Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enhanced DeepONet for Modeling Partial Differential Operators
  Considering Multiple Input Functions   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.

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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th