Probabilistic reach-avoid for Bayesian neural networks

A reliable Bayesian neural network for the prediction of reservoir thickness with quantified uncertainty

Bayesian neural network analysis has been used to develop an accurate model for predicting the ferrite content in stainless steel welds. The analysis reveals the influence of compositional variations on ferrite content for the stainless steel weld metals, and examines the significance of individual elements on ferrite content in stainless steel welds based on the optimised neural network model. This neural network model for ferrite prediction in stainless steel welds has been developed using the database used for generating the WRC-1992 diagram and our laboratory data. The optimised committee model predicts the ferrite number (FN) in stainless steel welds with better accuracy than the constitution diagrams and the other FN prediction methods. Using this generalised Bayesian Neural Network (BNN) model, the influence of variations of the individual elements on the FN in austenitic and duplex stainless steel welds has been determined. It is found that the change in FN is a non-linear function of the variation in the concentration of the elements, with elements such as chromium, nickel, nitrogen, molybdenum, silicon, titanium and vanadium are found to influence the FN more significantly than the rest of the elements in stainless steel welds. Manganese is found to have less influence on the FN. While titanium influences the FN more significantly than niobium, the WRC-1992 diagram considers only the niobium for calculating chromium equivalent. The role of silicon and titanium in influencing the FN in stainless steel welds has been brought out clearly, while these elements are not given due considerations in the WRC-1992 diagram.

The intermittence and fluctuation of renewable energy bring significant uncertainty to the power system, which enormously increases the operational risks of the power system. The development of efficient interval prediction models can provide data support for decision making and help improve the economy and reliability of energy interconnection operation. The performance of Bayesian deep learning models and Bayesian shallow neural networks in short-term interval prediction of photovoltaic power is compared in this study. Specifically, an LSTM Approximate Bayesian Neural Network model (ABNN-I) is built on the basis of the deep learning and Monte Carlo Dropout method. Meanwhile, a Feedforward Bayesian Neural Network (ABNN-II) model is introduced by Feedforward Neural Network and the Markov Chain Monte Carlo method. To better compare and verify the interval prediction capability of the ABNN models, a novel clustering method with three-dimensional features which include the number of peaks and valleys, the average power value, and the non-stationary measurement coefficient is proposed for generating sunny and non-sunny clustering sets, respectively. Results show that the ABNN-I model has an excellent performance in the field of photovoltaic short-term interval forecasting. At a 95% confidence level, the interval coverage from ABNN-I to ABNN-II can be increased by up to 3.1% and the average width of the interval can be reduced by 56%. Therefore, with the help of the high computational capacity of deep learning and the inherent ability to quantify uncertainty of the interval forecast from Bayesian methods, this research provides high-quality interval prediction results for photovoltaic power prediction and solves the problem of difficult modeling for over-fitting that exists in the training process, especially on the non-sunny clustering sets.

Adaptive behavior and different thermal experiences of real people: A Bayesian neural network approach to thermal preference prediction and classification

<div class="section abstract"><div class="htmlview paragraph">Self-piercing riveting (SPR) is a key joining method in multi/thin-material automotive structures, yet accurately predicting the mechanical strength of SPR joints remains challenging due to numerous influencing factors. Empirical engineering equations [<span class="xref">1</span>] provide a foundation for estimating lap-shear and cross-tension strength but require several geometric parameters that are often unavailable in the design phase.</div><div class="htmlview paragraph">To address this limitation, we extract and leverage the core physical relationships embedded in these formulas. By reformulating the dependence of joint strength on the yield strength and total thickness of the sheet stack as practical regression models, we enable strength prediction using only commonly available material properties.</div><div class="htmlview paragraph">Furthermore, a Bayesian convolutional neural network (BCNN) model is developed to incorporate additional material features, offering improved prediction accuracy and uncertainty quantification.</div></div>

As mobile traffic increases with the advent of 5 G an d 6G technologies, it is becoming increasingly crucial to effectivel y manage network traffic resources, which can be significantly en hanced by accurate traffic forecasting and practical management. While some machine learning and deep learning models have alr eady been utilized in the problem, the impact of uncertainty has not been paid enough attention to, and problem of corresponding resource management has not been fully considered. This study deploys the Bayesian Neural Network (BNN) to confront the joint problem of traffic forecasting and resource allocation, demonstr ating the advantages of BNN for capturing uncertainty and arran ging network resources. A BNN ensemble model further improve s forecasting performance, outperforming basic BNN and DNN models, and supporting superior resource allocation scheme com pared to even allocation scheme. Our results demonstrates that B NNs can significantly contribute to a more efficient management of network resources in modern networks.

