Comparsion of Julia's GPU based ensemble ODE solvers with other open-source implementations in C++, JAX and PyTorch. These artifacts are part of the paper:

Automated Translation and Accelerated Solving of Differential Equations on Multiple GPU Platforms

NOTE: This repository is meant to contain scripts for benchmarking existing ensemble ODE solvers. For external purposes, one can directly use the solvers from the respective libraries.

The methods are written in Julia, and are part of the repository, https://github.com/SciML/DiffEqGPU.jl. The benchmark suite also consists of the raw data, such as simulation times and plots mentioned in the paper. The supported OS for the benchmark suite is Linux.

Firstly, we will need to install Julia. The user can download the binaries from the official JuliaLang website https://julialang.org/downloads/. Alternatively, one can use the convenience of a Julia version multiplexer, https://github.com/JuliaLang/juliaup. The recommended OS for installation is Linux. The recommended Julia installation version is v1.8. To use AMD GPUs, please install v1.9. The Julia installation should also be added to the user's path.

The user must install the GPU backend library for testing DiffEqGPU.jl-related code.

    julia> using Pkg
    julia> #Run either of them
    julia> Pkg.add("CUDA") # NVIDIA GPUs
    julia> Pkg.add("AMDGPU") #AMD GPUs
    julia> Pkg.add("oneAPI") #Intel GPUs
    julia> Pkg.add("Metal") #Apple M series GPUs

DiffEqGPU.jl is a test suite that regularly checks functionality by testing features like multiple backend support, event handling, and automatic differentiation. To test the functionality, one can follow the below instructions. The user needs to specify the "backend" for example "CUDA" for NVIDIA, "AMDGPU" for AMD, "oneAPI" for Intel and "Metal" for Apple GPUs. The estimated time of completion is 20 minutes.

    $ julia --project=.
    julia> using Pkg
    julia> Pkg.instantiate()
    julia> Pkg.precompile()

Finally test the package by this command

    $ backend="CUDA"
    $ julia --project=. test_DiffEqGPU.jl $backend

Additionally, the GitHub discussion https://github.com/SciML/DiffEqGPU.jl/issues/224#issuecomment-1453769679 highlights the use of textured memory with ODE solvers, accelerated the code by $2\times$ over CPU.

DiffEqGPU.jl is a fully featured library with regression testing, semver versioning, and version control. The tests are performed on cloud machines having a multitude of different GPUs https://buildkite.com/julialang/diffeqgpu-dot-jl/builds/705. These tests approximately completes in 30 minutes. The publicly visible testing framework serves as a testimonial of compatibility with multiple platforms and said features in the paper.

We will need to install CUDA.jl for benchmarking. It is the only backend compatible with the ODE solvers in JAX, PyTorch, and MPGOS. To do so, one can follow the below process in the Julia Terminal:

    $ julia
    julia> using Pkg
    julia> Pkg.add("CUDA")

Let's clone the benchmark suite repository to start benchmarking;

    $ git clone https://github.com/utkarsh530\
    /GPUODEBenchmarks.git

We will instantiate and pre-compile all the packages beforehand to avoid the wait times during benchmarking. The folder ./GPU_ODE_Julia contains all the related scripts for the GPU solvers.

    $ cd ./GPUODEBenchmarks
    $ julia --project=./GPU_ODE_Julia --threads=auto
    julia> using Pkg
    julia> Pkg.instantiate()
    julia> Pkg.precompile()
    julia> exit()

It may take a few minutes to complete (< 10 minutes). After this, we can generate the timings of ODE solvers written in Julia. There is a script to benchmark ODE solvers for the different number of trajectories to demonstrate scalability and performance. The script invocation and timings can be generated through the following:

    $ bash ./run_benchmark.sh -l julia -d gpu -m ode

It might take around 20 minutes to finish. The flag -n N can be used to specify the upper bound of the trajectories to benchmark. By default $N = 2^{24}$, where the simulation runs for $n \in 8 \le n &lt; N$, with the multiples of $4$.

The data will be generated in the data/Julia directory, with two files for fixed and adaptive time-stepping simulations. The first column in the ".txt" file will be the number of trajectories, and the section column will contain the time in milliseconds.

Additionally, to benchmark ODE solvers for other backends:

    $ N = $((2**24))
    Benchmark
    $ backend = "Metal"
    $ ./runner_scripts/gpu/run_ode_mult_device.sh\
    $N $backend

Benchmarking MPGOS ODE solverse requires the CUDA C++ compiler to be installed correctly. The recommended CUDA Toolkit version is >= 11. The installation can be checked through:

    $ nvcc
    If the installation exists, it will return 
    something like this:
    nvcc fatal   : No input files specified; 
    use option --help for more information

If nvcc is not found, the user needs to install CUDA Toolkit. The NVIDIA website lists out the resource https://developer.nvidia.com/cuda-downloads for installation.

The MPGOS scripts are in the GPU_ODE_MPGOS folder. The file GPU_ODE_MPGOS/Lorenz.cu is the main executed code. However, the MPGOS programs can be run with the same bash script by changing the arguments as:

    $ bash ./run_benchmark.sh -l cpp -d gpu -m ode

It will generate the data files in data/cpp folder.

