Understanding how these systems arrive at their decisions is a necessary first step before these biases can be corrected.

In scientific applications, predictive modeling is often of limited use without accurate uncertainty quantification (UQ) to indicate when a model may be extrapolating or when more data needs to be collected. Bayesian Neural Networks (BNNs) produce predictive uncertainty by propagating uncertainty in neural network (NN) weights and offer the promise of obtaining not only an accurate predictive model but also accurate UQ. However, in practice, obtaining accurate UQ with BNNs is difficult due in part to the approximations used for practical model training and in part to the need to choose a suitable set of hyperparameters; these hyperparameters outnumber those needed for traditional NNs and often have opaque effects on the results. We aim to shed light on the effects of hyperparameter choices for BNNs by performing a global sensitivity analysis of BNN performance under varying hyperparameter settings. Our results indicate that many of the hyperparameters interact with each other to affect both predictive accuracy and UQ. For improved usage of BNNs in real-world applications, we suggest that global sensitivity analysis, or related methods such as Bayesian optimization, should be used to aid in dimensionality reduction and selection of hyperparameters to ensure accurate UQ in BNNs.

Understanding how these systems arrive at their decisions is a necessary first step before these biases can be corrected.

Finite element (FE) simulations of structures and materials are getting increasingly more accurate, but also more computationally expensive as a collateral result. This development happens in parallel with a growing demand of data-driven design. To reconcile the two, a robust and data-efficient optimization method called Bayesian optimization (BO) has been previously established as a technique to optimize expensive objective functions. In parallel, the mesh width of an FE model can be exploited to evaluate an objective at a lower or higher fidelity (cost & accuracy) level. The multi-fidelity setting applied to BO, called multi-fidelity BO (MFBO), has also seen previous success. However, BO and MFBO have not seen a direct comparison with when faced with with a real-life engineering problem, such as metamaterial design for deformation and absorption qualities. Moreover, sampling quality and assessing design parameter sensitivity is often an underrepresented part of data-driven design. This paper aims to address these shortcomings by employing Sobol' samples with variance-based sensitivity analysis in order to reduce design problem complexity. Furthermore, this work describes, implements, applies and compares the performance BO with that MFBO when maximizing the energy absorption (EA) problem of spinodoid cellular structures is concerned. The findings show that MFBO is an effective way to maximize the EA of a spinodoid structure and is able to outperform BO by up to 11% across various hyperparameter settings. The results, which are made open-source, serve to support the utility of multi-fidelity techniques across expensive data-driven design problems.

High-fidelity simulations and physical experiments are essential for engineering analysis and design. However, their high cost often limits their applications in two critical tasks: global sensitivity analysis (GSA) and optimization. This limitation motivates the common use of Gaussian processes (GPs) as proxy regression models to provide uncertainty-aware predictions based on a limited number of high-quality observations. GPs naturally enable efficient sampling strategies that support informed decision-making under uncertainty by extracting information from a subset of possible functions for the model of interest. Despite their popularity in machine learning and statistics communities, sampling from GPs has received little attention in the community of engineering optimization. In this paper, we present the formulation and detailed implementation of two notable sampling methods -- random Fourier features and pathwise conditioning -- for generating posterior samples from GPs. Alternative approaches are briefly described. Importantly, we detail how the generated samples can be applied in GSA, single-objective optimization, and multi-objective optimization. We show successful applications of these sampling methods through a series of numerical examples.

Functional ANOVA (FANOVA) is a widely used variance-based sensitivity analysis tool. However, studies on functional-output FANOVA remain relatively scarce, especially for black-box computer experiments, which often involve complex and nonlinear functional-output relationships with unknown data distribution. Conventional approaches often rely on predefined basis functions or parametric structures that lack the flexibility to capture complex nonlinear relationships. Additionally, strong assumptions about the underlying data distributions further limit their ability to achieve a data-driven orthogonal effect decomposition. To address these challenges, this study proposes a functional-output orthogonal additive Gaussian process (FOAGP) to efficiently perform the data-driven orthogonal effect decomposition. By enforcing a conditional orthogonality constraint on the separable prior process, the proposed functional-output orthogonal additive kernel enables data-driven orthogonality without requiring prior distributional assumptions. The FOAGP framework also provides analytical formulations for local Sobol' indices and expected conditional variance sensitivity indices, enabling comprehensive sensitivity analysis by capturing both global and local effect significance. Validation through two simulation studies and a real case study on fuselage shape control confirms the model's effectiveness in orthogonal effect decomposition and variance decomposition, demonstrating its practical value in engineering applications.

This paper presents a novel framework for prioritizing urban green space development in Tehran using diverse socio-economic, environmental, and sensitivity indices. The indices were derived from various sources including Google Earth Engine, air pollution measurements, municipal reports and the Weather Research & Forecasting (WRF) model. The WRF model was used to estimate the air temperature at a 1 km resolution due to insufficient meteorological stations, yielding RMSE and MAE values of 0.96°C and 0.92°C, respectively. After data preparation, several machine learning models were used for binary vegetation cover classification including XGBoost, LightGBM, Random Forest (RF) and Extra Trees. RF achieved the highest performance, exceeding 94% in Overall Accuracy, Recall, and F1-score. Then, the probability of areas lacking vegetation cover was assessed using socio-economic, environmental and sensitivity indices. This resulted in the RF generating an urban green space development prioritization map. Feature Importance Analysis revealed that the most significant indices were nightly land surface temperature (LST) and sensitive population. Finally, the framework performance was validated through microclimate simulation to assess the critical areas after and before the green space development by green roofs. The simulation demonstrated reducing air temperature by up to 0.67°C after utilizing the green roof technology in critical areas. As a result, this framework provides a valuable tool for urban planners to develop green spaces.

Complex events originate from other primitive events combined according to defined patterns and rules. Instead of using specialists' manual work to compose the model rules, we use machine learning (ML) to self-define these patterns and regulations based on incoming input data to produce the desired complex event. Complex events processing (CEP) uncertainty is critical for embedded and safety-critical systems. This paper exemplifies how we can measure uncertainty for the perception and prediction of events, encompassing embedded systems that can also be critical to safety. Then, we propose an approach (ML\_CP) incorporating ML and sensitivity analysis that verifies how the output varies according to each input parameter. Furthermore, our model also measures the uncertainty associated with the predicted complex event. Therefore, we use conformal prediction to build prediction intervals, as the model itself has uncertainties, and the data has noise. Also, we tested our approach with classification (binary and multi-level) and regression problems test cases. Finally, we present and discuss our results, which are very promising within our field of research and work.

In real case applications within the virtual prototyping process, it is not always possible to reduce the complexity of the physical models and to obtain numerical models which can be solved quickly. Usually, every single numerical simulation takes hours or even days. Although the progresses in numerical methods and high performance computing, in such cases, it is not possible to explore various model configurations, hence efficient surrogate models are required. Generally the available meta-model techniques show several advantages and disadvantages depending on the investigated problem. In this paper we present an automatic approach for the selection of the optimal suitable meta-model for the actual problem. Together with an automatic reduction of the variable space using advanced filter techniques an efficient approximation is enabled also for high dimensional problems.