Physics Informed Neural Networks: Reducing Data Size Requirements via Hybrid Learning

Training physics informed neural networks (PINN) in a supervised manner requires enormous amounts of data. This is a strain on hard disk space and RAM. To decrease the amount of data required, and to increase accuracy, we can train a PINN using both supervised and unsupervised learning. In this method, we use a smaller dataset to nudge the PINN in the correct direction; then, the unsupervised training takes control to smooth out the final results and increase accuracy. While some research has been done using this hybrid approach, there is a gap in literature regarding the size of the requisite training set and the correct method to weigh the supervised and unsupervised losses. In this research, we used a hybrid approach to model the Allen-Cahn equation. We found that even applying a tiny weight to the unsupervised loss of 0.00255 was sufficient to dramatically increase the accuracy of our PINN.