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GPU accelerated solvers#492

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ErikQQY wants to merge 9 commits into
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qqy/gpu
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GPU accelerated solvers#492
ErikQQY wants to merge 9 commits into
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qqy/gpu

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@ErikQQY

@ErikQQY ErikQQY commented May 20, 2026 •
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Some TODOs:

  • Finalize the utimate APIs
  • Support for other FIRK solvers
  • Fix NonlinearSolve compatiability
  • Fix SparseMatrixColorings compatiability
  • Fix LinearSolve compatiability

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github-actions Bot commented May 20, 2026 •
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Benchmark Results

Click to check benchmark results
master 71eac75... master / 71eac75...
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK2() 0.645 ± 0.0094 s 0.645 ± 0.009 s 1 ± 0.02
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK3() 13.3 ± 1 ms 13.5 ± 1 ms 0.989 ± 0.11
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK4() 2.97 ± 0.53 ms 2.95 ± 0.54 ms 1.01 ± 0.26
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK5() 3.52 ± 0.63 ms 3.52 ± 0.64 ms 1 ± 0.26
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK6() 1.68 ± 0.35 ms 1.7 ± 0.35 ms 0.986 ± 0.29
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false) 1.69 ± 0.61 ms 1.68 ± 0.61 ms 1.01 ± 0.52
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true) 3.3 ± 1.1 ms 3.32 ± 1.1 ms 0.993 ± 0.47
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false) 0.0425 ± 0.0089 s 0.0427 ± 0.013 s 0.995 ± 0.36
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true) 0.0691 ± 0.021 s 0.0682 ± 0.023 s 1.01 ± 0.46
Simple Pendulum/IIP/Shooting(Tsit5()) 0.249 ± 0.087 ms 0.254 ± 0.086 ms 0.979 ± 0.47
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK2() 0.81 ± 0.021 s 0.821 ± 0.014 s 0.986 ± 0.031
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK3() 17.8 ± 6 ms 17.3 ± 6.3 ms 1.03 ± 0.51
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK4() 3.52 ± 0.3 ms 3.55 ± 0.2 ms 0.992 ± 0.1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK5() 4.29 ± 0.36 ms 4.32 ± 0.35 ms 0.993 ± 0.11
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK6() 2.01 ± 0.47 ms 2.04 ± 0.49 ms 0.988 ± 0.33
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false) 3.88 ± 3.2 ms 3.99 ± 3.2 ms 0.973 ± 1.1
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true) 7.26 ± 6.8 ms 7.55 ± 6.4 ms 0.962 ± 1.2
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false) 0.103 ± 0.0097 s 0.115 ± 0.022 s 0.897 ± 0.19
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true) 0.156 ± 0.016 s 0.159 ± 0.012 s 0.982 ± 0.12
Simple Pendulum/OOP/Shooting(Tsit5()) 0.637 ± 0.11 ms 0.651 ± 0.14 ms 0.977 ± 0.27
time_to_load 6.27 ± 0.061 s 6.24 ± 0.043 s 1 ± 0.012
### Benchmark Plots A plot of the benchmark results has been uploaded as an artifact to the workflow run for this PR. Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

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github-actions Bot commented Jun 16, 2026 •
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Benchmark Results (Julia v1.11)

