distributions of predictive means and variances from the MCDO demonstrate the results of the dual-output MCDO DNNs. The proposed method achieves a significant improvement in forecast accuracy, with an RMSE reduction of about 10% compared to the seasonal autoregressive integrated moving average model. Additionally, the method provides more reliable forecast intervals, as evidenced by a higher coverage proportion and narrower interval widths. A case study on Thailand's durian export data showcases the method's utility and applicability to other datasets with trends and/or seasonal components. [ABSTRACT FROM AUTHOR]

Autism Spectrum Disorder (ASD) is a chronic condition characterised by impairments in social interaction and communication. Early detection of ASD is desired, and there exists a demand for the development of diagnostic aids to facilitate this. A lightweight Involutional Neural Network (INN) architecture has been developed to diagnose ASD. The model follows a simpler architectural design and has less number of parameters than the state‐of‐the‐art (SOTA) image classification models, requiring lower computational resources. The proposed model is trained to detect ASD from eye‐tracking scanpath (SP), heatmap (HM), and fixation map (FM) images. Monte Carlo Dropout has been applied to the model to perform an uncertainty analysis and ensure the effectiveness of the output provided by the proposed INN model. The model has been trained and evaluated using two publicly accessible datasets. From the experiment, it is seen that the model has achieved 98.12% accuracy, 96.83% accuracy, and 97.61% accuracy on SP, FM, and HM, respectively, which outperforms the current SOTA image classification models and other existing works conducted on this topic. [ABSTRACT FROM AUTHOR]

Deep neural networks (DNNs) are prominent in predictive analytics for accurately forecasting target variables. However, inherent uncertainties necessitate constructing prediction intervals for reliability. The existing literature often lacks practical methodologies for creating predictive intervals, especially for time series with trends and seasonal patterns. This paper explicitly details a practical approach integrating dual-output Monte Carlo Dropout (MCDO) with DNNs to approximate predictive means and variances within a Bayesian framework, enabling forecast interval construction. The dual-output architecture employs a custom loss function, combining mean squared error with Softplus-derived predictive variance, ensuring non-negative variance values. Hyperparameter optimization is performed through a grid search exploring activation functions, dropout rates, epochs, and batch sizes. Empirical distributions of predictive means and variances from the MCDO demonstrate the results of the dual-output MCDO DNNs. The proposed method achieves a significant improvement in forecast accuracy, with an RMSE reduction of about 10% compared to the seasonal autoregressive integrated moving average model. Additionally, the method provides more reliable forecast intervals, as evidenced by a higher coverage proportion and narrower interval widths. A case study on Thailand’s durian export data showcases the method’s utility and applicability to other datasets with trends and/or seasonal components.

Abstract Autism Spectrum Disorder (ASD) is a chronic condition characterised by impairments in social interaction and communication. Early detection of ASD is desired, and there exists a demand for the development of diagnostic aids to facilitate this. A lightweight Involutional Neural Network (INN) architecture has been developed to diagnose ASD. The model follows a simpler architectural design and has less number of parameters than the state‐of‐the‐art (SOTA) image classification models, requiring lower computational resources. The proposed model is trained to detect ASD from eye‐tracking scanpath (SP), heatmap (HM), and fixation map (FM) images. Monte Carlo Dropout has been applied to the model to perform an uncertainty analysis and ensure the effectiveness of the output provided by the proposed INN model. The model has been trained and evaluated using two publicly accessible datasets. From the experiment, it is seen that the model has achieved 98.12% accuracy, 96.83% accuracy, and 97.61% accuracy on SP, FM, and HM, respectively, which outperforms the current SOTA image classification models and other existing works conducted on this topic.

