Enhanced DeepONet for Modeling Partial Differential Operators Considering Multiple Input Functions
Enhanced DeepONet for Modeling Partial Differential Operators Considering Multiple Input Functions
复制标题
用于考虑多个输入函数的偏微分算子建模的增强型 DeepONet
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Liang Chen
中科院分区：
文献类型：
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作者：
Lesley Tan;Liang Chen
机器学习，特别是深度学习，由于在各种认知应用中的突破性表现而备受关注。最近，神经网络（NN）已被广泛探索，以模拟偏微分方程，神经网络可以被视为非线性函数的通用逼近器。提出了一种深度网络算子（DeepONet）架构，用于建模偏微分方程（PDE）的一般非线性连续算子，因为它比现有主流深度神经网络架构具有更好的泛化能力。然而，现有的DeepONet只能接受一个输入函数，这限制了它的应用。在这项工作中，我们探索了DeepONet架构，以扩展它来接受两个或更多的输入函数。我们提出了一种新的增强型DeepONet或EDeepONet高级神经网络结构，其中两个输入函数由两个分支DNN子网络表示，然后通过内积与输出卡车网络连接，以生成整个神经网络的输出。所提出的EDeepONet结构可以很容易地扩展到处理多个输入功能。我们对两个偏微分方程示例进行建模的数值结果表明，所提出的增强型DeepONet比完全连接的神经网络精确约7倍至17倍或约一个数量级，并且在训练和测试方面比简单的扩展DeepONet精确约2倍至3倍。
Machine learning, especially deep learning is gaining much attention due to the breakthrough performance in various cognitive applications. Recently, neural networks (NN) have been intensively explored to model partial differential equations as NN can be viewed as universal approximators for nonlinear functions. A deep network operator (DeepONet) architecture was proposed to model the general non-linear continuous operators for partial differential equations (PDE) due to its better generalization capabilities than existing mainstream deep neural network architectures. However, existing DeepONet can only accept one input function, which limits its application. In this work, we explore the DeepONet architecture to extend it to accept two or more input functions. We propose new Enhanced DeepONet or EDeepONet high-level neural network structure, in which two input functions are represented by two branch DNN sub-networks, which are then connected with output truck network via inner product to generate the output of the whole neural network. The proposed EDeepONet structure can be easily extended to deal with multiple input functions. Our numerical results on modeling two partial differential equation examples shows that the proposed enhanced DeepONet is about 7X-17X or about one order of magnitude more accurate than the fully connected neural network and is about 2X-3X more accurate than a simple extended DeepONet for both training and test.