Convolutional Neural Operators

Bogdan Raonic, Roberto Molinaro, Tobias Rohner, Siddhartha Mishra, Emmanuel de Bezenac

Keywords: PDEs, Neural Operators, Scientific Machine Learning, Convolutional Neural Networks

TL;DR: A new convolution based neural operator architecture is proposed for accurately and robustly learning solution operators of PDEs.

Abstract: Although very successfully used in machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of PDEs. Here, we adapt convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs. The resulting architecture, termed as convolutional neural operators (CNOs), is shown to significantly outperform competing models on benchmark experiments, paving the way for the design of an alternative robust and accurate framework for learning operators.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2302.01178/code)