Using sparse GP models is a popular method for reducing the computational cost of BO.

Our sequential optimization setting is as follows. Consider an objective functionf defined over a domainX Rd, whered N is the dimension of the input.

The model proposed here enables proper uncertainty quantification of the causal effects thus allowing the definition of optimal experimental design strategies.

We introduce a new family of non-linear neural network activation functions that mimic the properties induced by the widely-used Mat\'ern family of kernels in Gaussian process (GP) models.

Fractional-order models provide an effective means of describing intrinsically time-dependent viscoelastic dynamics with few parameters, as these models can naturally capture memory effects. However, due to the unintuitive frequency-dependent coupling between the order of the fractional element and the other parameters, determining appropriate parameters for fractional-order models that yield high perceived realism remains a significant challenge. In this study, we propose a systematic means of determining the parameters of fractional-order viscoelastic models that optimizes the perceived realism of haptic rendering across general populations. First, we demonstrate that the parameters of fractional-order models can be effectively optimized through active learning, via qualitative feedback-based human-in-the-loop (HiL) optimizations, to ensure consistently high realism ratings for each individual. Second, we propose a rigorous method to combine HiL optimization results to form an aggregate perceptual map trained on the entire dataset and demonstrate the selection of population-level optimal parameters from this representation that are broadly perceived as realistic across general populations. Finally, we provide evidence of the effectiveness of the generalized fractional-order viscoelastic model parameters by characterizing their perceived realism through human-subject experiments. Overall, generalized fractional-order viscoelastic models established through the proposed HiL optimization and aggregation approach possess the potential to significantly improve the sim-to-real transition performance of medical training simulators. Index T erms--Viscoelastic materials, fractional-order standard linear solid model, haptic rendering, human-in-the-loop optimization, perceived realism, and medical training simulators.