Utility companies lose approximately 35 liters of water for every 100 produced due to incorrect, illegal connections and the poor condition of pipes. This study develops an intelligent model to detect leaks using the Kalman filter, BiLSTM neural networks, and the Monte Carlo Dropout algorithm. Using data from the Empresa de Acueductos y Alcantarillados de Bogotá (EAAB), Colombia, autocorrelation analysis, PCA, cluster analysis, ADF and Durbin-Watson tests, Hurst exponent, spectral analysis, and wavelet transform were performed. Then, Kalman filtering techniques were applied, and a BiLSTM architecture controlled with Monte Carlo dropout was implemented. The results showed an accuracy of 87.48% in training and 80.48% in validation. Temporal analysis revealed a stationary behavior in the flow series, and the decrease in spectral intensity around 0.25 Hz was related to pressure perturbations caused by leaks. A detailed evaluation of pressure and flow signals identified leak patterns with high precision, demonstrating the effectiveness of the wavelet spectrogram in detecting energy disturbances. The novelty of the study lies in the integration of advanced artificial intelligence and combinatorial optimization techniques to improve water resource management, allowing early and accurate detection of leaks, significantly improving compared to traditional methods. [ABSTRACT FROM AUTHOR]

Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical models in prediction accuracy, statistical inference, such as estimating the effects of covariates and quantifying the prediction uncertainty, is not trivial due to the highly complicated model structure and overparameterization. To address this challenge, we propose a new Bayesian approach by embedding CNNs within the generalized linear models (GLMs) framework. We use extracted nodes from the last hidden layer of CNN with Monte Carlo (MC) dropout as informative covariates in GLM. This improves accuracy in prediction and regression coefficient inference, allowing for the interpretation of coefficients and uncertainty quantification. By fitting ensemble GLMs across multiple realizations from MC dropout, we can account for uncertainties in extracting the features. We apply our methods to biological and epidemiological problems, which have both high-dimensional correlated inputs and vector covariates. Specifically, we consider malaria incidence data, brain tumor image data, and fMRI data. By extracting information from correlated inputs, the proposed method can provide an interpretable Bayesian analysis. The algorithm can be broadly applicable to image regressions or correlated data analysis by enabling accurate Bayesian inference quickly. [ABSTRACT FROM AUTHOR]

This paper investigates uncertainty quantification (UQ) techniques in multi-class classification of chest X-ray images (COVID-19, Pneumonia, and Normal). We evaluate Bayesian Neural Networks (BNN) and the Deep Neural Network with UQ (DNN with UQ) techniques, including Monte Carlo dropout, Ensemble Bayesian Neural Network (EBNN), Ensemble Monte Carlo (EMC) dropout, across different evaluation metrics. Our analysis reveals that DNN with UQ, especially EBNN and EMC dropout, consistently outperform BNNs. For example, in Class 0 vs. All, EBNN achieved a UAcc of 92.6%, UAUC-ROC of 95.0%, and a Brier Score of 0.157, significantly surpassing BNN's performance. Similarly, EMC Dropout excelled in Class 1 vs. All with a UAcc of 83.5%, UAUC-ROC of 95.8%, and a Brier Score of 0.165. These advanced models demonstrated higher accuracy, better discriaminative capability, and more accurate probabilistic predictions. Our findings highlight the efficacy of DNN with UQ in enhancing model reliability and interpretability, making them highly suitable for critical healthcare applications like chest X-ray imageQ6 classification.

Plant phenology is the study of cyclical events in a plant life cycle such as leaf bud burst, flowering, and fruiting. In this article the problem of olive phenology prediction is addressed through the use of Deep Learning. Although Neural Networks have already been used in this area, to the best of our knowledge, this is the first implementation of Probabilistic Bayesian Neural Networks for olive phenology prediction. This architecture gives particular emphasis to estimating the model uncertainty, both aleatoric and epistemic. The Bayesian Inference method, more precisely the Variational Inference one, is compared with the Monte Carlo Dropout technique, which is known to be a less computationally intensive approximation of Variational Inference. For validation purposes, models performance is compared to the state-of-the-art results.

