  We propose a conservative energy method based on neural networks with
subdomains for solving variational problems (CENN), where the admissible
function satisfying the essential boundary condition without boundary penalty
is constructed by the radial basis function (RBF), particular solution neural
network, and general neural network. The loss term is the potential energy,
optimized based on the principle of minimum potential energy. The loss term at
the interfaces has the lower order derivative compared to the strong form PINN
with subdomains. The advantage of the proposed method is higher efficiency,
more accurate, and less hyperparameters than the strong form PINN with
subdomains. Another advantage of the proposed method is that it can apply to
complex geometries based on the special construction of the admissible
function. To analyze its performance, the proposed method CENN is used to model
representative PDEs, the examples include strong discontinuity, singularity,
complex boundary, non-linear, and heterogeneous problems. Furthermore, it
outperforms other methods when dealing with heterogeneous problems.
