BVProblem with constraints

Project.toml

@@ -73,14 +73,16 @@ MTKBifurcationKitExt = "BifurcationKit"
 MTKChainRulesCoreExt = "ChainRulesCore"
 MTKDeepDiffsExt = "DeepDiffs"
 MTKHomotopyContinuationExt = "HomotopyContinuation"
-MTKLabelledArraysExt = "LabelledArrays"
 MTKInfiniteOptExt = "InfiniteOpt"
+MTKLabelledArraysExt = "LabelledArrays"
 
 [compat]
 AbstractTrees = "0.3, 0.4"
 ArrayInterface = "6, 7"
 BifurcationKit = "0.4"
 BlockArrays = "1.1"
+BoundaryValueDiffEq = "5.12.0"
+BoundaryValueDiffEqAscher = "1.1.0"
 ChainRulesCore = "1"
 Combinatorics = "1"
 CommonSolve = "0.2.4"
@@ -139,8 +141,8 @@ SimpleNonlinearSolve = "0.1.0, 1, 2"
 SparseArrays = "1"
 SpecialFunctions = "0.7, 0.8, 0.9, 0.10, 1.0, 2"
 StaticArrays = "0.10, 0.11, 0.12, 1.0"
-StochasticDiffEq = "6.72.1"
 StochasticDelayDiffEq = "1.8.1"
+StochasticDiffEq = "6.72.1"
 SymbolicIndexingInterface = "0.3.36"
 SymbolicUtils = "3.7"
 Symbolics = "6.19"
@@ -152,6 +154,8 @@ julia = "1.9"
 [extras]
 AmplNLWriter = "7c4d4715-977e-5154-bfe0-e096adeac482"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+BoundaryValueDiffEq = "764a87c0-6b3e-53db-9096-fe964310641d"
+BoundaryValueDiffEqAscher = "7227322d-7511-4e07-9247-ad6ff830280e"
 ControlSystemsBase = "aaaaaaaa-a6ca-5380-bf3e-84a91bcd477e"
 DataInterpolations = "82cc6244-b520-54b8-b5a6-8a565e85f1d0"
 DeepDiffs = "ab62b9b5-e342-54a8-a765-a90f495de1a6"
@@ -183,4 +187,4 @@ Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["AmplNLWriter", "BenchmarkTools", "ControlSystemsBase", "DataInterpolations", "DelayDiffEq", "NonlinearSolve", "ForwardDiff", "Ipopt", "Ipopt_jll", "ModelingToolkitStandardLibrary", "Optimization", "OptimizationOptimJL", "OptimizationMOI", "OrdinaryDiffEq", "OrdinaryDiffEqCore", "OrdinaryDiffEqDefault", "REPL", "Random", "ReferenceTests", "SafeTestsets", "StableRNGs", "Statistics", "SteadyStateDiffEq", "Test", "StochasticDiffEq", "Sundials", "StochasticDelayDiffEq", "Pkg", "JET", "OrdinaryDiffEqNonlinearSolve"]
+test = ["AmplNLWriter", "BenchmarkTools", "BoundaryValueDiffEq", "BoundaryValueDiffEqAscher", "ControlSystemsBase", "DataInterpolations", "DelayDiffEq", "NonlinearSolve", "ForwardDiff", "Ipopt", "Ipopt_jll", "ModelingToolkitStandardLibrary", "Optimization", "OptimizationOptimJL", "OptimizationMOI", "OrdinaryDiffEq", "OrdinaryDiffEqCore", "OrdinaryDiffEqDefault", "REPL", "Random", "ReferenceTests", "SafeTestsets", "StableRNGs", "Statistics", "SteadyStateDiffEq", "Test", "StochasticDiffEq", "Sundials", "StochasticDelayDiffEq", "Pkg", "JET", "OrdinaryDiffEqNonlinearSolve"]

src/systems/diffeqs/abstractodesystem.jl

@@ -849,6 +849,213 @@ function DiffEqBase.ODEProblem{iip, specialize}(sys::AbstractODESystem, u0map =
 end
 get_callback(prob::ODEProblem) = prob.kwargs[:callback]
 