This study aims to enhance diagnostic capabilities for optimising the performance of the anaerobic sewage treatment lagoon at Melbourne Water's Western Treatment Plant (WTP) through a novel machine learning (ML)-based monitoring strategy. This strategy employs ML to make accurate probabilistic predictions of biogas performance by leveraging diverse real-life operational and inspection sensor and other measurement data for asset management, decision making, and structural health monitoring (SHM). The paper commences with data analysis and preprocessing of complex irregular datasets to facilitate efficient learning in an artificial neural network. Subsequently, a Bayesian mixture density neural network model incorporating an attention-based mechanism in bidirectional long short-term memory (BiLSTM) was developed. This probabilistic approach uses a distribution output layer based on the Gaussian mixture model and Monte Carlo (MC) dropout technique in estimating data and model uncertainties, respectively. Furthermore, systematic hyperparameter optimisation revealed that the optimised model achieved a negative log-likelihood (NLL) of 0.074, significantly outperforming other configurations. It achieved an accuracy approximately 9 times greater than the average model performance (NLL = 0.753) and 22 times greater than the worst performing model (NLL = 1.677). Key factors influencing the model's accuracy, such as the input window size and the number of hidden units in the BiLSTM layer, were identified, while the number of neurons in the fully connected layer was found to have no significant impact on accuracy. Moreover, model calibration using the expected calibration error was performed to correct the model's predictive uncertainty. The findings suggest that the inherent data significantly contribute to the overall uncertainty of the model, highlighting the need for more high-quality data to enhance learning. This study lays the groundwork for applying ML in transforming high-value assets into intelligent structures and has broader implications for ML in asset management, SHM applications, and renewable energy sectors. [ABSTRACT FROM AUTHOR]

Karst springs are essential drinking water resources, however, modeling them poses challenges due to complex subsurface flow processes. Deep learning models can capture complex relationships due to their ability to learn non‐linear patterns. This study evaluates the performance of the Transformer in forecasting spring discharges for up to 4 days. We compare it to the Long Short‐Term Memory (LSTM) Neural Network and a common baseline model on a well‐studied Austrian karst spring (LKAS2) with an extensive hourly database. We evaluated the models for two further karst springs with diverse discharge characteristics for comparing the performances based on four metrics. In the discharge‐based scenario, the Transformer performed significantly better than the LSTM for the spring with the longest response times (9% mean difference across metrics), while it performed poorer for the spring with the shortest response time (4% difference). Moreover, the Transformer better predicted the shape of the discharge during snowmelt. Both models performed well across all lead times and springs with 0.64–0.92 for the Nash–Sutcliffe efficiency and 10.8%–28.7% for the symmetric mean absolute percentage error for the LKAS2 spring. The temporal information, rainfall and electrical conductivity were the controlling input variables for the non‐discharge based scenario. The uncertainty analysis revealed that the prediction intervals are smallest in winter and autumn and highest during snowmelt. Our results thus suggest that the Transformer is a promising model to support the drinking water abstraction management, and can have advantages due to its attention mechanism particularly for longer response times. Key Points: The Transformer architecture was applied in karst hydrology for the first time, showing high performance for discharge forecastingMonte Carlo dropout revealed that the prediction intervals are smallest and cover the measured discharges best in winter and autumnThe high temporal resolution of the input data sets improved the forecasting performance [ABSTRACT FROM AUTHOR]

AbstractReactivity measurement methods, like the Amplified Source Method (ASM), link observable quantities to integral physics parameters characterizing subcritical assemblies (SCAs). These methods were mostly derived from point reactor kinetics, which assumes fundamental mode distribution. However, in SCAs, external sources cannot be neglected, leading to a nonideal response, such as the detector position dependence of measured $${k_{eff}}$$keff.This work investigates deterministic and probabilistic deep learning (DL) in determining $${k_{eff}}$$keff and kinetics/subcritical parameters using core map and foil/active detector responses as inputs, which distinguishes DL from neutronics codes. Convolutional neural networks surpassed dense neural networks with higher accuracy, while assigning a strong signature to appropriate core map features. Expansion into multi-input networks, which also process reaction rates, highlighted DL’s flexibility by accurate prediction regardless of reaction type.Uncertainty quantification of DL was done using Monte Carlo (MC) Dropout and Bayesian neural network (BNN). The results favored BNN over MC Dropout, showing greater improvement with increasing data. An assessment of ASM, applicable in a SCA at source equilibrium, showed a reactivity bias of up to −3.59%Δk/k (−4.86 $). In contrast, DL had a maximum bias of only 0.38%Δk/k (0.5 $). Underestimation by ASM represents a nonconservative scenario in criticality safety, while DL proved robust against spatial effects. This demonstrates DL’s potential in ensuring reactivity margins and a safe approach to criticality in reactor operation regimes where standard techniques can fail. [ABSTRACT FROM AUTHOR]

