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

computer methods in applied mechanics and engineering

CENN: Conservative energy method based on neural networks with  subdomains for solving variational problems involving heterogeneous and  complex geometries