Residual Gaussian Process: A Tractable Nonparametric Bayesian Emulator for Multi-fidelity Simulations
This work addresses multi-fidelity modeling for simulations, which is incremental as it builds on existing Gaussian process methods with a new additive structure.
The paper tackles the challenges of accuracy, uncertainty estimation, and high-dimensionality in multi-fidelity simulations by introducing a novel additive structure with Gaussian process priors, resulting in a tractable nonparametric Bayesian emulator that demonstrates advantages on benchmarks and multivariate problems.
Challenges in multi-fidelity modeling relate to accuracy, uncertainty estimation and high-dimensionality. A novel additive structure is introduced in which the highest fidelity solution is written as a sum of the lowest fidelity solution and residuals between the solutions at successive fidelity levels, with Gaussian process priors placed over the low fidelity solution and each of the residuals. The resulting model is equipped with a closed-form solution for the predictive posterior, making it applicable to advanced, high-dimensional tasks that require uncertainty estimation. Its advantages are demonstrated on univariate benchmarks and on three challenging multivariate problems. It is shown how active learning can be used to enhance the model, especially with a limited computational budget. Furthermore, error bounds are derived for the mean prediction in the univariate case.