With the recent advancements in machine learning technology, the accuracy of autonomous driving object detection models has significantly improved. However, due to the complexity and variability of real-world traffic scenarios, such as extreme weather conditions, unconventional lighting, and unknown traffic participants, there is inherent uncertainty in autonomous driving object detection models, which may affect the planning and control in autonomous driving. Thus, the rapid and accurate quantification of this uncertainty is crucial. It contributes to a better understanding of the intentions of autonomous vehicles and strengthens trust in autonomous driving technology. This research pioneers in quantifying uncertainty in the YOLOv5 object detection model, thereby improving the accuracy and speed of probabilistic object detection, and addressing the real-time operational constraints of current models in autonomous driving contexts. Specifically, a novel probabilistic object detection model named M-YOLOv5 is proposed, which employs the MC-drop method to capture discrepancies between detection results and the real world. These discrepancies are then converted into Gaussian parameters for class scores and predicted bounding box coordinates to quantify uncertainty. Moreover, due to the limitations of the Mean Average Precision (MAP) evaluation metric, we introduce a new measure, Probability-based Detection Quality (PDQ), which is incorporated as a component of the loss function. This metric simultaneously assesses the quality of label uncertainty and positional uncertainty. Experiments demonstrate that compared to the original YOLOv5 algorithm, the M-YOLOv5 algorithm shows a 74.7% improvement in PDQ. When compared with the most advanced probabilistic object detection models targeting the MS COCO dataset, M-YOLOv5 achieves a 14% increase in MAP, a 17% increase in PDQ, and a 65% improvement in FPS. Furthermore, against the state-of-the-art probabilistic object detection models for the BDD100K dataset, M-YOLOv5 exhibits a 31.67% enhancement in MAP and a 125.6% increase in FPS.

Gas turbines are thermoelectric plants with various applications, such as large-scale electricity production, petrochemical industry, and steam generation. In order to optimize the operation of a gas turbine, it is necessary to develop system identification models that allow for the development of studies and analyses to increase the system's reliability. Current strategies for modeling complex and non-linear systems can be based on artificial intelligence techniques, using autoregressive neural networks of the NARX and LSTM type. In this context, this work aims to develop a model of a gas turbine capable of estimating the rotation speed of the turbine and simultaneously estimating the uncertainty associated with the estimation. These methodologies are based on artificial neural networks and the Monte Carlo dropout simulation method. The results were obtained from experimental data from a 215 MW gas turbine, getting the best model with a MAPE of 0.02% and an uncertainty associated with the turbine rotation speed of 2.2 RPM. [ABSTRACT FROM AUTHOR]

Gas turbines are thermoelectric plants with various applications, such as large-scale electricity production, petrochemical industry, and steam generation. In order to optimize the operation of a gas turbine, it is necessary to develop system identification models that allow for the development of studies and analyses to increase the system’s reliability. Current strategies for modeling complex and non-linear systems can be based on artificial intelligence techniques, using autoregressive neural networks of the NARX and LSTM type. In this context, this work aims to develop a model of a gas turbine capable of estimating the rotation speed of the turbine and simultaneously estimating the uncertainty associated with the estimation. These methodologies are based on artificial neural networks and the Monte Carlo dropout simulation method. The results were obtained from experimental data from a 215 MW gas turbine, getting the best model with a MAPE of 0.02% and an uncertainty associated with the turbine rotation speed of 2.2 RPM.

The goal of this work is to develop accurate Machine Learning (ML) models for predicting the assembly axial neutron flux profiles in the SAFARI-1 research reactor, trained by measurement data from historical cycles. Affinity Propagation and k-means algorithms are used to identify clusters in the set of measured axial neutron flux profiles. Pair-counting-based and information-theoretic measures are applied to compare the clusterings. Deep Neural Network (DNN) and Gaussian Process (GP) ML models are then trained for different clusters, with prediction uncertainties quantified with the Monte Carlo Dropout. The proposed procedure improves the prediction accuracy for the control assemblies and reduces the prediction uncertainty, with axial flux shapes predicted by DNN and GP being very close and the overall accuracy becoming comparable to the fuel assemblies. • Machine Learning models for predicting the axial neutron flux profile are developed. • Models are trained with measured data from historical cycles of SAFARI-1 reactor. • Clustering algorithms are used to identify flux shape clusters in the dataset. • DNN and GP model are trained for each cluster and prediction uncertainty quantified. • The proposed procedure improves the prediction accuracy and reduces the uncertainty. [ABSTRACT FROM AUTHOR]

