Evaluating Different Neural Networks Architectures for the Solution of Heat Conduction Problems in NVIDIA Modulus

Resumo

The use of neural networks to address engineering problems is increasing considerably. A limitation
of using neural networks is the need for large amounts of data to fit nonlinear problems with acceptable accuracy.
An alternative to the purely data-driven approach is the physics-informed neural networks, which add physical
constraints that significantly reduce the amount of data needed to achieve acceptable accuracy. In this work, we
solve two simple heat conduction problems using PINNs, evaluating the complexity of different neural network
architectures. A direct comparison to the analytical solution proved the PINNs to be good solvers for the evaluated

partial differential equations. A fully connected neural network (FCN) handles the problem well for the steady-
state case. However, a gated recursive unit (GRU) architecture is needed to solve a transient problem. For both

problems, an architecture of 6 layers with 64 units each is sufficient to achieve good results.