Accelerating IC Thermal Simulation Data Generation via Block Krylov and Operator Action

2025-10-27

AI Summary

To address the prohibitively high cost of generating high-fidelity training data for integrated circuit thermal simulation, this paper proposes a physics-constrained, efficient data synthesis method. Our approach uniquely couples the block Krylov algorithm with thermal operator application, enabling rapid computation of fundamental solutions to the heat equation and simultaneous generation—via linear superposition and thermal operator mapping—of physically consistent, large-scale temperature fields and their corresponding heat source distributions. Theoretical analysis shows a reduction of one order in computational complexity. Evaluated on 5,000 chip designs, the method achieves a 420× speedup: it generates training data in only 4% of the time required by conventional approaches while attaining equivalent model performance for neural operators. This substantially enhances the data supply efficiency and practical feasibility of data-driven thermal modeling techniques.

Technology Category

• Machine Learning: Kernel Methods
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Recent advances in data-driven approaches, such as neural operators (NOs), have shown substantial efficacy in reducing the solution time for integrated circuit (IC) thermal simulations. However, a limitation of these approaches is requiring a large amount of high-fidelity training data, such as chip parameters and temperature distributions, thereby incurring significant computational costs. To address this challenge, we propose a novel algorithm for the generation of IC thermal simulation data, named block Krylov and operator action (BlocKOA), which simultaneously accelerates the data generation process and enhances the precision of generated data. BlocKOA is specifically designed for IC applications. Initially, we use the block Krylov algorithm based on the structure of the heat equation to quickly obtain a few basic solutions. Then we combine them to get numerous temperature distributions that satisfy the physical constraints. Finally, we apply heat operators on these functions to determine the heat source distributions, efficiently generating precise data points. Theoretical analysis shows that the time complexity of BlocKOA is one order lower than the existing method. Experimental results further validate its efficiency, showing that BlocKOA achieves a 420-fold speedup in generating thermal simulation data for 5000 chips with varying physical parameters and IC structures. Even with just 4% of the generation time, data-driven approaches trained on the data generated by BlocKOA exhibits comparable performance to that using the existing method.

Problem

• Accelerates IC thermal simulation data generation process
• Reduces computational costs for training neural operators
• Enhances precision of generated thermal distribution data

Innovation

• Block Krylov algorithm accelerates basic solution generation
• Combining solutions creates temperature distributions with constraints
• Applying heat operators determines source distributions efficiently