Enhanced surrogate modelling of heat conduction problems using physics-informed neural network framework

Solving partial differential equations (PDEs) using deep-learning techniques provides opportunities for surrogate models that require no labelled data, e.g., CFD results, from the domain interior other than the boundary and initial conditions. We propose a new ansatz of the solution incorporated with a physics-informed neural network (PINN) for solving PDEs to impose the boundary conditions (BCs) with hard constraints. This ansatz comprises three subnetworks: a boundary function, a distance function, and a deep neural network (DNN). The new model performance is assessed thoroughly in terms of convergence speed and accuracy. To this end, we apply the PINN models to conduction heat transfer problems with different geometries and BCs. The results of 1D, 2D and 3D problems are compared with conventional numerical methods and analytical results. The results reveal that the neural networks (NNs) model with the proposed ansatz outperforms counterpart PINN models in the literature and leads to faster convergence with better accuracy, especially for higher dimensions, i.e., three-dimensional case studies.

Automated summary

Using deep-learning techniques to solve partial differential equations (PDEs) allows for the development of surrogate models without the need for labeled data from the interior of the domain other than the boundary and initial conditions. A new solution approach incorporating a physics-informed neural network (PINN) is proposed, which enforces boundary conditions (BCs) with hard constraints. The proposed approach outperforms existing PINN models in terms of convergence speed and accuracy, especially for higher dimensions, as demonstrated through comparisons with conventional numerical methods and analytical results in 1D, 2D, and 3D conduction heat transfer problems.