Gradient-enhanced multifidelity neural networks for high-dimensional\n function approximation

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