Failure-informed adaptive sampling for PINNs, Part II: combining with re-sampling and subset simulation

Understand

This is the second part of our series works on failure-informed adaptive sampling for physic-informed neural networks (FI-PINNs).

• In our previous work \cite{gao2022failure}, we have presented an adaptive sampling framework by using the failure probability as the posterior error indicator, where the truncated Gaussian model has been adopted for estimating the indicator.
• In this work, we present two novel extensions to FI-PINNs.
• The first extension consist in combining with a re-sampling technique, so that the new algorithm can maintain a constant training size.