+"""
+```julia
+SciMLBase.BVProblem{iip}(sys::AbstractODESystem, u0map, tspan,
+                         parammap = DiffEqBase.NullParameters();
+                         constraints = nothing, guesses = nothing,
+                         version = nothing, tgrad = false,
+                         jac = true, sparse = true,
+                         simplify = false,
+                         kwargs...) where {iip}
+```
+
+Create a boundary value problem from the [`ODESystem`](@ref). 
+
+`u0map` is used to specify fixed initial values for the states. Every variable 
+must have either an initial guess supplied using `guesses` or a fixed initial 
+value specified using `u0map`.
+
+`constraints` are used to specify boundary conditions to the ODESystem in the
+form of equations. These values should specify values that state variables should
+take at specific points, as in `x(0.5) ~ 1`). More general constraints that 
+should hold over the entire solution, such as `x(t)^2 + y(t)^2`, should be 
+specified as one of the equations used to build the `ODESystem`. Below is an example.
+
+```julia
+    @parameters g
+    @variables x(..) y(t) [state_priority = 10] λ(t)
+    eqs = [D(D(x(t))) ~ λ * x(t)
+           D(D(y)) ~ λ * y - g
+           x(t)^2 + y^2 ~ 1]
+    @mtkbuild pend = ODESystem(eqs, t)
+
+    tspan = (0.0, 1.5)
+    u0map = [x(t) => 0.6, y => 0.8]
+    parammap = [g => 1]
+    guesses = [λ => 1]
+    constraints = [x(0.5) ~ 1]
+
+    bvp = SciMLBase.BVProblem{true, SciMLBase.AutoSpecialize}(pend, u0map, tspan, parammap; constraints, guesses, check_length = false)
+```
+
+If no `constraints` are specified, the problem will be treated as an initial value problem.
+
+If the `ODESystem` has algebraic equations like `x(t)^2 + y(t)^2`, the resulting 
+`BVProblem` must be solved using BVDAE solvers, such as Ascher.
+"""
+function SciMLBase.BVProblem(sys::AbstractODESystem, args...; kwargs...)
+    BVProblem{true}(sys, args...; kwargs...)
+end
+
+function SciMLBase.BVProblem(sys::AbstractODESystem,
+        u0map::StaticArray,
+        args...;
+        kwargs...)
+    BVProblem{false, SciMLBase.FullSpecialize}(sys, u0map, args...; kwargs...)
+end
+
+function SciMLBase.BVProblem{true}(sys::AbstractODESystem, args...; kwargs...)
+    BVProblem{true, SciMLBase.AutoSpecialize}(sys, args...; kwargs...)
+end
+
+function SciMLBase.BVProblem{false}(sys::AbstractODESystem, args...; kwargs...)
+    BVProblem{false, SciMLBase.FullSpecialize}(sys, args...; kwargs...)
+end
+
+function SciMLBase.BVProblem{iip, specialize}(sys::AbstractODESystem, u0map = [],
+        tspan = get_tspan(sys),
+        parammap = DiffEqBase.NullParameters();
+        constraints = nothing, guesses = Dict(),
+        version = nothing, tgrad = false,
+        callback = nothing,
+        check_length = true,
+        warn_initialize_determined = true,
+        eval_expression = false,
+        eval_module = @__MODULE__,
+        kwargs...) where {iip, specialize}
+
+    if !iscomplete(sys)
+        error("A completed system is required. Call `complete` or `structural_simplify` on the system before creating an `BVProblem`")
+    end
+    !isnothing(callback) && error("BVP solvers do not support callbacks.")
+
+    has_alg_eqs(sys) && error("The BVProblem currently does not support ODESystems with algebraic equations.") # Remove this when the BVDAE solvers get updated, the codegen should work when it does.
+
+    constraintsts = nothing
+    constraintps = nothing
+    sts = unknowns(sys)
+    ps = parameters(sys)
+
+    # Constraint validation
+    if !isnothing(constraints)
+        constraints isa Equation || 
+            constraints isa Vector{Equation} || 
+            error("Constraints must be specified as an equation or a vector of equations.")
+
+        (length(constraints) + length(u0map) > length(sts)) && 
+        error("The BVProblem is overdetermined. The total number of conditions (# constraints + # fixed initial values given by u0map) cannot exceed the total number of states.")
+    end
+
+    # ODESystems without algebraic equations should use both fixed values + guesses
