Bayesian Neural Network Model Research Articles

From drought hazard to risk: A spring wheat vulnerability assessment in the Canadian Prairies

The Canadian drought monitor (CDM) provides monthly assessments of drought severity but does not provide guidance on the potential agricultural impacts. This study extends the CDM to a comprehensive risk assessment framework by assessing the vulnerability of spring wheat to drought timing and severity in the Canadian Prairies. To achieve this, a bayesian neural network (BNN) model was developed that predicts high-resolution wheat yields and uncertainties using the CDM and normalized difference vegetation index (NDVI) data from 2010 to 2021. Model performance is comparable to previous studies, with errors ranging from 13% to 18% of mean yields and R2 values from 0.43 to 0.70 that peak in early August. The model was then applied under various drought conditions to evaluate how different drought timings and severities affect yield vulnerability. The results demonstrate that drought exposure from June to August reduces wheat yields in proportion to drought severity while abnormally dry conditions may have a positive impact of yield, particularly in August. Yield uncertainty decreases substantially from June to July while yield prediction accuracy increases, suggesting that mitigation efforts are most effective prior to July. The final component of the research involved creating operational risk maps that integrate the yield vulnerability assessment with the CDM. These maps were applied in a case study to demonstrate their utility in providing actionable, real-time information for agricultural stakeholders. Overall, this study contributes to the body of knowledge regarding crop sensitivities to varying drought conditions and represents a methodological advancement by enabling high-resolution, operational agricultural risk assessments at scale. By integrating detailed vulnerability data with drought hazard monitoring from the CDM, the information provided by these risk maps can be leveraged by agricultural stakeholders in near real-time to make well-informed decisions that mitigate the impacts of drought on wheat production, enhancing the resilience of agricultural systems to climatic variability.

Liquid droplet entrainment in an annular flow boiling regime—A Bayesian regularization algorithm based study

Accurate prediction of the entrained liquid droplet fraction in an annular two-phase flow regime plays a crucial role for estimating the dryout type critical heat flux to identify the optimized flow characteristics in the thermal systems across different industries. Existing studies have provided different correlations based on the limited experimental data. However, these correlations are applicable to certain operating conditions. Therefore, the present study aims at applying a deep learning method, specifically an artificial neural network (ANN), to enhance the prediction of the entrained liquid droplet fraction. Experimental data from various works on annular flow, covering a wide spectrum of pressure and flow conditions, are utilized for training the ANN model. Eight input variables, viz, superficial gas velocity (JSG), superficial liquid velocity (JSL), gas viscosity (μG), liquid viscosity (μL), gas density (ρG), liquid density (ρL), pipe diameter (d) and liquid surface tension (σLV) are considered as input features. The entrained liquid droplet fraction is the single output feature. The present model employs the Bayesian regularization backpropagation algorithm for training. The present ANN model is compared against the performance of linear regression, decision tree and support vector machine algorithms, and found that the performance of the present Bayesian regularization neural network (BRNN) model is superior within ∼7.5% deviation. Further, the BRNN model is coupled with the film mass flow rate model to obtain the axial variation of the liquid film mass flow rate and good agreement is noticed when compared against the experimental data.

Loss-Based Variational Bayes Prediction

We propose a new approach to Bayesian prediction that caters for models with a large number of parameters and is robust to model misspecification. Given a class of high-dimensional (but parametric) predictive models, this new approach constructs a posterior predictive using a variational approximation to a generalized posterior that is directly focused on predictive accuracy. The theoretical behavior of the new prediction approach is analyzed and a form of optimality demonstrated. Applications to both simulated and empirical data using high-dimensional Bayesian neural network and autoregressive mixture models demonstrate that the approach provides more accurate results than various alternatives, including misspecified likelihood-based predictions.

Optimisation and Calibration of Bayesian Neural Network for Probabilistic Prediction of Biogas Performance in an Anaerobic Lagoon.

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.