This paper investigates the potential of using data-driven methods, namely Bayesian neural networks (BNN), recurrent multi-layer perceptrons (RMLP), time-lagged feed-forward networks (TLFN), and conventional multi-layer perceptrons (MLP) to forecast seasonal reservoir inflows of the Churchill Falls watershed in northeastern Canada. A climate variability indicator (the El Niño-Southern Oscillation, ENSO) is used as additional information to historical inflow time series in order to predict seasonal reservoir inflows. The prediction results showed that the Bayesian neural network model was best able to capture the additional information provided by the ENSO series, and provided improved predictions in spring and summer seasons relative to the same model using only reservoir inflows. Similarly, time-lagged feed-forward networks and recurrent multi-layer perceptrons showed some improved forecast skill in spring when the ENSO index series are used but generally provided superior performance overall. The conventional multi-layer perceptron appears unable to capture relevant information from the ENSO series regardless of the season. However, when only historical flow series are used, all the selected data-driven methods provide very competitive forecast performances.

<div class="section abstract"><div class="htmlview paragraph">Developing models for predicting the low-temperature cracking resistance of asphalt mixtures is a complex process with a wide variety and complex influence mechanisms of variables, leading to higher uncertainty in the prediction results. Several models have been developed in this regard. This study developed a Bayesian neural network (BNN) model for predicting the fracture energy of low-temperature semi-circular bending (SCB) tests based on pavement condition measurements, traffic, climate, and basic parameters of the material. The model was trained and evaluated using low-temperature SCB test data from in-situ pavement core samples, and the results showed that the coefficient of determination (R2) of the BNN model was greater than 0.8 for both the training and testing sets. The variable importance scores showed that the decrease of transverse crack rating index (TCEI) and gradation were the most important factor affecting low-temperature fracture energy and that the ambient temperature was relatively least important. The uncertainty of the BNN model variables was quantified using epistemic uncertainty and aleatoric uncertainty. The results of the uncertainty analyses showed that the epistemic uncertainty was less than or equal to the aleatoric uncertainty for most of the variables used in this study, which indicated that the uncertainty caused by the model parameters was less than that caused by the noise in the original data, that corroborated the reliability of the BNN model used in this study.</div></div>

There has been lots of research to improve the precision of IR system. These research have been studied on the document ranking, user profiles, relevance feedback and the information processing that includes document classification, clustering, routing and filtering. This paper proposes and incarnates method of neural approach about the information processing which makes users can search documents effectively and of the document clustering. In this paper the system calculates entropy between the query, the profile and the each of the web documents each other; and clusters documents using the calculated entropy as the value of the clustering variable through SOM. As the Bayesian Neural Network model has high classification accuracy with a rapid learning speed and clustering, it is possible that dynamic document clustering as it was combined with Bayesian probability model used in real-time document classification. We used KTSET which is a test collection to evaluate Korean IR system for the experiment.

This article develops and compares two Bayesian neural network models, a more restrictive Bayesian framework using Gaussian approximation and a less restrictive one using a hybrid version of Markov Chain Monte Carlo method (HMC), for the prediction of militarized interstate disputes (MIDs). In addition, to compare and analyze different Bayesian models for international conflict, the authors introduce a new measurement to interpret the relative influence of the model variables on the MIDs. The results indicate that the Gaussian approximation and HMC models are not statistically different in their performance. However HMC correctly recognized a marginally higher number of militarized disputes whose classification is important for policy purpose. On the variable effect, both models indicate similar patter of influences, where the two key liberal variables, democracy and economic interdependence, produce a strong dynamic feedback loop among each other, which greatly increases or decreases the probability of MIDs.

