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.

翻译：尽管卷积神经网络架构在机器学习中取得了非常成功的应用，但由于被认为在函数空间上不具备一致性，这类架构在学习偏微分方程解算子领域长期被忽视。本文通过调整卷积神经网络架构，证明其确实能够以函数作为输入和输出。由此产生的架构称为卷积神经算子（CNOs），在基准实验中显著优于竞争模型，为设计替代性稳健且精确的算子学习框架开辟了道路。