Brief

Researchers have developed a new framework called Cut-DeepONet to improve how neural operators handle discontinuities and sharp transitions in partial differential equations. This method partitions the domain into smooth regions and represents discontinuities in a higher-dimensional space, avoiding direct approximation. Experiments show Cut-DeepONet outperforms existing methods, even with low-resolution data, by using fewer parameters and changing the problem's representation. AI

Researchers have developed a new active learning technique called physics-based acquisition to improve the efficiency of training neural operators for solving partial differential equations. This method uses the equation's residual to intelligently select the most informative data samples, reducing the overall data requirements for training. Experiments on the 1D Burgers equation and 2D compressible Navier-Stokes equations demonstrate that this approach outperforms random acquisition and matches state-of-the-art data efficiency while incorporating a physics-based inductive bias. AI