Sobolev Training for Operator Learning

arXiv:2402.09084v1 Announce Type: new
Abstract: 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.

abstract arxiv cs.ai cs.lg derivatives framework frameworks function impact information loss meshes novel performance process research study training type