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

Challenges in multi-fidelity modeling relate to accuracy, uncertainty\nestimation and high-dimensionality. A novel additive structure is introduced in\nwhich the highest fidelity solution is written as a sum of the lowest fidelity\nsolution and residuals between the solutions at successive fidelity levels,\nwith Gaussian process priors placed over the low fidelity solution and each of\nthe residuals. The resulting model is equipped with a closed-form solution for\nthe predictive posterior, making it applicable to advanced, high-dimensional\ntasks that require uncertainty estimation. Its advantages are demonstrated on\nunivariate benchmarks and on three challenging multivariate problems. It is\nshown how active learning can be used to enhance the model, especially with a\nlimited computational budget. Furthermore, error bounds are derived for the\nmean prediction in the univariate case.\n