  One of the main challenges in surrogate modeling is the limited availability
of data due to resource constraints associated with computationally expensive
simulations. Multi-fidelity methods provide a solution by chaining models in a
hierarchy with increasing fidelity, associated with lower error, but increasing
cost. In this paper, we compare different multi-fidelity methods employed in
constructing Gaussian process surrogates for regression. Non-linear
autoregressive methods in the existing literature are primarily confined to
two-fidelity models, and we extend these methods to handle more than two levels
of fidelity. Additionally, we propose enhancements for an existing method
incorporating delay terms by introducing a structured kernel. We demonstrate
the performance of these methods across various academic and real-world
scenarios. Our findings reveal that multi-fidelity methods generally have a
smaller prediction error for the same computational cost as compared to the
single-fidelity method, although their effectiveness varies across different
scenarios.
