Story 2 · silent surrogate failure

Where the shortcut breaks — and how to know

Fast surrogates assume the world changes smoothly. Mostly it does. But when two of a system's numbers approach each other, the modes behind them swap identities — and a smooth shortcut tracks the wrong thing, confidently.

Watch two numbers collide

The demo solves a small system live as you drag the design parameter. The symmetry toggle decides the collision's character: with symmetry, the two curves cross cleanly; break the symmetry, and they repel — an avoided crossing, where eigenvalue curves veer apart at close range.

Now add a lazy surrogate

The dashed line is what a cheap interpolant built from a few samples believes. Away from the collision it's fine. Near it, it's wrong exactly where the design is most sensitive — and nothing in the surrogate itself warns you. The shaded band is the region the research's error indicator flags: "do a real solve here."

Silent failure is the expensive kind: a flutter margin or a filter passband missed not because the model was bad everywhere, but because it was bad in the one narrow region that mattered.