Multi-Fidelity Surrogates

Multi-fidelity methods combine many cheap approximate runs with few expensive accurate ones to build a surrogate at high-fidelity accuracy for less effort.

Fidelity levels

Most simulations exist at several fidelity levels: a coarse mesh runs in seconds, a fine mesh in hours; a simplified physics model is fast, a full model slow. Low-fidelity models are cheap but biased; high-fidelity models are accurate but costly. Multi-fidelity surrogates fuse them, using the plentiful cheap runs to learn the shape of the response and the few expensive runs to correct the bias.

The key assumption

Kronos motion — fidelity

The methods work when the low-fidelity model is correlated with the high-fidelity one - when it captures trends even if it gets absolute values wrong. The stronger and simpler that relationship, the more the cheap model can substitute for the expensive one. A low-fidelity model that is merely cheap and unrelated adds nothing.

How correction works

Additive correction: high fidelity equals low fidelity plus a learned discrepancy
Multiplicative correction: high fidelity equals a learned factor times low fidelity
Comprehensive correction combines both
Co-kriging models the two fidelities jointly with correlated Gaussian processes

Autoregressive co-kriging

A widely used scheme models the high-fidelity output as a scaling of the low-fidelity output plus an independent Gaussian-process discrepancy. The low fidelity is learned from many points, the discrepancy from the few high-fidelity points where both are available. The result predicts high-fidelity values with uncertainty across the whole space.

Multi-fidelity UQ

The same idea accelerates uncertainty propagation. Multilevel and multifidelity Monte Carlo run most samples cheaply and few expensively, combining them to estimate statistics at high-fidelity accuracy for a fraction of the cost. Control-variate formulations make the variance reduction rigorous.

In fusion design

Kronos modeling has a natural fidelity ladder for the machines - reduced analytic models, coarse simulations, and full-fidelity codes. Multi-fidelity surrogates exploit this ladder so that broad design exploration draws mostly on cheap models, with expensive runs reserved for correcting bias and validating the final points.