Multi-Fidelity Surrogates

Multi-fidelity methods fuse many cheap, approximate model evaluations with a few expensive, accurate ones to build a surrogate that is both fast and trustworthy.

The idea

A single high-fidelity simulation may take hours of compute; a coarse-mesh or reduced-physics version of the same model may take seconds. Multi-fidelity surrogate modeling exploits the correlation between these levels: the low-fidelity model captures the general shape of the response, and a small number of high-fidelity runs correct the residual bias. The result approximates the high-fidelity response at a fraction of the total cost.

Fidelity hierarchy

Kronos motion — fast proton

Physics fidelity: fewer terms, linearized closures, or reduced dimensionality
Discretization fidelity: coarse vs fine mesh or time step
Convergence fidelity: loose vs tight solver tolerances
Model surrogates of surrogates: an emulator standing in for an intermediate solver

Why it works

The efficiency gain depends on two quantities: the cost ratio between levels and the correlation between their outputs. High correlation means the low-fidelity model is informative about the high-fidelity model, so few high-fidelity points are needed. When correlation is weak, multi-fidelity offers little benefit and can even mislead, so measuring cross-level correlation before committing is essential.

Common formulations

Autoregressive co-kriging (see Autoregressive Co-Kriging) models the high-fidelity output as a scaled low-fidelity Gaussian process plus an independent discrepancy process. Nonlinear extensions (see Nonlinear Multi-Fidelity GP) allow the mapping between fidelities to be a learned nonlinear function. For estimating statistics rather than the response surface, multi-fidelity Monte Carlo and multilevel Monte Carlo distribute samples across levels to minimize estimator variance.

Practice

In fusion design workflows a reduced 0-D or 1-D transport model can serve as the low-fidelity level and a full transport or MHD solver as the high-fidelity level. Kronos design studies for the Hyperion breeder use nested-fidelity sweeps to explore operating space cheaply, reserving expensive runs for candidate points near the frozen design. Multi-fidelity results are always reported with the fidelity provenance so a reader can see which points were resolved and which were inferred.