Probabilistic Reach-Avoid for Bayesian Neural Networks

Model-based reinforcement learning seeks to simultaneously learn the dynamics of an unknown stochastic environment and synthesise an optimal policy for acting in it. Ensuring the safety and robustness of sequential decisions made through a policy in such an environment is a key challenge for policies intended for safety-critical scenarios. In this work, we investigate two complementary problems: first, computing reach-avoid probabilities for iterative predictions made with dynamical models, with dynamics described by Bayesian neural network (BNN); second, synthesising control policies that are optimal with respect to a given reach-avoid specification (reaching a “target” state, while avoiding a set of “unsafe” states) and a learned BNN model. Our solution leverages interval propagation and backward recursion techniques to compute lower bounds for the probability that a policy's sequence of actions leads to satisfying the reach-avoid specification. Such computed lower bounds provide safety certification for the given policy and BNN model. We then introduce control synthesis algorithms to derive policies maximizing said lower bounds on the safety probability. We demonstrate the effectiveness of our method on a series of control benchmarks characterized by learned BNN dynamics models. On our most challenging benchmark, compared to purely data-driven policies the optimal synthesis algorithm is able to provide more than a four-fold increase in the number of certifiable states and more than a three-fold increase in the average guaranteed reach-avoid probability.

Application of Response Surface-Corrected Finite Element Model and Bayesian Neural Networks to Predict the Dynamic Response of Forth Road Bridges under Strong Winds.

With the rapid development of big data, the Internet of Things (IoT), and other technological advancements, digital twin (DT) technology is increasingly being applied to the field of bridge structural health monitoring. Achieving the precise implementation of DT relies significantly on a dual-drive approach, combining the influence of both physical model-driven and data-driven methodologies. In this paper, two methods are proposed to predict the displacement and dynamic response of structures under strong winds, namely, a Bayesian Neural Network (BNN) model based on Bayesian inference and a finite element model (FEM) method modified based on genetic algorithms (GAs) and multi-objective optimization (MOO) using response surface methodology (RSM). The characteristics of these approaches in predicting the dynamic response of large-span bridges are explored, and a comparative analysis is conducted to evaluate their differences in computational accuracy, efficiency, model complexity, interpretability, and comprehensiveness. The characteristics of the two methods were evaluated using data collected on the Forth Road Bridge (FRB) as an example under unusual weather conditions with strong wind action. This work proposes a dual-driven approach, integrating machine learning and FEM with GNSS and Earth Observation for Structural Health Monitoring (GeoSHM), to bridge the gap in the limited application of dual-driven methods primarily applied for small- and medium-sized bridges to large-span bridge structures. The research results show that the BNN model achieved higher R2 values for predicting the Y and Z displacements (0.9073 and 0.7969, respectively) compared to the FEM model (0.6167 and 0.6283). The BNN model exhibited significantly faster computation, taking only 20 s, while the FEM model required 5 h. However, the physical model provided higher interpretability and the ability to predict the dynamic response of the entire structure. These findings help to promote the further integration of these two approaches to obtain an accurate and comprehensive dual-driven approach for predicting the structural dynamic response of large-span bridge structures affected by strong wind loading.

Integrating Dropout and Kullback-Leibler Regularization in Bayesian Neural Networks for improved uncertainty estimation in Regression

The objective of the study is to enhance uncertainty prediction in regression problems by introducing a revolutionary Bayesian Neural Network (BNN) model. Experimental results reveal significant improvements in uncertainty prediction and point forecasts with the integrated BNN model compared to the plain BNN. Performance metrics, including mean squared error (MSE), mean absolute error (MAE), and R-squared (R²), demonstrate superior results for the proposed BNN. The experimental results show that for plain BNN, MSE is 87.3, MAE is 6.62 and R2 is −0.0492, whereas for the proposed BNN model MSE was found to be 44.64, MAE is 4.4 and R2 is 0.46. This research brings a fresh approach to Bayesian Neural Networks by incorporating both dropout and KL regularization techniques, resulting in a powerful tool for handling regression tasks with certainty. By combining these techniques, the study enhances model stability, avoids overfitting, and achieves more reliable uncertainty estimation. This study adds to our knowledge of uncertainty-aware machine learning models and offers a valuable solution for accurately assessing uncertainty in various applications.•The innovative BNN model merges the power of Bayesian principles with the effectiveness of dropout and KL regularization.•To test and refine our model, the study utilizes the Boston Housing dataset for both training and evaluation purposes.

