An unsupervised learning approach to solving heat equations on chip based on Auto Encoder and Image Gradient
This addresses the need for efficient simulation in chip design, but it is incremental as it builds on existing PINN methods by adding generalization capabilities.
The paper tackles the problem of solving heat transfer equations on chip for 5G and AI systems by proposing an unsupervised learning approach that avoids data-hungry supervised methods and retraining issues in Physics Informed Neural Networks (PINN). It introduces a hybrid Auto Encoder and Image Gradient network that, with limited training on source terms, solves given problems and generalizes to unseen cases without retraining, though no concrete numerical results are provided.
Solving heat transfer equations on chip becomes very critical in the upcoming 5G and AI chip-package-systems. However, batches of simulations have to be performed for data driven supervised machine learning models. Data driven methods are data hungry, to address this, Physics Informed Neural Networks (PINN) have been proposed. However, vanilla PINN models solve one fixed heat equation at a time, so the models have to be retrained for heat equations with different source terms. Additionally, issues related to multi-objective optimization have to be resolved while using PINN to minimize the PDE residual, satisfy boundary conditions and fit the observed data etc. Therefore, this paper investigates an unsupervised learning approach for solving heat transfer equations on chip without using solution data and generalizing the trained network for predicting solutions for heat equations with unseen source terms. Specifically, a hybrid framework of Auto Encoder (AE) and Image Gradient (IG) based network is designed. The AE is used to encode different source terms of the heat equations. The IG based network implements a second order central difference algorithm for structured grids and minimizes the PDE residual. The effectiveness of the designed network is evaluated by solving heat equations for various use cases. It is proved that with limited number of source terms to train the AE network, the framework can not only solve the given heat transfer problems with a single training process, but also make reasonable predictions for unseen cases (heat equations with new source terms) without retraining.