Multithreading

Tutorial by Jonas Wilfert, Tobias Thummerer

🚧 This tutorial is under revision and will be replaced by an up-to-date version soon 🚧

License

# Copyright (c) 2021 Tobias Thummerer, Lars Mikelsons, Josef Kircher, Johannes Stoljar, Jonas Wilfert
# Licensed under the MIT license. 
# See LICENSE (https://github.com/thummeto/FMI.jl/blob/main/LICENSE) file in the project root for details.

Motivation

This Julia Package FMI.jl is motivated by the use of simulation models in Julia. Here the FMI specification is implemented. FMI (Functional Mock-up Interface) is a free standard (fmi-standard.org) that defines a container and an interface to exchange dynamic models using a combination of XML files, binaries and C code zipped into a single file. The user can thus use simulation models in the form of an FMU (Functional Mock-up Units). Besides loading the FMU, the user can also set values for parameters and states and simulate the FMU both as co-simulation and model exchange simulation.

Introduction to the example

This example shows how to parallelize the computation of an FMU in FMI.jl. We can compute a batch of FMU-evaluations in parallel with different initial settings. Parallelization can be achieved using multithreading or using multiprocessing. This example shows multithreading, check multiprocessing.ipynb for multiprocessing. Advantage of multithreading is a lower communication overhead as well as lower RAM usage. However in some cases multiprocessing can be faster as the garbage collector is not shared.

The model used is a one-dimensional spring pendulum with friction. The object-orientated structure of the SpringFrictionPendulum1D can be seen in the following graphic.

Target group

The example is primarily intended for users who work in the field of simulations. The example wants to show how simple it is to use FMUs in Julia.

Other formats

Besides, this Jupyter Notebook there is also a Julia file with the same name, which contains only the code cells and for the documentation there is a Markdown file corresponding to the notebook.

Getting started

Installation prerequisites

Code section

To run the example, the previously installed packages must be included.

# imports
using FMI
using FMIZoo
using Folds
using BenchmarkTools
using DifferentialEquations

First, check the amount of available threads:

Threads.nthreads()

1

If the number of available threads doesn't match your expections, you can increase the number of threads available to the Julia process like described here.

Simulation setup

Next, the start time and end time of the simulation are set. Here we also decide the size of the batch.

t_start = 0.0
t_step = 0.1
t_stop = 10.0
tspan = (t_start, t_stop)
tData = collect(t_start:t_step:t_stop)

# Best if batchSize is a multiple of the threads/cores
batchSize = Threads.nthreads()

# Define an array of arrays randomly
input_values = collect(collect.(eachrow(rand(batchSize,2))))

1-element Vector{Vector{Float64}}:
 [0.8114274503172423, 0.6711929928134508]

We need to instantiate one FMU for each parallel execution, as they cannot be easily shared among different threads.

# a single FMU to compare the performance
realFMU = loadFMU("SpringPendulum1D", "Dymola", "2022x")

# the FMU batch
realFMUBatch = [loadFMU("SpringPendulum1D", "Dymola", "2022x") for _ in 1:batchSize]

1-element Vector{FMU2}:
 Model name:	SpringPendulum1D
Type:		1

We define a helper function to calculate the FMU solution and combine it into an Matrix.

function runCalcFormatted(fmu::FMU2, x0::Vector{Float64}, recordValues::Vector{String}=["mass.s", "mass.v"])
    data = simulateME(fmu, tspan; recordValues=recordValues, saveat=tData, x0=x0, showProgress=false, dtmax=1e-4)
    return reduce(hcat, data.states.u)
end

runCalcFormatted (generic function with 2 methods)

Running a single evaluation is pretty quick, therefore the speed can be better tested with BenchmarkTools.

@benchmark data = runCalcFormatted(realFMU, rand(2))

BenchmarkTools.Trial: 2 samples with 1 evaluation.
 Range (min … max):  3.169 s …  3.174 s  ┊ GC (min … max): 0.35% … 0.73%
 Time  (median):     3.172 s             ┊ GC (median):    0.54%
 Time  (mean ± σ):   3.172 s ± 3.615 ms  ┊ GC (mean ± σ):  0.54% ± 0.27%

  █                                                      █  
  █▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁█ ▁
  3.17 s        Histogram: frequency by time        3.17 s <

 Memory estimate: 300.75 MiB, allocs estimate: 7602418.

Single Threaded Batch Execution

To compute a batch we can collect multiple evaluations. In a single threaded context we can use the same FMU for every call.

println("Single Threaded")
@benchmark collect(runCalcFormatted(realFMU, i) for i in input_values)

Single Threaded





BenchmarkTools.Trial: 2 samples with 1 evaluation.
 Range (min … max):  3.200 s …  3.201 s  ┊ GC (min … max): 0.42% … 0.35%
 Time  (median):     3.200 s             ┊ GC (median):    0.39%
 Time  (mean ± σ):   3.200 s ± 1.134 ms  ┊ GC (mean ± σ):  0.39% ± 0.05%

  █                                                      █  
  █▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁█ ▁
  3.2 s         Histogram: frequency by time         3.2 s <

 Memory estimate: 300.75 MiB, allocs estimate: 7602421.

Multithreaded Batch Execution

In a multithreaded context we have to provide each thread it's own fmu, as they are not thread safe. To spread the execution of a function to multiple threads, the library Folds can be used.

println("Multi Threaded")
@benchmark Folds.collect(runCalcFormatted(fmu, i) for (fmu, i) in zip(realFMUBatch, input_values))

Multi Threaded





BenchmarkTools.Trial: 2 samples with 1 evaluation.
 Range (min … max):  3.213 s …  3.217 s  ┊ GC (min … max): 0.40% … 0.35%
 Time  (median):     3.215 s             ┊ GC (median):    0.37%
 Time  (mean ± σ):   3.215 s ± 2.921 ms  ┊ GC (mean ± σ):  0.37% ± 0.04%

  █                                                      █  
  █▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁█ ▁
  3.21 s        Histogram: frequency by time        3.22 s <

 Memory estimate: 300.75 MiB, allocs estimate: 7602436.

As you can see, there is a significant speed-up in the median execution time. But: The speed-up is often much smaller than Threads.nthreads(), this has different reasons. For a rule of thumb, the speed-up should be around n/2 on a n-core-processor with n threads for the Julia process.

Unload FMU

After calculating the data, the FMU is unloaded and all unpacked data on disc is removed.

unloadFMU(realFMU)
unloadFMU.(realFMUBatch)

1-element Vector{Nothing}:
 nothing

Summary

In this tutorial it is shown how multi threading with Folds.jl can be used to improve the performance for calculating a Batch of FMUs.