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:虽然在机器学习中非常成功地使用,但是在PDE的学习解决方案操作者中,以神经网络结构(在功能空间中被认为不一致)为基础的神经网络结构,基本上被忽略了。在这里,我们调整了神经网络,以表明这些网络确实能够作为投入和产出处理功能。 由此形成的结构,被称为神经神经操作者(CNOs),明显优于基准实验中相互竞争的模式,为设计一个强有力和准确的学习操作者备选框架铺平了道路。