Quantile-based recursive non-additive multi-fidelity emulator with application to seismic response prediction

Multi-fidelity emulation offers an efficient approach to addressing the computational challenges of high-fidelity simulations, which are crucial for predicting complex system behavior in engineering. Traditional models often rely on linear autoregressive structures, which are limited in their ability to capture nonlinear relationships between fidelity levels. The Recursive Non-Additive (RNA) emulator was introduced to overcome these limitations by providing a flexible, nonlinear formulation for modeling interactions across multiple fidelities. However, prior studies of RNA have been restricted to noise-free settings, limiting its applicability to real-world scenarios characterized by stochastic variability. To address this gap, this study integrates an additional Gaussian process (GP) at each fidelity level of the RNA framework to model input-dependent variance, thereby enabling the emulator to account for noisy data and variable noise levels across the input space. In addition, the RNA framework is refined by replacing mean predictions from lower fidelity levels with statistical quantiles, which capture distributional behavior more effectively and improve robustness in representing complex data patterns and uncertainty. The proposed framework is validated through numerical examples, demonstrating improved accuracy and reliability under noisy conditions compared with the original RNA. Furthermore, it is applied to seismic response prediction in structural engineering and evaluated not only against RNA but also against four linear autoregressive multi-fidelity models. The results show improved performance over RNA and competitive, and in some cases superior, performance relative to the linear autoregressive baselines, while maintaining computational efficiency for practical civil engineering applications. • Introduces a multi-fidelity, nonlinear RNA approach with heteroskedastic GPs. • Manages stochastic variability and input-dependent noise effectively. • Replaces mean-based predictions with quantiles for enhanced uncertainty estimation. • Validated on benchmarks and a multi-story building, achieving improved performance. • Delivers a computationally efficient tool for seismic response predictions.