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| 1 | +using Enzyme, OrdinaryDiffEqTsit5, StaticArrays, DiffEqBase, ForwardDiff, Test |
| 2 | +using OrdinaryDiffEq, SciMLSensitivity, Zygote |
| 3 | +using LinearSolve, LinearAlgebra |
| 4 | + |
| 5 | +@testset "Direct Differentiation of Explicit ODE Solve" begin |
| 6 | + function lorenz!(du, u, p, t) |
| 7 | + du[1] = 10.0(u[2] - u[1]) |
| 8 | + du[2] = u[1] * (28.0 - u[3]) - u[2] |
| 9 | + du[3] = u[1] * u[2] - (8 / 3) * u[3] |
| 10 | + end |
| 11 | + |
| 12 | + _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] |
| 13 | + |
| 14 | + function f_dt(y::Array{Float64}, u0::Array{Float64}) |
| 15 | + tspan = (0.0, 3.0) |
| 16 | + prob = ODEProblem{true, SciMLBase.FullSpecialize}(lorenz!, u0, tspan) |
| 17 | + sol = DiffEqBase.solve(prob, Tsit5(), saveat = _saveat, sensealg = DiffEqBase.SensitivityADPassThrough(), abstol=1e-12, reltol=1e-12) |
| 18 | + y .= sol[1,:] |
| 19 | + return nothing |
| 20 | + end; |
| 21 | + |
| 22 | + function f_dt(u0) |
| 23 | + tspan = (0.0, 3.0) |
| 24 | + prob = ODEProblem{true, SciMLBase.FullSpecialize}(lorenz!, u0, tspan) |
| 25 | + sol = DiffEqBase.solve(prob, Tsit5(), saveat = _saveat, sensealg = DiffEqBase.SensitivityADPassThrough(), abstol=1e-12, reltol=1e-12) |
| 26 | + sol[1,:] |
| 27 | + end; |
| 28 | + |
| 29 | + u0 = [1.0; 0.0; 0.0] |
| 30 | + fdj = ForwardDiff.jacobian(f_dt, u0) |
| 31 | + |
| 32 | + ezj = stack(map(1:3) do i |
| 33 | + d_u0 = zeros(3) |
| 34 | + dy = zeros(13) |
| 35 | + y = zeros(13) |
| 36 | + d_u0[i] = 1.0 |
| 37 | + Enzyme.autodiff(Forward, f_dt, Duplicated(y, dy), Duplicated(u0, d_u0)); |
| 38 | + dy |
| 39 | + end) |
| 40 | + |
| 41 | + @test ezj ≈ fdj |
| 42 | + |
| 43 | + function f_dt2(u0) |
| 44 | + tspan = (0.0, 3.0) |
| 45 | + prob = ODEProblem{true, SciMLBase.FullSpecialize}(lorenz!, u0, tspan) |
| 46 | + sol = DiffEqBase.solve(prob, Tsit5(), dt=0.1, saveat = _saveat, sensealg = DiffEqBase.SensitivityADPassThrough(), abstol=1e-12, reltol=1e-12) |
| 47 | + sum(sol[1,:]) |
| 48 | + end |
| 49 | + |
| 50 | + fdg = ForwardDiff.gradient(f_dt2, u0) |
| 51 | + d_u0 = zeros(3) |
| 52 | + Enzyme.autodiff(Reverse, f_dt2, Active, Duplicated(u0, d_u0)); |
| 53 | + |
| 54 | + @test d_u0 ≈ fdg |
| 55 | +end |
| 56 | + |
| 57 | +odef(du, u, p, t) = du .= u .* p |
| 58 | +prob = ODEProblem(odef, [2.0], (0.0, 1.0), [3.0]) |
| 59 | +struct senseloss0{T} |
| 60 | + sense::T |
| 61 | +end |
| 62 | +function (f::senseloss0)(u0p) |
| 63 | + prob = ODEProblem{true}(odef, u0p[1:1], (0.0, 1.0), u0p[2:2]) |
| 64 | + sum(solve(prob, Tsit5(), abstol = 1e-12, reltol = 1e-12, saveat = 0.1)) |
| 65 | +end |
| 66 | + |
| 67 | +@testset "SciMLSensitivity Adjoint Interface" begin |
| 68 | + u0p = [2.0, 3.0] |
| 69 | + du0p = zeros(2) |
| 70 | + @test senseloss0(InterpolatingAdjoint())(u0p) isa Number |
| 71 | + dup = Zygote.gradient(senseloss0(InterpolatingAdjoint()), u0p)[1] |
| 72 | + Enzyme.autodiff(Reverse, senseloss0(InterpolatingAdjoint()), Active, Duplicated(u0p, du0p)) |
| 73 | + @test du0p ≈ dup |
| 74 | +end |
| 75 | + |
| 76 | + @testset "LinearSolve Adjoints" begin |
| 77 | + n = 4 |
| 78 | + A = rand(n, n); |
| 79 | + dA = zeros(n, n); |
| 80 | + b1 = rand(n); |
| 81 | + db1 = zeros(n); |
| 82 | + |
| 83 | + function f(A, b1; alg = LUFactorization()) |
| 84 | + prob = LinearProblem(A, b1) |
| 85 | + |
| 86 | + sol1 = solve(prob, alg) |
| 87 | + |
| 88 | + s1 = sol1.u |
| 89 | + norm(s1) |
| 90 | + end |
| 91 | + |
| 92 | + f(A, b1) # Uses BLAS |
| 93 | + |
| 94 | + Enzyme.autodiff(Reverse, f, Duplicated(copy(A), dA), Duplicated(copy(b1), db1)) |
| 95 | + dA2 = ForwardDiff.gradient(x -> f(x, eltype(x).(b1)), copy(A)) |
| 96 | + db12 = ForwardDiff.gradient(x -> f(eltype(x).(A), x), copy(b1)) |
| 97 | + |
| 98 | + @test dA ≈ dA2 |
| 99 | + @test db1 ≈ db12 |
| 100 | +end |
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