  Big-data-based artificial intelligence (AI) supports profound evolution in
almost all of science and technology. However, modeling and forecasting
multi-physical systems remain a challenge due to unavoidable data scarcity and
noise. Improving the generalization ability of neural networks by "teaching"
domain knowledge and developing a new generation of models combined with the
physical laws have become promising areas of machine learning research.
Different from "deep" fully-connected neural networks embedded with physical
information (PINN), a novel shallow framework named physics-informed
convolutional network (PICN) is recommended from a CNN perspective, in which
the physical field is generated by a deconvolution layer and a single
convolution layer. The difference fields forming the physical operator are
constructed using the pre-trained shallow convolution layer. An efficient
linear interpolation network calculates the loss function involving boundary
conditions and the physical constraints in irregular geometry domains. The
effectiveness of the current development is illustrated through some numerical
cases involving the solving (and estimation) of nonlinear physical operator
equations and recovering physical information from noisy observations. Its
potential advantage in approximating physical fields with multi-frequency
components indicates that PICN may become an alternative neural network solver
in physics-informed machine learning.
