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| 1 | +using Enzyme, OrdinaryDiffEqTsit5, StaticArrays, DiffEqBase, ForwardDiff, Test |
| 2 | + |
| 3 | +function lorenz!(du, u, p, t) |
| 4 | + du[1] = 10.0(u[2] - u[1]) |
| 5 | + du[2] = u[1] * (28.0 - u[3]) - u[2] |
| 6 | + du[3] = u[1] * u[2] - (8 / 3) * u[3] |
| 7 | +end |
| 8 | + |
| 9 | +const _saveat = SA[0.0,0.25,0.5,0.75,1.0,1.25,1.5,1.75,2.0,2.25,2.5,2.75,3.0] |
| 10 | + |
| 11 | +function f_dt(y::Array{Float64}, u0::Array{Float64}) |
| 12 | + tspan = (0.0, 3.0) |
| 13 | + prob = ODEProblem{true, SciMLBase.FullSpecialize}(lorenz!, u0, tspan) |
| 14 | + sol = DiffEqBase.solve(prob, Tsit5(), saveat = _saveat, sensealg = DiffEqBase.SensitivityADPassThrough(), abstol=1e-12, reltol=1e-12) |
| 15 | + y .= sol[1,:] |
| 16 | + return nothing |
| 17 | +end; |
| 18 | + |
| 19 | +function f_dt(u0) |
| 20 | + tspan = (0.0, 3.0) |
| 21 | + prob = ODEProblem{true, SciMLBase.FullSpecialize}(lorenz!, u0, tspan) |
| 22 | + sol = DiffEqBase.solve(prob, Tsit5(), saveat = _saveat, sensealg = DiffEqBase.SensitivityADPassThrough(), abstol=1e-12, reltol=1e-12) |
| 23 | + sol[1,:] |
| 24 | +end; |
| 25 | + |
| 26 | +u0 = [1.0; 0.0; 0.0] |
| 27 | +fdj = ForwardDiff.jacobian(f_dt, u0) |
| 28 | + |
| 29 | +ezj = stack(map(1:3) do i |
| 30 | + d_u0 = zeros(3) |
| 31 | + dy = zeros(13) |
| 32 | + y = zeros(13) |
| 33 | + d_u0[i] = 1.0 |
| 34 | + Enzyme.autodiff(Forward, f_dt, Duplicated(y, dy), Duplicated(u0, d_u0)); |
| 35 | + dy |
| 36 | +end) |
| 37 | + |
| 38 | +@test ezj ≈ fdj |
| 39 | + |
| 40 | +function f_dt2(u0) |
| 41 | + tspan = (0.0, 3.0) |
| 42 | + prob = ODEProblem{true, SciMLBase.FullSpecialize}(lorenz!, u0, tspan) |
| 43 | + sol = DiffEqBase.solve(prob, Tsit5(), dt=0.1, saveat = _saveat, sensealg = DiffEqBase.SensitivityADPassThrough(), abstol=1e-12, reltol=1e-12) |
| 44 | + sum(sol[1,:]) |
| 45 | +end |
| 46 | + |
| 47 | +fdg = ForwardDiff.gradient(f_dt2, u0) |
| 48 | +d_u0 = zeros(3) |
| 49 | +Enzyme.autodiff(Reverse, f_dt2, Active, Duplicated(u0, d_u0)); |
| 50 | + |
| 51 | +@test d_u0 ≈ fdg |
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