Plant phenology is the study of cyclical events in a plant life cycle such as leaf bud burst, flowering, and fruiting. In this article the problem of olive phenology prediction is addressed through the use of Deep Learning. Although Neural Networks have already been used in this area, to the best of our knowledge, this is the first implementation of Probabilistic Bayesian Neural Networks for olive phenology prediction. This architecture gives particular emphasis to estimating the model uncertainty, both aleatoric and epistemic. The Bayesian Inference method, more precisely the Variational Inference one, is compared with the Monte Carlo Dropout technique, which is known to be a less computationally intensive approximation of Variational Inference. For validation purposes, models performance is compared to the state-of-the-art results. • Novel approach to ML-based olive phenology modeling. • Model uncertainty estimation using Bayesian theory within a Deep Learning framework. • Comparison between Variational Inference and Monte Carlo Dropout implementations. • Proven usefulness of the target feature re-labeling during the training phase. • Competitive results with state-of-the-art models. [ABSTRACT FROM AUTHOR]

This paper investigates uncertainty quantification (UQ) techniques in multi-class classification of chest X-ray images (COVID-19, Pneumonia, and Normal). We evaluate Bayesian Neural Networks (BNN) and the Deep Neural Network with UQ (DNN with UQ) techniques, including Monte Carlo dropout, Ensemble Bayesian Neural Network (EBNN), Ensemble Monte Carlo (EMC) dropout, across different evaluation metrics. Our analysis reveals that DNN with UQ, especially EBNN and EMC dropout, consistently outperform BNNs. For example, in Class 0 vs. All, EBNN achieved a U Acc of 92.6%, U AUC-ROC of 95.0%, and a Brier Score of 0.157, significantly surpassing BNN's performance. Similarly, EMC Dropout excelled in Class 1 vs. All with a U Acc of 83.5%, U AUC-ROC of 95.8%, and a Brier Score of 0.165. These advanced models demonstrated higher accuracy, better discriaminative capability, and more accurate probabilistic predictions. Our findings highlight the efficacy of DNN with UQ in enhancing model reliability and interpretability, making them highly suitable for critical healthcare applications like chest X-ray imageQ6 classification., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Whata, Dibeco, Madzima and Obagbuwa.)

Objective . Prior to radiation therapy planning, accurate delineation of gross tumour volume (GTVs) and organs at risk (OARs) is crucial. In the current clinical practice, tumour delineation is performed manually by radiation oncologists, which is time-consuming and prone to large inter-observer variability. With the advent of deep learning (DL) models, automated contouring has become possible, speeding up procedures and assisting clinicians. However, these tools are currently used in the clinic mostly for contouring OARs, since these systems are not reliable yet for contouring GTVs. To improve the reliability of these systems, researchers have started exploring the topic of probabilistic neural networks. However, there is still limited knowledge of the practical implementation of such networks in real clinical settings. Approach . In this work, we developed a 3D probabilistic system that generates DL-based uncertainty maps for lung cancer CT segmentations. We employed the Monte Carlo (MC) dropout technique to generate probabilistic and uncertainty maps, while the model calibration was evaluated by using reliability diagrams. A clinical validation was conducted in collaboration with a radiation oncologist to qualitatively assess the value of the uncertainty estimates. We also proposed two novel metrics, namely mean uncertainty (MU) and relative uncertainty volume (RUV), as potential indicators for clinicians to assess the need for independent visual checks of the DL-based segmentation . Main results . Our study showed that uncertainty mapping effectively identified cases of under or over-contouring. Although the overconfidence of the model, a strong correlation was observed between the clinical opinion and MU metric. Moreover, both MU and RUV revealed high AUC values in discretising between low and high uncertainty cases. Significance . Our study is one of the first attempts to clinically validate uncertainty estimates in DL-based contouring. The two proposed metrics exhibited promising potential as indicators for clinicians to independently assess the quality of tumour delineation., (© 2024 Institute of Physics and Engineering in Medicine.)