Data-driven approaches to price computations of financial options are gaining in importance relative to methods based on numerical solutions of the pricing equations. Comparisons between artificial neural networks and the Black–Scholes pricing model have shown that the machine learning technique compares well in terms of performance with the parametric model. A Bayesian neural network model has recently been employed for predicting the price of options under jump-diffusion models since jump processes have a better capability of fitting market options data. The potential applicability of data-driven models for generating price approximations under jump processes is high, but due to the need of ensuring that computed prices are arbitrage-free, validation by the often employed partial differential equations approach is important. This work proposes a new algorithm that can be used for comparing prices obtained by a learning algorithm for diffusion models with jumps. Two directions are chosen in order to develop a competitive algorithm. The first is employing a higher-order discretisation of the pricing partial integro-differential equation and second using a more efficient numerical procedure for the solution of the resulting linear complementarity problem. Howard’s algorithm or policy iteration is one such procedure for the second phase, but application of this method requires that the coefficient matrix is monotone. The combination of high-order approximations for the derivative and integral terms with policy iteration yields an accurate and efficient computational technique, and these properties are illustrated using an extensive set of numerical examples.

Predicting the Nature of Terrorist Attacks in Nigeria Using Bayesian Neural Network Model

Ductile fracture micro-mechanisms of high strength low alloy steels

Future flood dynamics in a lowland karst catchment draining into Galway Bay, Ireland, have been assessed under climate-change scenarios. Bayesian neural network model (BNN) was calibrated on 1980-2015 observations of rainfall, tides, and turlough flood volumes, yielding correlations of R = 0.95 (training) and R = 0.78 (overall). Projections driven by CORDEX under RCP 4.5 and 8.5 for 2016-2100 reveal ensemble-mean rainfall increases of 1.2mm decade-1 and 2.5mm decade-1, respectively, corresponding to flood-volume growth rates of 5 × 10⁶ m3 decade-1 and 1.1 × 107 m3 decade-1. Wavelet coherence indicated high-frequency coupling (> 0.7) between rainfall and floods under RCP 8.5 versus < 0.5 under RCP 4.5. Extreme-event analysis showed a 40% rise in joint 95th -percentile rainfall and flood-volume events under RCP 8.5 (p < 0.05). Generalized extreme-value fits to annual maxima for 2018-2037 versus 2080-2099 project that a historical 100-year storm becomes 1-in-16-year event under RCP 8.5. 10-year rolling 90th -percentile analysis revealed rapid intensification of upper-tail floods under RCP 8.5 than RCP 4.5. These findings demonstrated that high-emission pathways substantially amplify flood magnitudes and frequencies and underscores the utility of integrated statistical and machine-learning frameworks for robust flood-risk assessment and climate-adaptation planning.

El Ni&amp;#241;o Southern Oscillation (ENSO) significantly influences Earth's system and regional climate patterns. Despite dedicated efforts spanning decades, the precise prediction of ENSO events through numerical modelling beyond&amp;#160; one-year lead time remains a formidable challenge. The advent of deep learning-based approaches marks a transformative era in climate and weather prediction. However, many machine learning-based studies attempting ENSO prediction are confined to singular estimates, lacking adequate quantification of uncertainty in learned parameters and overlooking the crucial need for a nuanced understanding of ENSO prediction confidence. Here, we introduce a deep learning-based Bayesian Convolutional Neural Network (BCNN) model that provides probabilistic predictions for ENSO&amp;#160; with a lead time of up to 24 months. The Bayesian layers within the CNN maintain the capability to predict a distribution of learned parameters. The inherent capacity for uncertainty modeling enhances the reliability of BNNs, making them particularly valuable in operational services. The model was initially trained using globally gridded monthly sea surface temperature and upper 300 m integrated ocean potential temperature predictors from 25 Climate Model Intercomparison Project (CMIP) models, including 11 CMIP5 and 14 CMIP6. To address systematic errors in the BCNN, reflecting those of the CMIP samples, a learning transfer technique was applied using Simple Ocean Data Assimilation (SODA) reanalysis predictors spanning from 1871 to 1980. Validation of the all-season correlation skill of the Nino3.4 index in the BCNN model demonstrates significantly higher accuracy compared to current state-of-the-art dynamical forecast systems. This research holds substantial socio-economic implications as it enhances our forecasting capabilities and rigorously quantifies forecast uncertainties, providing valuable insights for planning and policy-making.