Add codegen for BVProblems with cost functions

Co-Authored-By: Claude Opus 4.5 <[email protected]>

Author: SebastianM-C

lib/ModelingToolkitBase/src/problems/bvproblem.jl

@@ -22,6 +22,9 @@
         checkbounds, time_dependent_init = false, expression, kwargs...
     )
 
+    fcost = generate_bvp_cost(sys; expression = Val{false}, wrap_gfw = Val{false},
+        eval_expression, eval_module, cse, checkbounds)
+
     stidxmap = Dict([v => i for (i, v) in enumerate(dvs)])
     u0_idxs = has_alg_eqs(sys) ? collect(1:length(dvs)) :
         [stidxmap[k] for (k, v) in op if haskey(stidxmap, k)]
@@ -30,20 +33,25 @@
         wrap_gfw = Val{true}, cse, checkbounds
     )
 
+    n_controls = length(unbound_inputs(sys))
+    f_prototype = n_controls > 0 ? zeros(eltype(u0), length(dvs) - n_controls) : nothing
+    bcresid_prototype = zeros(eltype(u0), length(u0_idxs) + length(constraints(sys)))
+
+    bvpfn = BVPFunction{iip}(fode, fbc; cost = fcost, f_prototype, bcresid_prototype)
+
     if (length(constraints(sys)) + length(op) > length(dvs))
         @warn "The BVProblem is overdetermined. The total number of conditions (# constraints + # fixed initial values given by op) exceeds the total number of states. The BVP solvers will default to doing a nonlinear least-squares optimization."
     end
 
     kwargs = process_kwargs(sys; expression, kwargs...)
-    args = (; fode, fbc, u0, tspan, p)
+    args = (; bvpfn, u0, tspan, p)
 
     return maybe_codegen_scimlproblem(expression, BVProblem{iip}, args; kwargs...)
 end
 
 function check_compatible_system(T::Type{BVProblem}, sys::System)
     check_time_dependent(sys, T)
     check_not_dde(sys)
-    check_no_cost(sys, T)
     check_no_jumps(sys, T)
     check_no_noise(sys, T)
     check_is_continuous(sys, T)

lib/ModelingToolkitBase/src/systems/codegen.jl

@@ -699,6 +699,56 @@ function generate_cost(
     )
 end
 
+"""
+    $(TYPEDSIGNATURES)
+
+Generate the cost function for a BVP [`System`](@ref). The generated function has the
+signature `cost(sol, p)` where `sol` is a solution interpolation object (callable as
+`sol(t)` to get state at time `t`) and `p` is the parameter object.
+
+# Keyword Arguments
+
+$GENERATE_X_KWARGS
+
+All other keyword arguments are forwarded to [`build_function_wrapper`](@ref).
+"""
+function generate_bvp_cost(
+        sys::System; expression = Val{true}, wrap_gfw = Val{false},
+        eval_expression = false, eval_module = @__MODULE__, cse = true,
+        checkbounds = false, kwargs...
+    )
+    obj = cost(sys)
+    _iszero(obj) && return nothing
+
+    iv = get_iv(sys)
+    sts = unknowns(sys)
+    ps = reorder_parameters(sys)
+    stidxmap = Dict([v => i for (i, v) in enumerate(sts)])
+
+    # Substitute x(t_val) -> BVP_SOLUTION(t_val)[idx] for all state evaluations
+    costsubs = Dict()
+    get_constraint_unknown_subs!(costsubs, [obj], stidxmap, iv, BVP_SOLUTION)
+    obj = substitute(obj, costsubs)
+
+    # Build function with signature (sol, p) where sol = BVP_SOLUTION
+    # The histfn mechanism replaces BVP_SOLUTION with the sol argument
+    res = build_function_wrapper(
+        sys, obj, ps...;
+        expression = Val{true},
+        p_start = 1,  # sol goes before parameters
+        p_end = length(ps),
+        wrap_delays = true,
+        histfn = (p, t) -> BVP_SOLUTION(t),
+        histfn_symbolic = BVP_SOLUTION,
+        cse, checkbounds, kwargs...
+    )
+
+    # (2, 2, is_split) means: 2 args out-of-place, 2 original args, split status
+    return maybe_compile_function(
+        expression, wrap_gfw, (2, 2, is_split(sys)), res; eval_expression, eval_module
+    )
+end
+
 """
     $(TYPEDSIGNATURES)
 
@@ -1113,7 +1163,7 @@ end
 
 Generates a function that computes the observed value(s) `ts` in the system `sys`, while making the assumption that there are no cycles in the equations.
 
-## Arguments 
+## Arguments
 - `sys`: The system for which to generate the function
 - `ts`: The symbolic observed values whose value should be computed