  This research presents the development of an innovative algorithm tailored
for the adaptive sampling of residual points within the framework of
Physics-Informed Neural Networks (PINNs). By addressing the limitations
inherent in existing adaptive sampling techniques, our proposed methodology
introduces a direct mesh refinement approach that effectively ensures both
computational efficiency and adaptive point placement. Verification studies
were conducted to evaluate the performance of our algorithm, showcasing
reasonable agreement between the model based on our novel approach and
benchmark model results. Comparative analyses with established adaptive
resampling techniques demonstrated the superior performance of our approach,
particularly when implemented with higher refinement factor. Overall, our
findings highlight the enhancement of simulation accuracy achievable through
the application of our adaptive sampling algorithm for Physics-Informed Neural
Networks.
