Sobolev Training for Operator Learning
This addresses the challenge of approximating solution operators between infinite-dimensional spaces in operator learning, with incremental improvements to existing methods.
The study tackled the problem of improving model performance in operator learning by integrating derivative information into the loss function, resulting in enhanced training and a novel framework for approximating derivatives on irregular meshes, supported by experimental and theoretical evidence.
This study investigates the impact of Sobolev Training on operator learning frameworks for improving model performance. Our research reveals that integrating derivative information into the loss function enhances the training process, and we propose a novel framework to approximate derivatives on irregular meshes in operator learning. Our findings are supported by both experimental evidence and theoretical analysis. This demonstrates the effectiveness of Sobolev Training in approximating the solution operators between infinite-dimensional spaces.