+    # for initialization.
+    _u0map = has_alg_eqs(sys) ? u0map : merge(Dict(u0map), Dict(guesses)) 
+    f, u0, p = process_SciMLProblem(ODEFunction{iip, specialize}, sys, _u0map, parammap;
+        t = tspan !== nothing ? tspan[1] : tspan, guesses,
+        check_length, warn_initialize_determined, eval_expression, eval_module, kwargs...)
+
+    stidxmap = Dict([v => i for (i, v) in enumerate(sts)])
+    u0_idxs = has_alg_eqs(sys) ? collect(1:length(sts)) : [stidxmap[k] for (k,v) in u0map]
+
+    bc = process_constraints(sys, constraints, u0, u0_idxs, tspan, iip)
+
+    return BVProblem{iip}(f, bc, u0, tspan, p; kwargs...)
+end
+
+get_callback(prob::BVProblem) = error("BVP solvers do not support callbacks.")
+
+# Validate that all the variables in the BVP constraints are well-formed states or parameters.
+function validate_constraint_syms(eq, constraintsts, constraintps, sts, ps, iv) 
+    for var in constraintsts
+        if length(arguments(var)) > 1
+            error("Too many arguments for variable $var.")
+        elseif arguments(var) == iv
+            var ∈ sts || error("Constraint equation $eq contains a variable $var that is not a variable of the ODESystem.")
+            error("Constraint equation $eq contains a variable $var that does not have a specified argument. Such equations should be specified as algebraic equations to the ODESystem rather than a boundary constraints.")
+        else
+            operation(var)(iv) ∈ sts || error("Constraint equation $eq contains a variable $(operation(var)) that is not a variable of the ODESystem.")
+        end
+    end
+
+    for var in constraintps
+        if !iscall(var)
+            var ∈ ps || error("Constraint equation $eq contains a parameter $var that is not a parameter of the ODESystem.")
+        else
+            length(arguments(var)) > 1 && error("Too many arguments for parameter $var.")
+            operation(var) ∈ ps || error("Constraint equations contain a parameter $var that is not a parameter of the ODESystem.")
+        end
+    end
+end
+
+"""
+    process_constraints(sys, constraints, u0, tspan, iip)
+
+    Given an ODESystem with some constraints, generate the boundary condition function.
+"""
+function process_constraints(sys::ODESystem, constraints, u0, u0_idxs, tspan, iip)
+
+    iv = get_iv(sys)
+    sts = get_unknowns(sys)
+    ps = get_ps(sys)
+    np = length(ps)
+    ns = length(sts)
+
+    stidxmap = Dict([v => i for (i, v) in enumerate(sts)])
+    pidxmap = Dict([v => i for (i, v) in enumerate(ps)])
+
+    @variables sol(..)[1:ns] p[1:np]
+    exprs = Any[]
+
+    constraintsts = OrderedSet()
+    constraintps = OrderedSet()
+
+    !isnothing(constraints) && for cons in constraints
+        collect_vars!(constraintsts, constraintps, cons, iv)
+        validate_constraint_syms(cons, constraintsts, constraintps, Set(sts), Set(ps), iv)
+        expr = cons.rhs - cons.lhs
+
+        for st in constraintsts
+            x = operation(st)
+            t = arguments(st)[1]
+            idx = stidxmap[x(iv)]
+
+            expr = Symbolics.substitute(expr, Dict(x(t) => sol(t)[idx]))
+        end
+
+        for var in constraintps
+            if iscall(var)
+                x = operation(var)
+                t = arguments(var)[1]
+                idx = pidxmap[x]
+
+                expr = Symbolics.substitute(expr, Dict(x(t) => p[idx]))
+            else
+                idx = pidxmap[var]
+                expr = Symbolics.substitute(expr, Dict(var => p[idx]))
+            end
+        end
+
+        empty!(constraintsts)
+        empty!(constraintps)
+        push!(exprs, expr)
+    end
+
+    init_cond_exprs = Any[]
+
+    for i in u0_idxs
+        expr = sol(tspan[1])[i] - u0[i]
+        push!(init_cond_exprs, expr)
+    end
+
+    exprs = vcat(init_cond_exprs, exprs)
+    bcs = Symbolics.build_function(exprs, sol, p, expression = Val{false})
+    if iip
+        return (resid, u, p, t) -> bcs[2](resid, u, p)
+    else
+        return (u, p, t) -> bcs[1](u, p)
+    end
+end
+
 """
 ```julia
 DiffEqBase.DAEProblem{iip}(sys::AbstractODESystem, du0map, u0map, tspan,