Uncertainty quantification in multiaxial fatigue life prediction using Bayesian neural networks

In practical engineering scenarios, unforeseen failures may result in significant costs and risks. Assessing the uncertainty related to multiaxial fatigue life prediction is crucial for engineering applications. However, establishing a reliable multiaxial fatigue life prediction model remains challenging due to uncertainties in physical models, material properties, and measurement data. This paper proposes an effective Bayesian Neural Network (BNN) model for quantifying the uncertainty in multiaxial fatigue life prediction. Fatigue parameters in the multiaxial fatigue life prediction model are used as inputs for the BNN. The BNN method utilizes No-U-turn Sampler (NUTS) and Automatic Differentiation Variational Inference (ADVI) to address the inference problem in the model and perform life predictions for unknown non-proportional loading paths and different materials. Validation using experimental data from six different materials confirms the effectiveness of the BNN model. Experiments show that the performance of BNN models is beneficial in most cases compared to classical ML models, assessed through different error standards, statistical tests, Taylor diagrams, uncertainty analysis, and scatter index analysis. The proposed method provides a clear understanding of the uncertainty in multiaxial fatigue life prediction, offering a promising approach for simulating fatigue life under multiaxial loading in engineering applications.

Aviation Safety Risk Analysis Based on Bayesian Network Modeling

The occurrence of serious flight accidents not only brings huge economic losses to airlines but also poses a great threat to passengers' lives. The occurrence of serious flight accidents will not only bring great economic losses to airlines but also cause great threats to the lives of passengers. Therefore, in this paper, based on the flight records of different flight crews, flight routes, airports, and specific flight conditions, aircraft safety risk analysis is conducted to calculate and evaluate the risk propensity. Firstly, the data are preprocessed, and then the QAR data are clustered to extract the key data items affecting the safe flight of the aircraft; then the data are transformed to the attached data, and a hierarchical clustering model is established based on the K-means clustering algorithm, which classifies the factors affecting the safety quality of the aircraft flight into the three main aspects of environmental factors, crew maneuvering, and aircraft state, and the key parameters are weighted by the Random Forest algorithm. weights of the key parameters. Then, based on the 3 criterion, the outliers exceeding 3 were selected as the dependent variables leading to the occurrence of deviation; based on the three-layer model, a Bayesian neural network model based on the three-layer model, and then determine the Bayesian nodes; finally, calculate the Bayesian node probability, and then provide a reasonable quantitative description of the flight maneuver.

A Latent Factor-Based Bayesian Neural Networks Model in Cloud Platform for Used Car Price Prediction

The selling price of a used car can be predicted based on its historical information. Accurate and reasonable used car price evaluation will be able to promote the healthy progress of the used car industry. Current used car price prediction models are troubled by data quality and the inability to provide estimates of uncertain information, and the prediction accuracy cannot meet the needs of real-world scenarios. In this work, we propose a price prediction model based on a Bayesian neural networks with latent factor (LFBNN) in a cloud platform, which is capable of performing latent factor extraction operations on structured data of used cars as a way to remove the effect of noise in the dataset on the model performance. Moreover, the weight parameters of the Bayesian neural networks (NNs) are represented as probability distributions, which is equivalent to introducing uncertainty and acting as a regularization effect compared to a NN with fixed weights, thus making it possible to alleviate the overfitting problem. The LFBNN model uses a cloud platform for data transmission and storage, enabling it to run faster. Compared with the current benchmark models, the model proposed in this work achieves excellent experimental results on two real datasets. The experimental results on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Car_{1}$</tex-math></inline-formula> dataset are 1.498 for mse, 1.224 for rmse, and 0.995 for MAE, and 1.519 for mse, 1.232 for rmse, and 1.002 for MAE on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Car_{2}$</tex-math></inline-formula> dataset.

Direct short-term net load forecasting in renewable integrated microgrids using machine learning: A comparative assessment

Modern microgrids require accurate net load forecasting (NLF) for optimal operation and management at high shares of renewable energy sources. Machine learning (ML) principles can be used to develop precise and reliable NLF models. This paper evaluates the performance of different ML models, that are optimally trained using supervised learning regimes, for direct short-term net load forecasting (STNLF) in renewable microgrids. Different categories of ML models, such as neural network, ensemble, linear regression, nearest neighbor, and support vector machine were used. The comparative assessment was conducted utilizing historical net load, meteorological, and time-related categorical data acquired from the renewable integrated microgrid of the University of Cyprus in Nicosia, Cyprus. The results showed that all STNLF ML models achieved normalized root mean square error (nRMSE) values below 10%. Amongst the investigated models, the Bayesian neural network (BNN) presented the highest forecasting accuracy, exhibiting a daily average error of 3.58%. In addition, the BNN model yielded robust forecasts regardless of the season and weather conditions. Finally, the results demonstrated that optimally constructed ML models can be applied to provide STNLF in renewable integrated microgrids, which can be used by microgrid operators to efficiently control and manage their assets.

