Deep energy method in topology optimization applications

This paper explores the possibilities of applying physics-informed neural networks (PINNs) in topology optimization (TO) by introducing a fully self-supervised TO framework that is based on PINNs. solves forward elasticity problem deep energy method (DEM). Instead training separate network to update density distribution, we leverage fact compliance minimization self-adjoint express element sensitivity directly terms displacement field from DEM model, and thus no additional needed for inverse problem. The moving asymptotes used as optimizer updating distribution. implementation Neumann, Dirichlet, periodic boundary conditions are described context model. Three numerical examples presented demonstrate capabilities: (1) Compliance 2D under different geometries loading, (2) 3D, (3) Maximization homogenized shear modulus design meta material unit cells. results show optimized designs DEM-based very comparable those generated finite method, shed light new way integrating PINN-based simulation methods into classical computational mechanics problems.