Publications Details

On Coordinate Encoding in Multifidelity Neural Networks

Villatoro, Cristian; Geraci, Gianluca; Schiavazzi, Daniele E.

Multifidelity emulators have found wide-ranging applications in both forward and inverse problems within the computational sciences. Thanks to recent advancements in neural architectures, they provide significant flexibility for integrating information from multiple models, all while retaining substantial efficiency advantages over single-fidelity methods. In this context, existing neural multifidelity emulators operate by separately resolving the linear and nonlinear correlation between equally parameterized high-and low-fidelity approximants. However, many complex models ensembles in science and engineering applications only exhibit a limited degree of linear correlation between models. In such a case, the effectiveness of these approaches is impeded, i.e., larger datasets are needed to obtain satisfactory predictions. In this work, we present a general strategy that seeks to maximize the linear correlation between two models through input encoding. We showcase the effectiveness of our approach through six numerical test problems, and we show the ability of the proposed multifidelity emulator to accurately recover the high-fidelity model response under an increasing number of quasi-random samples. In our experiments, we show that input encoding produces in many cases emulators with significantly simpler nonlinear correlations. Finally, we demonstrate how the input encoding can be leveraged to facilitate the fusion of information between low-and high-fidelity models with dissimilar parametrization, i.e., situations in which the number of inputs is different between low-and high-fidelity models.