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Scaling the semidefinite program solver SDPB

Walter Landry, David Simmons-Duffin

TL;DR

The paper presents SDPB 2.0, a scalable semidefinite program solver engineered for the conformal bootstrap by replacing OpenMP/MPACK with MPI/Elemental for distributed, arbitrary-precision computation. It details load balancing, global reductions, and memory management improvements that enable solving much larger bootstrap problems across hundreds of cores on multiple nodes, and demonstrates speedups over the previous version on 3d Ising and O(2) benchmarks. correctness checks confirm consistent results with the older version while achieving substantial performance gains. Future work targets precision management, MPI optimization, and potential GPU acceleration to push scalability further.

Abstract

We present enhancements to SDPB, an open source, parallelized, arbitrary precision semidefinite program solver designed for the conformal bootstrap. The main enhancement is significantly improved performance and scalability using the Elemental library and MPI. The result is a new version of SDPB that runs on multiple nodes with hundreds of cores with excellent scaling, making it practical to solve larger problems. We demonstrate performance on a moderate-size problem in the 3d Ising CFT and a much larger problem in the $O(2)$ Model.

Scaling the semidefinite program solver SDPB

TL;DR

The paper presents SDPB 2.0, a scalable semidefinite program solver engineered for the conformal bootstrap by replacing OpenMP/MPACK with MPI/Elemental for distributed, arbitrary-precision computation. It details load balancing, global reductions, and memory management improvements that enable solving much larger bootstrap problems across hundreds of cores on multiple nodes, and demonstrates speedups over the previous version on 3d Ising and O(2) benchmarks. correctness checks confirm consistent results with the older version while achieving substantial performance gains. Future work targets precision management, MPI optimization, and potential GPU acceleration to push scalability further.

Abstract

We present enhancements to SDPB, an open source, parallelized, arbitrary precision semidefinite program solver designed for the conformal bootstrap. The main enhancement is significantly improved performance and scalability using the Elemental library and MPI. The result is a new version of SDPB that runs on multiple nodes with hundreds of cores with excellent scaling, making it practical to solve larger problems. We demonstrate performance on a moderate-size problem in the 3d Ising CFT and a much larger problem in the Model.

Paper Structure

This paper contains 12 sections, 8 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Elemental and MPI
  4. Parallelization strategy
  5. Block timings
  6. Load balancing
  7. Global operations
  8. Memory Optimization
  9. Change to primal error
  10. Correctness check
  11. Benchmarks
  12. Future directions

Figures (2)

  • Figure 1: Time to compute the second iteration of an Ising model with 117 blocks (as in Simmons-Duffin:2015qma) and an O(2) model with 261 blocks on the Yale Grace cluster. SDPB 1.0 is limited to the number of cores on a single node (28), while SDPB 2.0 can scale across multiple nodes.
  • Figure 2: Maximum memory used on a node for the computation in Figure \ref{['fig:Scaling-Time']}.