Addressing posterior collapse by splitting decoders in variational recurrent autoencoders

Variational recurrent autoencoder model (VRAE) is an appealing technique for capturing the variabilities underlying complex sequential data, which is realized by introducing high-level latent random variables as hidden states. Existing models suffer from the well-known ‘posterior collapse’ problem, meaning that a powerful autoregressive decoder equipped in the model itself could capture all the variabilities and hence leave the latent variables learning nothing from the data. From the perspective of model training, the posterior collapse problem can result in a very low Kullback–Leibler divergence (KL-divergence) value, which means the posteriors of the latent variables tend to be just the priors. In this paper, we address this problem by proposing a Bayesian variational recurrent neural network (BVRNN) model, in which two additional decoders are added into the original VRAE. These extra decoders can force the latent variables to learn meaningful knowledge during the training process. We conduct experiments on MNIST and Fashion-MNIST dataset. The experimental results show that the proposed model outperforms several baseline models. We further adapt the proposed model to a very challenging task in natural language processing, namely Named-Entity Recognition (NER). Experimental results show that our model is competitive to the state-of-the-art models on NER.

GlAIcomics: a deep neural network classifier for spectroscopy-augmented mass spectrometric glycans data

Carbohydrate sequencing is a formidable task identified as a strategic goal in modern biochemistry. It relies on identifying a large number of isomers and their connectivity with high accuracy. Recently, gas phase vibrational laser spectroscopy combined with mass spectrometry tools have been proposed as a very promising sequencing approach. However, its use as a generic analytical tool relies on the development of recognition techniques that can analyse complex vibrational fingerprints for a large number of monomers. In this study, we used a Bayesian deep neural network model to automatically identify and classify vibrational fingerprints of several monosaccharides. We report high performances of the obtained trained algorithm (GlAIcomics), that can be used to discriminate contamination and identify a molecule with a high degree of confidence. It opens the possibility to use artificial intelligence in combination with spectroscopy-augmented mass spectrometry for carbohydrates sequencing and glycomics applications.

Analysis of vehicle pedestrian crash severity using advanced machine learning techniques

In 2015, over 17% of pedestrians were killed during vehicle crashes in Hong Kong while it raised to 18% from 2017 to 2019 and expected to be 25% in the upcoming decade. In Hong Kong, buses and the metro are used for 89% of trips, and walking has traditionally been the primary way to use public transportation. This susceptibility of pedestrians to road crashes conflicts with sustainable transportation objectives. Most studies on crash severity ignored the severity correlations between pedestrian-vehicle units engaged in the same impacts. The estimates of the factor effects will be skewed in models that do not consider these within-crash correlations. Pedestrians made up 17% of the 20,381 traffic fatalities in which 66% of the fatalities on the highways were pedestrians. The motivation of this study is to examine the elements that pedestrian injuries on highways and build on safety for these endangered users. A traditional statistical model's ability to handle misfits, missing or noisy data, and strict presumptions has been questioned. The reasons for pedestrian injuries are typically explained using these models. To overcome these constraints, this study used a sophisticated machine learning technique called a Bayesian neural network (BNN), which combines the benefits of neural networks and Bayesian theory. The best construction model out of several constructed models was finally selected. It was discovered that the BNN model outperformed other machine learning techniques like K-Nearest Neighbors, a conventional neural network (NN), and a random forest (RF) model in terms of performance and predictions. The study also discovered that the time and circumstances of the accident and meteorological features were critical and significantly enhanced model performance when incorporated as input. To minimize the number of pedestrian fatalities due to traffic accidents, this research anticipates employing machine learning (ML) techniques. Besides, this study sets the framework for applying machine learning techniques to reduce the number of pedestrian fatalities brought on by auto accidents.

