We present a hybrid framework involving adaptive finite elements and deep neural networks to ultimately design a digital twin for laser melting and laser polishing processes.

In a first part, we consider generic parametric partial differential equations. We advocate a hybrid method that relies on deep neural network approximations to approximate the parameter-to-solution map. The neural network is trained with data generated from adaptive finite element simulations based on a posteriori error estimates. Our aim is to try to balance the errors coming from both the finite elements and the neural network approximations. Numerical results are presented for elliptic model problems, including briefly inverse problems for parameters identification.

In a second step, we introduce a computational framework for the solution of the full laser polishing problem (a multiphysics problem involving CFD, temperature and free surfaces). We introduce a method based on two neural networks to approximate the free surface and the temperature respectively. Numerical experiments are presented in two dimensions of space.

Joint work with Dr Maude Girardin, Prof. Marco Picasso (EPFL).


Contatto:
nicola.parolini@polimi.it