MultiFidelitySurrogat

MultiFidelitySurrogat, or multi-fidelity surrogate, refers to a surrogate modeling approach that combines information from simulations or measurements of different fidelity levels to approximate an expensive-to-evaluate function. The goal is to exploit inexpensive low-fidelity data to improve predictions at high fidelity while reducing overall computational or experimental cost.

A common framework for multi-fidelity surrogates is based on Gaussian processes and co-kriging. In a two-level setting, a high-fidelity output f_h(x) is modeled as f_h(x) = rho(x) f_l(x) + delta_h(x), where f_l(x) is the low-fidelity model, rho(x) is a scaling or calibration function, and delta_h(x) is a high-fidelity discrepancy modeled as a Gaussian process. This idea extends to more than two fidelities through hierarchical or autoregressive formulations, enabling information transfer across multiple fidelity levels. Other approaches include multi-fidelity neural networks and transfer-learning-based surrogates.

Training utilizes data collected at various fidelities, aligning inputs and accounting for differences in bias and noise. The resulting surrogate provides not only point predictions but also quantified uncertainty, which is valuable for downstream tasks such as Bayesian optimization, design optimization, and sensitivity analysis. The method aims to maximize the value of expensive high-fidelity evaluations by leveraging abundant, cheaper low-fidelity data.

Applications are common in engineering and science, including computational fluid dynamics, structural analysis, thermo-fluid simulations, and aerospace design. Challenges include selecting appropriate fidelity levels, ensuring sufficient correlation between fidelities, managing computational costs of multi-fidelity models, and mitigating model misspecification when fidelities diverge.