Physics-Based Active Learning Boosts Neural Operator Training Efficiency

A new active learning algorithm, physics-based acquisition, reduces training data needs for neural operators solving partial differential equations. The method uses the PDE residual to guide sample selection, outperforming random acquisition in experiments with 1D Burgers and 2D compressible Navier-Stokes equations. It matches state-of-the-art data efficiency while injecting a physics inductive bias, ensuring simulation cost is spent where the model's physical understanding is weakest. The approach addresses a key bottleneck in neural operator training: high data requirements. The work is described in arXiv preprint 2605.21348.