The core idea
A surrogate model learns the input-output behavior of an expensive simulation from a set of sample runs. Once trained, it predicts new outputs almost instantly, trading a one-time training cost for near-free inference.
How they're built
You sample the real solver across a parameter grid, then fit an interpolator — radial basis functions, Gaussian processes, or neural networks. PolySim's built-in surrogate uses RBF interpolation with ridge regularization.
Reading the accuracy
Always evaluate a surrogate on held-out data (R², RMSE). A surrogate is only trustworthy inside the region it was trained on; extrapolation is where they fail silently.
When to use one
Reach for a surrogate in optimization loops, real-time dashboards, and design exploration — anywhere you'd otherwise re-run a slow solve thousands of times. Keep the full solver for final validation.