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GPU-Accelerated Simulated Oscillator Ising/Potts Machine Solving Combinatorial Optimization Problems

Yilmaz Ege Gonul, Ceyhun Efe Kayan, Ilknur Mustafazade, Nagarajan Kandasamy, Baris Taskin

TL;DR

The paper tackles NP-hard COPs by developing a GPU-accelerated simulated oscillator Ising/Potts framework based on a modified Kuramoto model with SHIL and noise. It leverages CUDA to achieve massive parallelism, enabling precise phase dynamics simulation on large graphs and yielding up to ~$10^4$x CPU speedups while maintaining high accuracy on Max-Cut and Graph Coloring tasks. Key contributions include a detailed GPU implementation, annealing schedules, and a comprehensive benchmarking against CPU and prior GPU approaches, demonstrating scalable performance for dense and large-scale COP instances. The approach offers a practical digital realization of OIM/OPM with high fidelity and substantial potential for industrial and research applications in combinatorial optimization.

Abstract

Oscillator-based Ising machines (OIMs) and oscillator-based Potts machines (OPMs) have emerged as promising hardware accelerators for solving NP-hard combinatorial optimization problems by leveraging the phase dynamics of coupled oscillators. In this work, a GPU-accelerated simulated OIM/OPM digital computation framework capable of solving combinatorial optimization problems is presented. The proposed implementation harnesses the parallel processing capabilities of GPUs to simulate large-scale OIM/OPMs, leveraging the advantages of digital computing to offer high precision, programmability, and scalability. The performance of the proposed GPU framework is evaluated on the max-cut problems from the GSET benchmark dataset and graph coloring problems from the SATLIB benchmarks dataset, demonstrating competitive speed and accuracy in tackling large-scale problems. The results from simulations, reaching up to 11295x speed-up over CPUs with up to 99% accuracy, establish this framework as a scalable, massively parallelized, and high-fidelity digital realization of OIM/OPMs.

GPU-Accelerated Simulated Oscillator Ising/Potts Machine Solving Combinatorial Optimization Problems

TL;DR

The paper tackles NP-hard COPs by developing a GPU-accelerated simulated oscillator Ising/Potts framework based on a modified Kuramoto model with SHIL and noise. It leverages CUDA to achieve massive parallelism, enabling precise phase dynamics simulation on large graphs and yielding up to ~x CPU speedups while maintaining high accuracy on Max-Cut and Graph Coloring tasks. Key contributions include a detailed GPU implementation, annealing schedules, and a comprehensive benchmarking against CPU and prior GPU approaches, demonstrating scalable performance for dense and large-scale COP instances. The approach offers a practical digital realization of OIM/OPM with high fidelity and substantial potential for industrial and research applications in combinatorial optimization.

Abstract

Oscillator-based Ising machines (OIMs) and oscillator-based Potts machines (OPMs) have emerged as promising hardware accelerators for solving NP-hard combinatorial optimization problems by leveraging the phase dynamics of coupled oscillators. In this work, a GPU-accelerated simulated OIM/OPM digital computation framework capable of solving combinatorial optimization problems is presented. The proposed implementation harnesses the parallel processing capabilities of GPUs to simulate large-scale OIM/OPMs, leveraging the advantages of digital computing to offer high precision, programmability, and scalability. The performance of the proposed GPU framework is evaluated on the max-cut problems from the GSET benchmark dataset and graph coloring problems from the SATLIB benchmarks dataset, demonstrating competitive speed and accuracy in tackling large-scale problems. The results from simulations, reaching up to 11295x speed-up over CPUs with up to 99% accuracy, establish this framework as a scalable, massively parallelized, and high-fidelity digital realization of OIM/OPMs.

Paper Structure

This paper contains 21 sections, 6 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Technical Background
  3. Ising/Potts Models and Machines
  4. The Ising Model
  5. The Potts Model
  6. OIM and OPM based on the Kuramoto Model of Coupled Oscillators
  7. Mapping COPs to Ising/Potts Models
  8. Max-Cut Problem
  9. Graph Coloring Problem
  10. Sub-Harmonic Injection Locking (SHIL)
  11. Modified Kuramoto Model for Optimization
  12. GPU Implementation Details
  13. Numerical Simulation Algorithm
  14. CUDA Implementation
  15. CUDA Optimization Techniques
  16. ...and 6 more sections

Figures (3)

  • Figure 1: a) An example 9-node graph b) Problem mapped to a coupled oscillator array c) Energy minimization to ground states d) Max-cut of the graph e) 3-coloring of the graph
  • Figure 2: Ks parameter ramped up and down in a triangular waveform and the Ising hamiltonian pushed out of local minima to converge into lower energy states
  • Figure 3: a) Speed comparison of CPU vs GPU against the G-set benchmark problems b) Parameter sweep analysis on $K$ and $Ks_{max}$, and accuracy with each combination c) CPU vs GPU run-time scaling in log scale