This paper presents a hybrid model that combines Artificial Neural Networks (ANN) and Gaussian Processes (GP). The goal is to achieve high prediction accuracy while quantifying uncertainty. The proposed structure is a simple ANN used as the trend of the GP, particularly emphasizing the joint training of the two models. The ANN+GP exploits the ability of the ANN to capture complex, non-linear relationships in the data. At the same time, the GP provides an approach to uncertainty estimation, thus improving the accuracy of the predictions. This paper emphasizes the importance of concurrent training, which can improve the accuracy of the prediction model. The algorithm is suitable for any application where both accurate, robust predictions and uncertainty estimates are critical to enhance the interpretability of the model. The proposed method has been successfully applied to the frequency response functions of a simple structure.

The present study aims to develop a k-nearest neighbors (k-NN) based active learning methodology for the surrogate modeling of composite materials using sparse Gaussian process regression (SGPR) [1].

The proposed technique is a pool-based [2] methodology aiming to identify the most informative points from the pool dataset using a score estimation that consists of the bias plus the variance at each point. The points selected as the most informative are the ones with the highest score. The variance at each point is calculated by the SGPR surrogate model, while the bias is calculated as the weighted sum of the actual responses of the k-NN points from the initial training dataset. The weights are defined as a function of the normalized inverse distance of each pool point to its corresponding k-NN points.

The major goal of this study is to develop a robust and scalable active learning and surrogate modeling technique for the simulation of composite laminated materials, whose inputs and outputs are obtained from computationally expensive and complex finite element analyses [3].

Several benchmarks and real-word numerical examples are presented and compared to well-established active learning methods in the literature.