An unsupervised learning approach to solving heat equations on chip based on Auto Encoder and Image Gradient

TL;DR

This paper introduces an unsupervised hybrid Auto Encoder and Image Gradient framework to solve heat equations on chips, capable of generalizing to unseen source terms without retraining, addressing limitations of existing PINN methods.

Contribution

The paper proposes a novel unsupervised learning approach combining Auto Encoder and Image Gradient networks to solve and generalize heat transfer equations on chips without solution data.

Findings

Successfully solves heat equations with limited training source terms.

Generalizes to unseen heat source cases without retraining.

Outperforms traditional PINN in flexibility and efficiency.

Abstract

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.