Random Resampling of Collocation Points Can Amplify Spectral Bias in PINNs

Random resampling of collocation points is standard practice in physics-informed neural network (PINN) training, and is widely expected to be especially beneficial for multi-scale problems where resolving fine-scale structure seems to demand sufficient coverage of the domain. We show that this expectation is misleading. Across a range of multi-scale PINN benchmarks, random resampling rapidly recovers the macro-scale solution but substantially delays high-frequency recovery. In contrast, fixed sampling recovers high-frequency components earlier, but introduces global distortion through collocation bias. This delay coincides with the regime where the variance of the residual gradient under resampling exceeds its mean magnitude. Guided by this diagnosis, we introduce spatial and temporal interpolations between fixed and random resampling that consistently reduce the delay in fine-scale recovery. These findings suggest that spectral bias in PINNs is not only a consequence of sparse collocation, but also a phenomenon shaped by how collocation points are resampled during training.