Certified trust in cheap approximations.
Every engineering team replaces something expensive with something cheap: a full simulation with a surrogate, a bespoke analysis with a lookup of similar past cases. The hard question is never "is the cheap version close?" — it's "how do I know, this time, without paying for the expensive one?" This research builds methods that answer with a certificate.
Three questions this work answers
My simulations are too expensive to run everywhere.
An adaptive method that decides where the next expensive solve is worth it — and certifies the regions it skipped.
My fast surrogate is great… until it silently isn't.
Where systems change character — frequencies collide, modes swap — smooth shortcuts fail. This method flags exactly those regions.
My model reasons from similar past cases. Should I trust it?
A certificate that grades the evidence behind a prediction: if the supporting cases churn when the input wiggles, don't trust it.
New to the vocabulary?
All three stories revolve around eigenvalues — the numbers a physical system answers with when you ask it to vibrate, resonate, or settle. Five-minute tour, with sound →