A neural network reduced order model for the elasticity problem

The work investigates two different approaches to solving the elasticity problem for material with inclusions. We apply the finite element method for the classic approach. Meanwhile, we also apply a neural network approach to construct a solver based on the solutions obtained firstly. This approach consists in training convolutional neural networks on a family of solutions represented as images. Based on the results of applying the two approaches, the effectiveness and applicability of the methods for solving the problem are demonstrated.