AI and the World's Hard Problems · Theoretical computer science · arXiv · 2026-10-20
Parameter misspecification in physics-informed neural networks: A closed-form audit and its limits
Physics-informed neural networks are trained to minimize an equation's residual, so a low loss does not reveal a wrongly specified coefficient. The study estimates the coefficient by least squares from a single evaluation of the trained network, and the accuracy of this estimate is tied to a normalized residual. For Burgers' equation, a bootstrap-based test flagged 3 of 300 correctly specified networks. When the incorrect parameter also entered the network architecture, errors of up to 2% were not detected at the precision reached.