surrogatemodels
LearnUnit 3 of 9Basics5 lessons

Fitting and testing

The core of every surrogate, before any neural network: fit a function to data, test it on runs it has never seen, and measure the error properly. Then the two classical workhorses, Gaussian processes and reduced-order models.

Start the unit Regression, honest tests, error
  1. 3.1Fitting a response surfaceA surrogate is a function with parameters, chosen so its predictions match the data.
  2. 3.2Train, validation and testJudge a model only on designs it has never seen, and split by design, never by point.
  3. 3.3Measuring errorRMSE, relative L2, R² and max error: which number to report, and what each one hides.
  4. 3.4Gaussian processesA smooth fit that also says how unsure it is, and becomes more unsure away from the data.
  5. 3.5Compressing fields: PODA field is often a few dominant shapes plus small corrections: predict the shapes’ weights instead of every value.

You can thenFit and test a scalar surrogate honestly.

samples · mean · uncertainty grows between samples
A few samples, a smooth fit, and an error measured on runs it has never seen.
Read and buildRead
Design and Analysis of Computer ExperimentsSacks, Welch, Mitchell, Wynn · Statistical Science 1989 ↗A Visual Exploration of Gaussian ProcessesGörtler, Kehlbeck, Deussen · Distill 2019 ↗

BuildFit a polynomial and a Gaussian process to lift against angle of attack and sweep, and report RMSE and relative L2 error on held-out runs.

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