ViT-Fourier Layer DeepONet: Effective Thermal Prediction Using Enhanced Deep Operator Networks with Fourier Layers and Vision Transformers

Abstract

For a long time, solving partial differential equations (PDEs) in physics has stimu- lated the development of various numerical methods and machine learning techniques. This paper aims to predict the temperature field of printed circuit boards (PCBs), the basic building blocks of many electronic devices, which is one of the important appli- cations of PDEs. To address these challenges, traditional numerical techniques such as finite difference methods (FDM) [1] and finite element methods (FEM) [2] have been widely used to provide robust and reliable solutions. Despite their success, these methods often face computational challenges. Additionally, traditional methods need to be solved for each new input and are typically used to represent a single input case, limiting their effectiveness when dealing with changing conditions. To over- come these limitations, we propose the ViT-Fourier Layer DeepONet, which utilizes the embeddings from Vision Transformers [3] in combination with the Fourier Neu- ral Operator (FNO) [4] for the branch network. The model consistently demonstrated superior predictive capabilities compared to Vanilla DeepONet in terms of lower test errors and elimination of overfitting issues, clearer distribution shapes, and improved prediction of high-temperature in small components. This makes it a fast and effective temperature prediction surrogate model.