Solving steady-state partial derivative equation with neural network - Application to steady-state heat transfer problem

This paper proposes to approximate the solution of Steady-state Partial Derivative Equations (SPDE) with a Feed Forward Artificial Neural Network, simply called Artificial Neural Network (ANN) in this paper. To realise this, we propose a special structure of ANN and an original way to train the ANN directly from its derivatives. The main advantage of this approximation is to obtain a solution of SPDE in form of non-linear functions (NLF). Because this solution can be easily included in VHDL-ANIS models, the method is certainly a way to introduce SPDE in multi-domain simulators. To validate our method, we applied it to a two-dimension steady-state heat transfer problem. ANN approximation is compared with the high precision solution of Finite Element Method (FEM). To conclude, the method presented in this paper is simple to implement, and seems to have several applications.