  In this article, we present an efficient deep learning method called coupled
deep neural networks (CDNNs) for coupled physical problems. Our method compiles
the interface conditions of the coupled PDEs into the networks properly and can
be served as an efficient alternative to the complex coupled problems. To
impose energy conservation constraints, the CDNNs utilize simple fully
connected layers and a custom loss function to perform the model training
process as well as the physical property of the exact solution. The approach
can be beneficial for the following reasons: Firstly, we sampled randomly and
only input spatial coordinates without being restricted by the nature of
samples. Secondly, our method is meshfree which makes it more efficient than
the traditional methods. Finally, our method is parallel and can solve multiple
variables independently at the same time. We give the theory to guarantee the
convergence of the loss function and the convergence of the neural networks to
the exact solution. Some numerical experiments are performed and discussed to
demonstrate the performance of the proposed method.
