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Obtaining high certainty in predictive models is crucial for making informed and trustworthy decisions in many scientific and engineering domains. However, extensive experimentation required for model accuracy can be both costly and time-consuming. This paper presents an adaptive sampling approach designed to reduce epistemic uncertainty in predictive models. Our primary contribution is the development of a metric that estimates potential epistemic uncertainty leveraging prediction interval-generation neural networks.This estimation relies on the distance between the predicted upper and lower bounds and the observed data at the tested positions and their neighboring points. Our second contribution is the proposal of a batch sampling strategy based on Gaussian processes (GPs). A GP is used as a surrogate model of the networks trained at each iteration of the adaptive sampling process. Using this GP, we design an acquisition function that selects a combination of sampling locations to maximize the reduction of epistemic uncertainty across the domain.We test our approach on three unidimensional synthetic problems and a multi-dimensional dataset based on an agricultural field for selecting experimental fertilizer rates.The results demonstrate that our method consistently converges faster to minimum epistemic uncertainty levels compared to Normalizing Flows Ensembles, MC-Dropout, and simple GPs. 

As objectives increase in many-objective optimization (MaOO), often so do the number of non-dominated solutions, potentially resulting in solution sets with thousands of non-dominated solutions. Such a larger final solution set increases difficulty in visualization and decision-making. This raises the question: how can we reduce this large solution set to a more manageable size? In this paper, we present a new objective archive management (OAM) strategy that performs post-optimization solution set reduction to help the end-user make an informed decision without requiring expert knowledge of the field of MaOO. We create separate archives for each objective, selecting solutions based on their fitness as well as diversity criteria in both the objective and variable space. We can then look for solutions that belong to more than one archive to create a reduced final solution set. We apply OAM to NSGA-II and compare our approach to environmental selection finding that the obtained solution set has better hypervolume and spread. Furthermore, we compare results found by OAM-NSGA-II to NSGA-III and get competitive results. Additionally, we apply OAM to reduce the solutions found by NSGA-III and find that the selected solutions perform well in terms of overall fitness, successfully reducing the number of solutions. 

Response curves exhibit the magnitude of the response of a sensitive system to a varying stimulus. However, response of such systems may be sensitive to multiple stimuli (i.e., input features) that are not necessarily independent. As a consequence, the shape of response curves generated for a selected input feature (referred to as “active feature”) might depend on the values of the other input features (referred to as “passive features”). In this work we consider the case of systems whose response is approximated using regression neural networks. We propose to use counterfactual explanations (CFEs) for the identification of the features with the highest relevance on the shape of response curves generated by neural network black boxes. CFEs are generated by a genetic algorithm-based approach that solves a multi-objective optimization problem. In particular, given a response curve generated for an active feature, a CFE finds the minimum combination of passive features that need to be modified to alter the shape of the response curve. We tested our method on a synthetic dataset with 1-D inputs and two crop yield prediction datasets with 2-D inputs. The relevance ranking of features and feature combinations obtained on the synthetic dataset coincided with the analysis of the equation that was used to generate the problem. Results obtained on the yield prediction datasets revealed that the impact on fertilizer responsivity of passive features depends on the terrain characteristics of each field. 

Performing general prognostics and health management (PHM), especially in electronic systems, continues to present significant challenges. The low availability of failure data makes learning generalized models difficult and constructing generalized models during the design phase often requires a level of understanding of the failure mechanisms that elude the designers. In this paper, we present a generalized approach to PHM based on two types of probabilistic models, Bayesian Networks (BNs) and Continuous-Time Bayesian Networks (CTBNs), and we pose the PHM problem from the perspective of risk mitigation rather than failure prediction. This paper also constitutes an extension of previous work where we proposed this framework initially [1]. In this extended version, we also provide a comparison of exact and approximate sample-based inference for CTBNs to provide practical guidance on conducting inference using the proposed framework. 

Accurate uncertainty quantification is necessary to enhance the reliability of deep learning (DL) models in realworld applications. In the case of regression tasks, prediction intervals (PIs) should be provided along with the deterministic predictions of DL models. Such PIs are useful or “high-quality (HQ)” as long as they are sufficiently narrow and capture most of the probability density. In this article, we present a method to learn PIs for regression-based neural networks (NNs) automatically in addition to the conventional target predictions. In particular, we train two companion NNs: one that uses one output, the target estimate, and another that uses two outputs, the upper and lower bounds of the corresponding PI. Our main contribution is the design of a novel loss function for the PI-generation network that takes into account the output of the target-estimation network and has two optimization objectives: minimizing the mean PI width and ensuring the PI integrity using constraints that maximize the PI probability coverage implicitly. Furthermore, we introduce a self-adaptive coefficient that balances both objectives within the loss function, which alleviates the task of fine-tuning. Experiments using a synthetic dataset, eight benchmark datasets, and a real-world crop yield prediction dataset showed that our method was able to maintain a nominal probability coverage and produce significantly narrower PIs without detriment to its target estimation accuracy when compared to those PIs generated by three state-of-the-art neuralnetwork-based methods. In other words, our method was shown to produce higher quality PIs.