Physics-informed neural networks (PINN) have been proven efficient at solving partial differential equations (PDE). However, previous works have failed to provide guarantees on the worstcase residual error of a PINN across the spatiotemporal domain – a measure akin to the tolerance of numerical solvers – focusing instead on pointwise comparisons between their solution and the ones obtained by a solver at a set of inputs. In real-world applications, one cannot consider tests on a finite set of po…