Christopher Rackauckas ChrisRackauckas

Torchdiffeq vs DifferentialEquations.jl (/ DiffEqFlux.jl) Neural ODE Compatible Solver Benchmarks

Only non-stiff ODE solvers are tested since torchdiffeq does not have methods for stiff ODEs. The ODEs are chosen to be representative of models seen in physics and model-informed drug development (MIDD) studies (quantiative systems pharmacology) in order to capture the performance on realistic scenarios.

Summary

Below are the timings relative to the fastest method (lower is better). For approximately 1 million ODEs and less, torchdiffeq was more than an order of magnitude slower than DifferentialEquations.jl

	[deps]
	ApproxFun = "28f2ccd6-bb30-5033-b560-165f7b14dc2f"
	ArrayInterface = "1f957be0-811d-5197-a864-00d3e8faeebd"
	Atom = "c52e3926-4ff0-5f6e-af25-54175e0327b1"
	BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
	BoundaryValueDiffEq = "764a87c0-6b3e-53db-9096-fe964310641d"
	CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
	CUDAapi = "3895d2a7-ec45-59b8-82bb-cfc6a382f9b3"
	CUDAnative = "be33ccc6-a3ff-5ff2-a52e-74243cff1e17"
	Calculus = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"

	[[ASTInterpreter2]]
	deps = ["DebuggerFramework"]
	git-tree-sha1 = "8df3d36e0286777d226f4fd4956a432b73425186"
	uuid = "e6d88f4b-b52a-544c-a8d3-7a4f12cb39c3"
	version = "0.1.1"

	[[AbstractFFTs]]
	deps = ["Compat", "LinearAlgebra"]
	git-tree-sha1 = "8d59c3b1463b5e0ad05a3698167f85fac90e184d"
	uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"

	using Sundials, DiffEqBase
	function lorenz(du,u,p,t)
	du[1] = 10.0*(u[2]-u[1])
	du[2] = u[1]*(28.0-u[3]) - u[2]
	du[3] = u[1]u[2] - (8/3)u[3]
	end
	u0 = [1.0;0.0;0.0]
	tspan = (0.0,100.0)
	prob = ODEProblem(lorenz,u0,tspan)
	sol = solve(prob,CVODE_Adams(),reltol=1e-12,abstol=1e-12)

	using DifferentialEquations, Flux, DiffEqFlux, Plots

	####################################################
	## Solve an ODE
	####################################################

	function lotka_volterra(du,u,p,t)
	x, y = u
	α, β, δ, γ = p
	du[1] = dx = αx - βx*y

	using DifferentialEquations, Flux, DiffEqFlux, Plots

	####################################################
	## Solve an ODE
	####################################################

	function lotka_volterra(du,u,p,t)
	x, y = u
	α, β, δ, γ = p
	du[1] = dx = αx - βx*y

	macro test_allowed_failure(ex, kws...)
	test_expr!("@test_allowed_failure", ex, kws...)
	orig_ex = Expr(:inert, ex)
	result = Test.get_test_result(ex, __source__)
	# code to call do_test with execution result and original expr
	:(do_allowedfailure_test($result, $orig_ex))
	end


	function do_allowedfailure_test(result::Test.ExecutionResult, orig_expr)

	struct DirichletBC{T}
	l::T
	r::T
	end

	struct BoundaryPaddedArray{T,T2 <: AbstractVector{T}}
	l::T
	r::T
	u::T2
	end

	using DiffEqFlux, OrdinaryDiffEq, Flux, Plots

	# Generate data from a real ODE
	u0 = Float32[2.; 0.]; datasize = 30
	tspan = (0.0f0,1.5f0)
	function trueODEfunc(du,u,p,t)
	true_A = [-0.1 2.0; -2.0 -0.1]
	du .= ((u.^3)'true_A)'
	end
	t = range(tspan[1],tspan[2],length=datasize)

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