fix: hessian through nonlinear solvers

lib/NonlinearSolveBase/ext/NonlinearSolveBaseForwardDiffExt.jl

@@ -20,7 +20,7 @@ function NonlinearSolveBase.additional_incompatible_backend_check(
 end
 
 Utils.value(::Type{Dual{T, V, N}}) where {T, V, N} = V
-Utils.value(x::Dual) = Utils.value(ForwardDiff.value(x))
+Utils.value(x::Dual) = ForwardDiff.value(x)
 Utils.value(x::AbstractArray{<:Dual}) = Utils.value.(x)
 
 function NonlinearSolveBase.nonlinearsolve_forwarddiff_solve(

test/forward_ad_tests.jl

@@ -124,3 +124,57 @@ end
         end
     end
 end
+
+@testitem "NLLS Hessian SciML/NonlinearSolve.jl#445" tags=[:core] begin
+    using ForwardDiff, FiniteDiff
+
+    function objfn(F, init, params)
+        th1, th2 = init
+        px, py, l1, l2 = params
+        F[1] = l1 * cos(th1) + l2 * cos(th1 + th2) - px
+        F[2] = l1 * sin(th1) + l2 * sin(th1 + th2) - py
+        return F
+    end
+
+    function solve_nlprob(pxpy)
+        px, py = pxpy
+        theta1 = pi / 4
+        theta2 = pi / 4
+        initial_guess = [theta1; theta2]
+        l1 = 60
+        l2 = 60
+        p = [px; py; l1; l2]
+        prob = NonlinearLeastSquaresProblem(
+            NonlinearFunction(objfn, resid_prototype = zeros(2)),
+            initial_guess, p
+        )
+        resu = solve(
+            prob,
+            reltol = 1e-12, abstol = 1e-12
+        )
+        th1, th2 = resu.u
+        cable1_base = [-90; 0; 0]
+        cable2_base = [-150; 0; 0]
+        cable3_base = [150; 0; 0]
+        cable1_top = [l1 * cos(th1) / 2; l1 * sin(th1) / 2; 0]
+        cable23_top = [l1 * cos(th1) + l2 * cos(th1 + th2) / 2;
+                       l1 * sin(th1) + l2 * sin(th1 + th2) / 2; 0]
+        c1_length = sqrt((cable1_top[1] - cable1_base[1])^2 +
+                         (cable1_top[2] - cable1_base[2])^2)
+        c2_length = sqrt((cable23_top[1] - cable2_base[1])^2 +
+                         (cable23_top[2] - cable2_base[2])^2)
+        c3_length = sqrt((cable23_top[1] - cable3_base[1])^2 +
+                         (cable23_top[2] - cable3_base[2])^2)
+        return c1_length + c2_length + c3_length
+    end
+
+    grad1 = ForwardDiff.gradient(solve_nlprob, [34.0, 87.0])
+    grad2 = FiniteDiff.finite_difference_gradient(solve_nlprob, [34.0, 87.0])
+
+    @test grad1 ≈ grad2 atol = 1e-3
+
+    hess1 = ForwardDiff.hessian(solve_nlprob, [34.0, 87.0])
+    hess2 = FiniteDiff.finite_difference_hessian(solve_nlprob, [34.0, 87.0])
+
+    @test hess1 ≈ hess2 atol = 1e-3
+end