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Convolutional Neural Operators

by B. Raonic and R. Molinaro and T. Rohner and S. Mishra and E. de Bézenac

(Report number 2023-11)

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.

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

@Techreport{RMRMd23_1048,
  author = {B. Raonic and R. Molinaro and T. Rohner and S. Mishra and E. de Bézenac},
  title = {Convolutional Neural Operators},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2023-11},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2023/2023-11.pdf },
  year = {2023}
}

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