  One of the obstacles hindering the scaling-up of the initial successes of
machine learning in practical engineering applications is the dependence of the
accuracy on the size of the database that "drives" the algorithms.
Incorporating the already-known physical laws into the training process can
significantly reduce the size of the required database. In this study, we
establish a neural network-based computational framework to characterize the
finite deformation of elastic plates, which in classic theories is described by
the F\"oppl--von K\'arm\'an (FvK) equations with a set of boundary conditions
(BCs). A neural network is constructed by taking the spatial coordinates as the
input and the displacement field as the output to approximate the exact
solution of the FvK equations. The physical information (PDEs, BCs, and
potential energies) is then incorporated into the loss function, and a pseudo
dataset is sampled without knowing the exact solution to finally train the
neural network. The prediction accuracy of the modeling framework is carefully
examined by applying it to four different loading cases: in-plane tension with
non-uniformly distributed stretching forces, in-plane central-hole tension,
out-of-plane deflection, and buckling under compression. \hl{Three ways of
formulating the loss function are compared: 1) purely data-driven, 2)
PDE-based, and 3) energy-based. Through the comparison with the finite element
simulations, it is found that all the three approaches can characterize the
elastic deformation of plates with a satisfactory accuracy if trained properly.
Compared with incorporating the PDEs and BCs in the loss, using the total
potential energy shows certain advantage in terms of the simplicity of
hyperparameter tuning and the computational efficiency.