Large-scale spatiotemporal deep learning predicting urban residential indoor PM2.5 concentration

Indoor PM2.5 pollution is one of the leading causes of death and disease worldwide. As monitoring indoor PM2.5 concentrations on a large scale is challenging, it is urgent to assess population-level exposure and related health risks to develop an easy-to-use and generalized model to predict indoor PM2.5 concentrations and spatiotemporal variations at the global level. Existing machine learning models of indoor PM2.5 are prone to deliver single-point predictions, and their input strategies are not widely applicable. Here, we developed a Bayesian neural network (BNN) model for predicting the distribution of daily average urban residential PM2.5 concentration based on multiple data sources available from nationwide comprehensive sensor-monitoring records in China. The BNN model showed good performance with a 10-fold cross-validation R2 of 0.70, mean-absolute-error of 9.45 μg/m3, root-mean-square error of 13.3 μg/m3, and 95 % prediction interval coverage of 85 %. To demonstrate the application process, this model was applied to predict indoor PM2.5 concentrations on a large spatiotemporal scale. Our modeled population-weighted annual indoor PM2.5 concentration for China in 2019 was 22.8 μg/m3, far exceeding the WHO standard. The validity of the model at the population level can be further bolstered, making it valuable for assessing and managing indoor air pollution-related health risks.

A self‐evaluated predictive model: A Bayesian neural network approach to colorectal cancer diagnosis

AbstractArtificial intelligence has shown immense potential in cancer prediction, but existing models cannot estimate prediction uncertainty by themselves. Here, we developed a Bayesian neural network (BNN) model, BNN‐CRC15, for colorectal cancer (CRC) prediction while assessing its reliability. The model was trained on routine laboratory data obtained from 27,911 participants and provided quantified prediction uncertainty, allowing identification of a subset of participants in which the model was confident, mimicking the diagnostic process of human practitioners. Our model exhibited superior performance (area under the curve = 0.918) in the confident participant group, which accounted for 46.4% of the patients, indicating that routine laboratory data alone are sufficient for accurate predictions in this subset. For the non‐confident group, further advanced tests, such as colonoscopy, could be recommended to achieve more accurate predictions. In addition, our model demonstrated superior overall accuracy (0.848) in all patients, outperforming other five traditional algorithms (extreme gradient boosting, support vector machine, logistic regression, random forest, and artificial neural network) and fecal immunochemical test in distinguishing CRC from non‐CRC. These findings suggest that our BNN‐CRC15 model could serve as a valuable tool for improving CRC diagnosis and prevention.

Yield Optimization for Analog Circuits over Multiple Corners via Bayesian Neural Networks: Enhancing Circuit Reliability under Environmental Variation

The reliability of circuits is significantly affected by process variations in manufacturing and environmental variation during operation. Current yield optimization algorithms take process variations into consideration to improve circuit reliability. However, the influence of environmental variations (e.g., voltage and temperature variations) is often ignored in current methods because of the high computational cost. In this article, a novel and efficient approach named BNN-BYO is proposed to optimize the yield of analog circuits in multiple environmental corners. First, we use a Bayesian Neural Network (BNN) to simultaneously model the yields and performances of interest in multiple corners efficiently. Next, the multi-corner yield optimization can be performed by embedding BNN into a Bayesian optimization framework. Since the correlation among yields and performances of interest in different corners is implicitly encoded in the BNN model, it provides great modeling capabilities for yields and their uncertainties to improve the efficiency of yield optimization. Our experimental results demonstrate that the proposed method can save up to 45.3% of simulation cost compared to other baseline methods to achieve the same target yield. In addition, for the same simulation cost, our proposed method can find better design points with 3.2% yield improvement.

Machine learning methods for developments of binding kinetic models in predicting protein‐ligand dissociation rate constants

AbstractBinding kinetic properties of protein–ligand complexes are crucial factors affecting the drug potency. Nevertheless, the current in silico techniques are insufficient in providing accurate and robust predictions for binding kinetic properties. To this end, this work develops a variety of binding kinetic models for predicting a critical binding kinetic property, dissociation rate constant, using eight machine learning (ML) methods (Bayesian Neural Network (BNN), partial least squares regression, Bayesian ridge, Gaussian process regression, principal component regression, random forest, support vector machine, extreme gradient boosting) and the descriptors of the van der Waals/electrostatic interaction energies. These eight models are applied to two case studies involving the HSP90 and RIP1 kinase inhibitors. Both regression results of two case studies indicate that the BNN model has the state‐of‐the‐art prediction accuracy (HSP90: , MAEtest = 0.184, rtest = 0.976, RMSEtest = 0.220; RIP1 kinase: , MAEtest = 0.188, rtest = 0.961, RMSEtest = 0.290) in comparison with other seven ML models.

