TY - JOUR
T1 - Enhanced surrogate modelling of heat conduction problems using physics-informed neural network framework
AU - Manavi, Seyedalborz
AU - Becker, Thomas
AU - Fattahi, Ehsan
N1 - Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2023/3
Y1 - 2023/3
N2 - 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.
AB - 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.
KW - Hard constraint
KW - Hybrid enforcement
KW - Irregular geometries
KW - Machine learning
KW - Thermal simulation
UR - http://www.scopus.com/inward/record.url?scp=85147853374&partnerID=8YFLogxK
U2 - 10.1016/j.icheatmasstransfer.2023.106662
DO - 10.1016/j.icheatmasstransfer.2023.106662
M3 - Article
AN - SCOPUS:85147853374
SN - 0735-1933
VL - 142
JO - International Communications in Heat and Mass Transfer
JF - International Communications in Heat and Mass Transfer
M1 - 106662
ER -