HCP-PIGN: Efficient heat conduction prediction by physics-informed graph convolutional neural network

Abstract

This work proposes a novel surrogate model (noted as HCP-PIGN) combining two groups of neural networks: i.e., the physics-informed and the graph convolutional neural networks (noted as PINN and GCN). It aims to tackle the existing challenges: pixelated pre-processing of data and large amounts of training data. For predicting 2D steady-state heat conduction, the GCN acting as the prediction module, considering the interdependence between unstructured and neighboring nodes. The PINN serving as the physical constraint module, embeds governing equations into the neural network’s loss function. The HCP-PIGN model obtains precise predictions with diverse geometries and within milliseconds. The predictive performance of HCP-PIGN was further compared with three network structures: i.e., the physics-informed fully connected neural network (noted as FNN), purely data-driven based FNN, and GCN. The results indicate that HCP-PIGN has the lowest error of temperature field predictions, which are below 3 % and 1.3 % for the max and mean relative errors, respectively. The improvements of 28.1% and 34.6% in accuracy are achieved over the pure data-driven GCN, and the physics-driven FNN, respectively. Therefore, the proposed HCP-PIGN model improves the physical prior knowledge and model’s adaptabilities to geometry variations, resulting in superior performances.