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Multi-fidelity methods leverage low-cost surrogate models to speed upcomputations and make occasional recourse to expensive high-fidelity models toestablish accuracy guarantees. Because surrogate and high-fidelity models areused together, poor predictions by surrogate models can be compensated withfrequent recourse to high-fidelity models. Thus, there is a trade-off betweeninvesting computational resources to improve the accuracy of surrogate modelsversus simply making more frequent recourse to expensive high-fidelity models;however, this trade-off is ignored by traditional modeling methods thatconstruct surrogate models that are meant to replace high-fidelity modelsrather than being used together with high-fidelity models. This work considersmulti-fidelity importance sampling and theoretically and computationally tradesoff increasing the fidelity of surrogate models for constructing more accuratebiasing densities and the numbers of samples that are required from thehigh-fidelity models to compensate poor biasing densities. Numerical examplesdemonstrate that such context-aware surrogate models for multi-fidelityimportance sampling have lower fidelity than what typically is set as tolerancein traditional model reduction, leading to runtime speedups of up to one orderof magnitude in the presented examples.

Context-aware surrogate modeling for balancing approximation and sampling costs in multi-fidelity importance sampling and Bayesian inverse problems