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

Understand

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.