Choosing a Surrogate Model
The right surrogate depends on dimensionality, data budget, smoothness, output type, and whether you need calibrated uncertainty.
No universal best
Every surrogate family embodies assumptions. Choosing well means matching those assumptions to the problem: how many inputs, how many samples you can afford, how smooth and nonlinear the response is, whether outputs are scalars or fields, and whether the task needs honest uncertainty. The wrong match wastes the evaluation budget or produces overconfident predictions.
Guiding factors
- Input dimension - low favors GPs and polynomial chaos; high favors neural networks with dimension reduction
- Sample budget - small favors GPs and RBFs; large enables deep surrogates
- Smoothness - smooth favors polynomial chaos and squared-exponential kernels; rough favors Matern or trees
- Output type - scalars favor classical surrogates; fields favor POD-based ROMs or neural operators
- Uncertainty need - if error bars are required, favor GPs or Bayesian methods
Rules of thumb
Gaussian processes are the default for small, low-dimensional, smooth problems needing uncertainty. Polynomial chaos suits smooth responses with a handful of inputs where analytic statistics help. Reduced-order models fit field outputs governed by known equations. Neural surrogates earn their keep in high dimensions with abundant data, at the cost of extra machinery for uncertainty.
Selection by validation
Rather than choosing on intuition alone, fit several candidates and compare them by cross-validation error and calibration on the same data. This empirical bake-off is often more reliable than theory, especially when the response has unexpected structure. Ensembling several surrogates can beat any single one.
The complexity trade-off
More flexible surrogates fit complex responses but need more data and risk overfitting. Simpler surrogates generalize from little data but may miss structure. The bias-variance trade-off governs this balance; validation, not ambition, should set the model's complexity.
In practice
Kronos surrogate work starts simple - a Gaussian process or polynomial chaos on a Latin hypercube design of the machines - and escalates to reduced-order or neural surrogates only when dimensionality or field outputs demand it, with the final choice justified by validation and calibration, not preference.