  In this work, a novel multifidelity machine learning (ML) model, the
gradient-enhanced multifidelity neural networks (GEMFNNs), is proposed. This
model is a multifidelity version of gradient-enhanced neural networks (GENNs)
as it uses both function and gradient information available at multiple levels
of fidelity to make function approximations. Its construction is similar to
multifidelity neural networks (MFNNs). This model is tested on three analytical
function, a one, two, and a 20 variable function. It is also compared to neural
networks (NNs), GENNs, and MFNNs, and the number of samples required to reach a
global accuracy of 0.99 coefficient of determination (R^2) is measured. GEMFNNs
required 18, 120, and 600 high-fidelity samples for the one, two, and 20
dimensional cases, respectively, to meet the target accuracy. NNs performed
best on the one variable case, requiring only ten samples, while GENNs worked
best on the two variable case, requiring 120 samples. GEMFNNs worked best for
the 20 variable case, while requiring nearly eight times fewer samples than its
nearest competitor, GENNs. For this case, NNs and MFNNs did not reach the
target global accuracy even after using 10,000 high-fidelity samples. This work
demonstrates the benefits of using gradient as well as multifidelity
information in NNs for high-dimensional problems.
