When you have a fast but imperfect analytical model and limited expensive simulation data, teaching a neural network to correct the analytical model's errors—or pre-training it on the analytical model first—can cut your data requirements dramatically.
This paper shows how to make machine learning models more data-efficient by combining cheap analytical equations with expensive high-fidelity simulations. Using Helmholtz resonators as a test case, the authors demonstrate two approaches: learning to correct analytical predictions, or distilling analytical knowledge into a neural network before fine-tuning with limited simulation data.