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Simple exponential growth ODE example #1

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2950ada
Simple exponential growth ODE example
ali-ramadhan Apr 20, 2021
5b30bf0
Fix GPU case
ali-ramadhan Apr 20, 2021
1740f86
Move iteration loop inside kernel
ali-ramadhan Apr 20, 2021
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312 changes: 312 additions & 0 deletions Manifest.toml
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8 changes: 8 additions & 0 deletions Project.toml
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name = "EnzymaticOcean"
uuid = "1e308aaf-769c-447f-af17-2df7aeedce0a"
version = "0.1.0"

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45 changes: 45 additions & 0 deletions examples/simple_ode.jl
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using KernelAbstractions
using CUDAKernels
using CUDA

@kernel function time_step!(x, k, Δt, N)
I = @index(Global)
for _ in 1:N
@inbounds x[I] = x[I] + Δt * k * x[I]
end
end

"""
simulate_exponential_growth(; x₀, k, Δt, N, device)

Simulates exponential growth according to the ODE

dx/dt = k * x, x(t = 0) = x₀

using forward Euler time stepping with time step `Δt` for `N` iterations.
"""
function simulate_exponential_growth(; x₀, k, Δt, N, device)

if device isa CPU
x = [x₀]
elseif device isa CUDADevice
x = CuArray([x₀])
end

time_step_kernel! = time_step!(device, 1)
event = time_step_kernel!(x, k, Δt, N, ndrange=1)
wait(event)

return CUDA.@allowscalar x[1]
end

# 1 kernel launch
@show simulate_exponential_growth(x₀=1.0, k=2.5, Δt=0.01, N=1, device=CPU())
@show simulate_exponential_growth(x₀=1.0, k=2.5, Δt=0.01, N=1, device=CUDADevice())

# iterative kernel launches
@show simulate_exponential_growth(x₀=1.0, k=2.5, Δt=0.01, N=100, device=CPU())
@show simulate_exponential_growth(x₀=1.0, k=2.5, Δt=0.01, N=100, device=CUDADevice())
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@glwagner glwagner Apr 21, 2021

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These three lines are now also a single kernel launch, right?


# Optimization problem:
# If x₀=1, Δt = 0.01, N = 100, and x(t = 1) = π then what is k?
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@glwagner glwagner Apr 21, 2021 •
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Should we add something like

using Enzyme

simulate_exponential_growth(k) = simulate_exponential_growth(; x₀=1.0, k=k, Δt=0.01, N=100, device=CPU())

@show autodiff(simulate_exponential_growth, Active(1.0))

to see what happens?

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@glwagner glwagner Apr 21, 2021

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Hmm, I realized I was a little confused. We need to define a loss function and take the gradient of that. Perhaps we can define a k_truth, and compare the result of the simulation at a given k_test? I'll make a comment on the kernel.

5 changes: 5 additions & 0 deletions src/EnzymaticOcean.jl
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module EnzymaticOcean

greet() = print("Hello World!")

end # module