Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data

Abstract

Recently, surrogate models based on deep learning have attracted much attention for engineering analysis and optimization. As the construction of data pairs in most engineering problems is timeconsuming, data acquisition is becoming the predictive capability bottleneck of most deep surrogate models, which also exists in surrogate for thermal analysis and design. To address this issue, this paper develops a physics-informed convolutional neural network (CNN) for the thermal simulation surrogate. The network can learn a mapping from heat source layout to the steady-state temperature field without labeled data, which equals solving an entire family of partial difference equations (PDEs). To realize the physics-guided training without labeled data, we employ the heat conduction equation and finite difference method to construct the loss function. Since the solution is sensitive to boundary conditions, we properly impose hard constraints by padding in the Dirichlet and Neumann boundary conditions. In addition, the neural network architecture is well-designed to improve the prediction precision of the problem at hand, and pixel-level online hard example mining is introduced to overcome the imbalance of optimization difficulty in the computation domain. The experiments

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A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs

“…( 7)), since we cannot obtain the general solution u ∂Ω (x) analytically. Existing attempts are either meshdependent [10,47], which are time-consuming for high-dimensional and geometrically complex PDEs, or ad hoc methods for specific (geometrically simple) physical systems [30]. It is still lacking a unified hard-constraint framework for both geometrically complex PDEs and the most commonly used Dirichlet, Neumann, and Robin BCs.…”

Multi-fidelity surrogate modeling for temperature field prediction using deep convolution neural network

“…However, due to the limited representation ability of the model, especially in the high-dimensional prediction case such as temperature field prediction, these methods usually cannot meet the performance requirements in engineering systems. In recent years, deep learning (DL), which has powerful potential in solving high-dimensional and strongly nonlinear problems, has provided an alternative way for surrogate modeling [11,12,13,14,15]. The deep learning model represented by the convolutional neural network (CNN) [16,17] can extract both the local and global physical information of the system and thus provide good performance on temperature field prediction.…”