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Challenges in multi-fidelity modeling relate to accuracy, uncertaintyestimation and high-dimensionality. A novel additive structure is introduced inwhich the highest fidelity solution is written as a sum of the lowest fidelitysolution and residuals between the solutions at successive fidelity levels,with Gaussian process priors placed over the low fidelity solution and each ofthe residuals. The resulting model is equipped with a closed-form solution forthe predictive posterior, making it applicable to advanced, high-dimensionaltasks that require uncertainty estimation. Its advantages are demonstrated onunivariate benchmarks and on three challenging multivariate problems. It isshown how active learning can be used to enhance the model, especially with alimited computational budget. Furthermore, error bounds are derived for themean prediction in the univariate case.

Residual Gaussian Process: A Tractable Nonparametric Bayesian Emulator for Multi-fidelity Simulations