  Physics-Informed Neural Networks (PINNs) are gaining popularity as a method
for solving differential equations. While being more feasible in some contexts
than the classical numerical techniques, PINNs still lack credibility. A remedy
for that can be found in Uncertainty Quantification (UQ) which is just
beginning to emerge in the context of PINNs. Assessing how well the trained
PINN complies with imposed differential equation is the key to tackling
uncertainty, yet there is lack of comprehensive methodology for this task. We
propose a framework for UQ in Bayesian PINNs (B-PINNs) that incorporates the
discrepancy between the B-PINN solution and the unknown true solution. We
exploit recent results on error bounds for PINNs on linear dynamical systems
and demonstrate the predictive uncertainty on a class of linear ODEs.
