One of the best things about probabilistic machine learning is that it doesn’t just give you an answer — it tells you how sure it is about that answer. Gaussian processes (GPs) are the go-to model for this because they treat unknown functions as probability distributions, and they let us do some really handy things like conditioning on data, taking derivatives, and keeping all the maths neat and analytical.

Now, if you take a GP and combine it with the actual equations that describe your physical system, you get what’s called a physics-informed Gaussian process. In this post, you’ll see how we can combined the Euler–Bernoulli beam equation with a multi-output GP to jointly work out deflections, rotations, strains, and internal forces in a beam — and even update uncertain material parameters — straight from observed data. This has been presented during the IABSE Symposium in Prague, CZ. A preprint of the paper is available at arXiv.