Time benchmarks
master 5e3bc7c... master / 5e3bc7c...
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK2() 0.664 ± 0.0096 s 0.655 ± 0.0068 s 1.01 ± 0.018
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK3() 13.3 ± 0.38 ms 13.3 ± 0.38 ms 0.997 ± 0.041
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK4() 2.84 ± 0.069 ms 2.83 ± 0.096 ms 1 ± 0.042
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK5() 3.51 ± 0.13 ms 3.53 ± 0.18 ms 0.993 ± 0.061
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK6() 1.68 ± 0.068 ms 1.68 ± 0.076 ms 0.998 ± 0.061
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false) 1.62 ± 0.11 ms 1.64 ± 0.11 ms 0.984 ± 0.095
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true) 3.24 ± 0.18 ms 3.31 ± 0.19 ms 0.978 ± 0.078
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false) 0.043 ± 0.0041 s 0.0429 ± 0.0035 s 1 ± 0.13
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true) 0.0668 ± 0.0022 s 0.0661 ± 0.0022 s 1.01 ± 0.047
Simple Pendulum/IIP/Shooting(Tsit5()) 0.182 ± 0.084 ms 0.181 ± 0.085 ms 1 ± 0.66
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK2() 0.816 ± 0.0031 s 0.87 ± 0.0078 s 0.939 ± 0.0091
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK3() 22 ± 6.7 ms 18.1 ± 7.4 ms 1.22 ± 0.62
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK4() 3.54 ± 0.22 ms 3.52 ± 0.16 ms 1.01 ± 0.078
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK5() 4.23 ± 0.23 ms 4.26 ± 0.27 ms 0.993 ± 0.082
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK6() 1.99 ± 0.13 ms 1.99 ± 0.14 ms 1 ± 0.097
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false) 3.72 ± 0.68 ms 3.83 ± 0.85 ms 0.97 ± 0.28
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true) 7.08 ± 6.6 ms 7.12 ± 6.7 ms 0.995 ± 1.3
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false) 0.106 ± 0.0045 s 0.101 ± 0.0047 s 1.06 ± 0.066
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true) 0.162 ± 0.011 s 0.155 ± 0.007 s 1.05 ± 0.086
Simple Pendulum/OOP/Shooting(Tsit5()) 0.642 ± 0.047 ms 0.648 ± 0.079 ms 0.991 ± 0.14
time_to_load 7.02 ± 0.082 s 6.97 ± 0.048 s 1.01 ± 0.014
Memory benchmarks
master 5e3bc7c... master / 5e3bc7c...
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK2() 0.389 M allocs: 0.0442 GB 0.389 M allocs: 0.0442 GB 1
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK3() 0.0436 M allocs: 4.87 MB 0.0436 M allocs: 4.87 MB 1
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK4() 15.7 k allocs: 1.64 MB 15.7 k allocs: 1.64 MB 1
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK5() 22.1 k allocs: 2.03 MB 22.1 k allocs: 2.03 MB 1
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK6() 12.8 k allocs: 1.04 MB 12.8 k allocs: 1.04 MB 1
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false) 25.5 k allocs: 1.82 MB 25.5 k allocs: 1.82 MB 1
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true) 0.0491 M allocs: 3.39 MB 0.0491 M allocs: 3.39 MB 1
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false) 0.553 M allocs: 0.0535 GB 0.553 M allocs: 0.0535 GB 1
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true) 0.833 M allocs: 0.0778 GB 0.833 M allocs: 0.0778 GB 1
Simple Pendulum/IIP/Shooting(Tsit5()) 4.63 k allocs: 0.224 MB 4.63 k allocs: 0.224 MB 1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK2() 0.89 M allocs: 0.984 GB 0.89 M allocs: 0.984 GB 1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK3() 0.0932 M allocs: 24.8 MB 0.0932 M allocs: 24.8 MB 1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK4() 0.0324 M allocs: 3.95 MB 0.0324 M allocs: 3.95 MB 1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK5() 0.045 M allocs: 4.98 MB 0.045 M allocs: 4.98 MB 1
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK6() 25.3 k allocs: 2.17 MB 25.3 k allocs: 2.17 MB 1
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false) 0.142 M allocs: 10.2 MB 0.142 M allocs: 10.2 MB 1
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true) 0.266 M allocs: 18.7 MB 0.266 M allocs: 18.7 MB 1
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false) 2.52 M allocs: 0.279 GB 2.52 M allocs: 0.279 GB 1
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true) 3.82 M allocs: 0.404 GB 3.82 M allocs: 0.404 GB 1
Simple Pendulum/OOP/Shooting(Tsit5()) 0.0373 M allocs: 1.69 MB 0.0373 M allocs: 1.69 MB 1
time_to_load 0.159 k allocs: 11.2 kB 0.159 k allocs: 11.2 kB 1

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