  Physics-informed neural networks (PINNs) are an influential method of solving
differential equations and estimating their parameters given data. However,
since they make use of neural networks, they provide only a point estimate of
differential equation parameters, as well as the solution at any given point,
without any measure of uncertainty. Ensemble and Bayesian methods have been
previously applied to quantify the uncertainty of PINNs, but these methods may
require making strong assumptions on the data-generating process, and can be
computationally expensive. Here, we introduce Conformalized PINNs (C-PINNs)
that, without making any additional assumptions, utilize the framework of
conformal prediction to quantify the uncertainty of PINNs by providing
intervals that have finite-sample, distribution-free statistical validity.
