Conformalized Physics-Informed Neural Networks
This addresses the need for reliable uncertainty estimates in PINNs for scientific computing applications, offering a computationally efficient alternative to ensemble or Bayesian methods.
The authors tackled the problem of uncertainty quantification in physics-informed neural networks (PINNs) by introducing Conformalized PINNs (C-PINNs), which provide statistically valid uncertainty intervals without additional assumptions.
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.