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MathChief t1_izgdz7x wrote

Reply to comment by martenlienen in [R] torchode: A Parallel ODE Solver for PyTorch by martenlienen

One more question: for the Van der Pol benchmark

Using the old faithful ode45 in MATLAB (Runge-Kutta) to run test problem you listed in the poster

vdp1 = @(t, y) [y(2); 25*(1-y(1)^2)*y(2)-y(1)];
tic;
[t,y] = ode45(vdp1,[0 5],[1.2, 0.1]);
toc;

It takes only 0.007329 seconds for marching 389 steps using FP64 on CPU. What is the loop time's unit? What is the bottleneck of the implemented algorithm?

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martenlienen OP t1_izi8k3g wrote

First, the difference in steps is probably due to different tolerances in the step size controller.

The loop times is measured in milliseconds. Of course, that is much slower than what you got in matlab. The difference is that we did all benchmarks on GPU, because that is the usual mode for deep learning even though it is certainly inappropriate for the VdP equation if you were interested in it for anything else but benchmarking the inner loop of an ODE solver on a GPU. I think, you can get similar numbers to your matlab code in diffrax with JIT compilation on a CPU. However, you won't get it with torchode because PyTorch's JIT is not as good as JAX's and specifically this line is really slow on CPUs. Nonetheless, after comparing several alternatives we chose this because, as I said, in practice in most of deep learning only GPU performance matters.

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