Benchmarking JAX-based ODE solvers require installing Python 3.9 and conda. First, we will install all the Python packages for benchmarking:

    $ conda env create -f environment.yml
    $ conda activate venv_jax

It should install the correct version of JAX with CUDA enabled and the Diffrax library. The GitHub https://github.com/google/jax#installation is a guide to follow if the installation fails.

For our purposes, we can benchmark the solvers by:

    $ bash ./run_benchmark.sh -l jax -d gpu -m ode

Benchmarking PyTorch based ODE solvers is a similar process compared to JAX ones.

    $ conda env create -f environment.yml
    $ conda activate venv_torch

torchdiffeq does not fully support vectorized maps with ODE solvers. To circumvent this, we extended the functionality by rewriting some library parts. To download it:

    (venv_torch)$ pip uninstall torchdiffeq
    (venv_torch)$ pip uninstall torchdiffeq
    (venv_torch)$ pip install git+https://github.com/\
    utkarsh530/torchdiffeq.git@u/vmap

Then run the benchmarks by:

    $ bash ./run_benchmark.sh -l pytorch -d gpu -m ode

The benchmark suite can also be used to test the GPU acceleration of ODE solvers in comparison with CPUs. The process for generating simulation times for GPUs can be done by following the GPU section mentioned earlier. The following bash script allows the generation of CPU simulation times for ODEs:

    $ bash ./run_benchmark.sh -l julia -d cpu -m ode

The simulation times will be generated in data/CPU. Each of the workflow approximately takes around 20 minutes to finish.

The SDE solvers in Julia are benchmarked by comparing them to the CPU-accelerated simulation. This will benchmark the linear SDE with three states, as described in the "Benchmarks and case studies" section. To generate simulation times for GPU, do:

    $ bash ./run_benchmark.sh -l julia -d gpu -m sde

We can generate the simulation times for CPU accelerated codes through:

    $ bash ./run_benchmark.sh -l julia -d cpu -m sde

The results will get generated in data/SDE and data/CPU/SDE, taking around 10 minutes to complete.

Julia supports Message Passing Interface (MPI) to allow Single Program Multiple Data (SPMD) type parallel programming. The composability of the GPU ODE solvers enables seamless integration with MPI, enabling scaling the ODE solvers to clusters on multiple nodes.

    $ julia --project=./GPU_ODE_Julia
    julia> using Pkg
    # install MPI.jl
    julia> Pkg.add("MPI")

An example script solving the Lorenz problem for approximately 1 billion parameters is available in the MPI folder. A SLURM-based script is shown below.

    #!/bin/bash
    # Slurm Sbatch Options
    # Reqeust no. of GPUs/node
    #SBATCH --gres=gpu:volta:1
    # 1 process per node 
    #SBATCH -n 5 -N 5
    #SBATCH --output="./mpi_scatter_test.log-%j"
    # Loading the required module

    # MPI.jl requires memory pool disabled
    export JULIA_CUDA_MEMORY_POOL=none
    export JULIA_MPI_BINARY=system
    # Use local CUDA toolkit installation
    export JULIA_CUDA_USE_BINARYBUILDER=false

    source $HOME/.bashrc
    module load cuda mpi

    srun hostname > hostfile
    time mpiexec julia --project=./GPU_ODE_Julia\ 
    ./MPI/gpu_ode_mpi.jl

The plotting scripts to visualize the simulation times. The scripts are located in runner_scripts/plot folder. These scripts replicates the benchmark figures in the paper. The benchmark suite contains the simulation data generated by authors, which can be used to verify the plots. Various benchmarks can be plotted, which are described in the different sections. The plotting scripts are based on Julia. As a preliminary step:

    $ cd GPUODEBenchmarks
    $ julia project=.
    julia> using Pkg
    julia> Pkg.instantiate()
    julia> Pkg.precompile()

The plot comparison between Julia, C++, JAX, and PyTorch mentioned in the paper can be generated by using the below command:

    $ julia --project=. ./runner_scripts/plot\
    /plot_ode_comp.jl

The plot will get saved in plots folder.

Similarly, the other plots in the paper can generated by running the different scripts in the folder runner_scripts/plot.

    plot performance of GPU ODE solvers 
    with multiple backends
    $ julia --project=. ./runner_scripts/plot\
    /plot_mult_gpu.jl 
    plot GPU ODE solvers comparsion with CPUs
    $ julia --project=. ./runner_scripts/plot\
    /plot_ode_comp.jl 
    plot GPU SDE solvers comparsion with CPUs
    $ julia --project=. ./runner_scripts/plot\
    /plot_sde_comp.jl 
    plot CRN Network sim comparsion with CPUs
    $ julia --project=. ./runner_scripts/plot\
    /plot_sde_crn.jl 

To plot data generated by running the scripts, specify the location of the data as the argument to the mentioned command.

    $ julia --project=. ./runner_scripts/plot/\
    plot_mult_gpu.jl /path/to/data/