American society of anesthesiologists physical status classification significantly affects the performances of machine learning models in intraoperative hypotension inference

Study objectiveTo explore how American Society of Anesthesiologists (ASA) physical status classification affects different machine learning models in hypotension prediction and whether the prediction uncertainty could be quantified. DesignObservational Studies SettingUofL health hospital PatientsThis study involved 562 hysterectomy surgeries performed on patients (≥ 18 years) between June 2020 and July 2021. InterventionsNone MeasurementsPreoperative and intraoperative data is collected. Three parametric machine learning models, including Bayesian generalized linear model (BGLM), Bayesian neural network (BNN), a newly proposed BNN with multivariate mixed responses (BNNMR), and one nonparametric model, Gaussian Process (GP), were explored to predict patients' diastolic and systolic blood pressures (continuous responses) and patients' hypotensive event (binary response) for the next five minutes. Data was separated into American Society of Anesthesiologists (ASA) physical status class 1– 4 before being read in by four machine learning models. Statistical analysis and models' constructions are performed in Python. Sensitivity, specificity, and the confidence/credible intervals were used to evaluate the prediction performance of each model for each ASA physical status class. Main resultsASA physical status classes require distinct models to accurately predict intraoperative blood pressures and hypotensive events. Overall, high sensitivity (above 0.85) and low uncertainty can be achieved by all models for ASA class 4 patients. In contrast, models trained without controlling ASA classes yielded lower sensitivity (below 0.5) and larger uncertainty. Particularly, in terms of predicting binary hypotensive event, for ASA physical status class 1, BNNMR yields the highest sensitivity of 1. For classes 2 and 3, BNN has the highest sensitivity of 0.429 and 0.415, respectively. For class 4, BNNMR and GP are tied with the highest sensitivity of 0.857. On the other hand, the sensitivity is just 0.031, 0.429, 0.165 and 0.305 for BNNMR, BNN, GBLM and GP models respectively, when training data is not divided by ASA physical status classes. In terms of predicting systolic blood pressure, the GP regression yields the lowest root mean squared errors (RMSE) of 2.072, 7.539, 9.214 and 0.295 for ASA physical status classes 1, 2, 3 and 4, respectively, but a RMSE of 126.894 if model is trained without controlling the ASA physical status class. The RMSEs for other models are far higher. RMSEs are 2.175, 13.861, 17.560 and 22.426 for classes 1, 2, 3 and 4 respectively for the BGLM. In terms of predicting diastolic blood pressure, the GP regression yields the lowest RMSEs of 2.152, 6.573, 5.371 and 0.831 for ASA physical status classes 1, 2, 3 and 4, respectively; RMSE of 8.084 if model is trained without controlling the ASA physical status class. The RMSEs for other models are far higher. Finally, in terms of the width of the 95% confidence interval of the mean prediction for systolic and diastolic blood pressures, GP regression gives narrower confidence interval with much smaller margin of error across all four ASA physical status classes. ConclusionsDifferent ASA physical status classes present different data distributions, and thus calls for distinct machine learning models to improve prediction accuracy and reduce predictive uncertainty. Uncertainty quantification enabled by Bayesian inference provides valuable information for clinicians as an additional metric to evaluate performance of machine learning models for medical decision making.

A Bayesian defect-based physics-guided neural network model for probabilistic fatigue endurance limit evaluation

Accurate fatigue assessment of material plagued by defects is of utmost importance to guarantee safety and service continuity in engineering components. This study shows how state-of-the-art semi-empirical models can be endowed with additional defect descriptors to probabilistically predict the occurrence of fatigue failures by exploiting advanced Bayesian Physics-guided Neural Network (B-PGNN) approaches. A B-PGNN is thereby developed to predict the fatigue failure probability of a sample containing defects, referred to a given fatigue endurance limit.In this framework, a robustly calibrated El Haddad’s curve is exploited as the prior physics reinforcement of the probabilistic model, i.e., prior knowledge. Following, a likelihood function is built and the B-PGNN is trained via Bayesian Inference, thus calculating the posterior of the parameters. The arbitrariness of the choice of the related architecture is circumvented through a Bayesian model selection strategy. A case-study is analysed to prove the robustness of the proposed approach. This methodology proposes an advanced practical approach to help support the probabilistic design against fatigue failure.