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

Hong Wang, Wenkai Yang, Jie Wang, Huanshuo Dong, Zijie Geng, Zhen Huang, Depeng Xie, Zhezheng Hao, Hande Dong

TL;DR

This work tackles the heavy data-generation cost for neural-operator surrogates in IC thermal simulations by introducing BlocKOA, which leverages block Krylov methods and operator action to efficiently generate large, physics-consistent datasets. The approach first produces a compact set of basic solutions using a shared coefficient matrix with a block Krylov solver, then builds diverse temperature distributions from these bases and applies the discretized heat operator to obtain heat-source data without solving additional systems. Theoretical analysis shows BlocKOA reduces the dominant linear-system cost and, in practice, yields up to 420× faster data generation with machine-precision accuracy, enabling roughly 10× more data within the same time window and improving downstream NO training outcomes. This method has strong practical impact by removing a major bottleneck in data-driven IC thermal modeling, facilitating faster design optimization and more accurate surrogates. The results demonstrate robust speedups across problem scales, parameter variations, and boundary conditions, with clear guidelines on basis size, floorplan diversity, and noise for high-quality data generation.

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.

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

TL;DR

This work tackles the heavy data-generation cost for neural-operator surrogates in IC thermal simulations by introducing BlocKOA, which leverages block Krylov methods and operator action to efficiently generate large, physics-consistent datasets. The approach first produces a compact set of basic solutions using a shared coefficient matrix with a block Krylov solver, then builds diverse temperature distributions from these bases and applies the discretized heat operator to obtain heat-source data without solving additional systems. Theoretical analysis shows BlocKOA reduces the dominant linear-system cost and, in practice, yields up to 420× faster data generation with machine-precision accuracy, enabling roughly 10× more data within the same time window and improving downstream NO training outcomes. This method has strong practical impact by removing a major bottleneck in data-driven IC thermal modeling, facilitating faster design optimization and more accurate surrogates. The results demonstrate robust speedups across problem scales, parameter variations, and boundary conditions, with clear guidelines on basis size, floorplan diversity, and noise for high-quality data generation.

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.
Paper Structure (29 sections, 6 equations, 2 figures, 7 tables)

This paper contains 29 sections, 6 equations, 2 figures, 7 tables.

Table of Contents

  1. Introduction and Related Work
  2. Background
  3. Mathematical Form of IC Thermal Simulation
  4. Discretization for the Heat Equation
  5. Details of the Dataset
  6. Direct Solution Method
  7. Method
  8. Basic Solutions Generation
  9. Temperature Distributions Generation
  10. Operator Action
  11. Theoretical Analysis
  12. Computational Complexity Analysis
  13. Direct Solution Method
  14. BlocKOA Method
  15. Error Analysis
  16. ...and 14 more sections

Figures (2)

  • Figure 1: The typical generation process of the thermal simulation dataset: 1. Produce a collection of random parameters derived from chips 2. Generate the relevant chips using these parameters 3. Discretize the chips using the FEM 4. Solve linear systems 5. Acquire solutions for the linear systems and convert them into temperature distributions 6. Compile the data into a dataset.
  • Figure 2: Overview of the model architecture: the process of the existing direct solution method and our BlocKOA method.