Exploring Multi-Fidelity Networks and Adapting their Architecture: A Paradigm for Enhanced Learning and Efficiency

Multi-Fidelity Networks (MFNets) have emerged as a promising approach for surrogate modeling when dealing with limited data and heterogeneous models. They provide a means to establish relationships between different models based on their parameters, rather than relying solely on inputs or outputs. The covariance matrix, which captures the interconnections between the parameters, typically follows a peer structure assumption. However, when the low-fidelity models exhibit dependencies, alternative model architectures can be considered to better capture the underlying relationships. This paper proposes a modified MFNets model that incorporates a hierarchical structure and presents a generalized formulation applicable to diverse applications. A benchmark numerical problem is implemented to demonstrate the advantages of considering different underlying model architectures. The results showcase improved predictive capabilities of MFNets when estimating high-fidelity functions.