Merge pull request #3323 from vyudu/BVP-with-constraints

BVProblem with constraints

Author: ChrisRackauckas

Project.toml

@@ -83,6 +83,8 @@ AbstractTrees = "0.3, 0.4"
 ArrayInterface = "6, 7"
 BifurcationKit = "0.4"
 BlockArrays = "1.1"
+BoundaryValueDiffEqAscher = "1.1.0"
+BoundaryValueDiffEqMIRK = "1.4.0"
 ChainRulesCore = "1"
 Combinatorics = "1"
 CommonSolve = "0.2.4"
@@ -157,6 +159,8 @@ julia = "1.9"
 [extras]
 AmplNLWriter = "7c4d4715-977e-5154-bfe0-e096adeac482"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+BoundaryValueDiffEqMIRK = "1a22d4ce-7765-49ea-b6f2-13c8438986a6"
+BoundaryValueDiffEqAscher = "7227322d-7511-4e07-9247-ad6ff830280e"
 ControlSystemsBase = "aaaaaaaa-a6ca-5380-bf3e-84a91bcd477e"
 DataInterpolations = "82cc6244-b520-54b8-b5a6-8a565e85f1d0"
 DeepDiffs = "ab62b9b5-e342-54a8-a765-a90f495de1a6"
@@ -189,4 +193,4 @@ 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", "Logging"]
+test = ["AmplNLWriter", "BenchmarkTools", "BoundaryValueDiffEqMIRK", "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", "Logging"]

src/ModelingToolkit.jl

@@ -155,6 +155,10 @@ include("systems/codegen_utils.jl")
 include("systems/problem_utils.jl")
 include("linearization.jl")
 
+include("systems/optimization/constraints_system.jl")
+include("systems/optimization/optimizationsystem.jl")
+include("systems/optimization/modelingtoolkitize.jl")
+
 include("systems/nonlinear/nonlinearsystem.jl")
 include("systems/nonlinear/homotopy_continuation.jl")
 include("systems/diffeqs/odesystem.jl")
@@ -170,10 +174,6 @@ include("systems/discrete_system/discrete_system.jl")
 
 include("systems/jumps/jumpsystem.jl")
 
-include("systems/optimization/constraints_system.jl")
-include("systems/optimization/optimizationsystem.jl")
-include("systems/optimization/modelingtoolkitize.jl")
-
 include("systems/pde/pdesystem.jl")
 
 include("systems/sparsematrixclil.jl")

src/systems/abstractsystem.jl

@@ -823,6 +823,7 @@ for prop in [:eqs
              :structure
              :op
              :constraints
+             :constraintsystem
              :controls
              :loss
              :bcs

src/systems/diffeqs/abstractodesystem.jl

@@ -735,6 +735,12 @@ function DiffEqBase.ODEProblem{iip, specialize}(sys::AbstractODESystem, u0map =
     if !iscomplete(sys)
         error("A completed system is required. Call `complete` or `structural_simplify` on the system before creating an `ODEProblem`")
     end
+
+    if !isnothing(get_constraintsystem(sys))
+        error("An ODESystem with constraints cannot be used to construct a regular ODEProblem. 
+              Consider a BVProblem instead.")
+    end
+
     f, u0, p = process_SciMLProblem(ODEFunction{iip, specialize}, sys, u0map, parammap;
         t = tspan !== nothing ? tspan[1] : tspan,
         check_length, warn_initialize_determined, eval_expression, eval_module, kwargs...)
@@ -757,6 +763,164 @@ 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`.
+
+Boundary value conditions are supplied to ODESystems
+in the form of a ConstraintsSystem. These equations 
+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`.
+
+If an ODESystem without `constraints` is specified, it will be treated as an initial value problem. 
+
+```julia
+    @parameters g t_c = 0.5
+    @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]
+    cstr = [x(0.5) ~ 1]
+    @named cstrs = ConstraintsSystem(cstr, t)
+    @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 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();
+        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 constructor currently does not support ODESystems with algebraic equations.") # Remove this when the BVDAE solvers get updated, the codegen should work when it does.
+
+    sts = unknowns(sys)
+    ps = parameters(sys)
+    constraintsys = get_constraintsystem(sys)
+
+    if !isnothing(constraintsys)
+        (length(constraints(constraintsys)) + length(u0map) > length(sts)) && 
+        @warn "The BVProblem is overdetermined. The total number of conditions (# constraints + # fixed initial values given by u0map) exceeds the total number of states. The BVP solvers will default to doing a nonlinear least-squares optimization."
+    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]
+
+    fns = generate_function_bc(sys, u0, u0_idxs, tspan)
+    bc_oop, bc_iip = eval_or_rgf.(fns; eval_expression, eval_module) 
+    bc(sol, p, t) = bc_oop(sol, p, t)
+    bc(resid, u, p, t) = bc_iip(resid, u, p, t)
+
+    return BVProblem{iip}(f, bc, u0, tspan, p; kwargs...)
+end
+
+get_callback(prob::BVProblem) = error("BVP solvers do not support callbacks.")
+
+"""
+    generate_function_bc(sys::ODESystem, u0, u0_idxs, tspan)
+
+    Given an ODESystem with constraints, generate the boundary condition function to pass to boundary value problem solvers.
+    Expression uses the constraints and the provided initial conditions.
+"""
+function generate_function_bc(sys::ODESystem, u0, u0_idxs, tspan; kwargs...)
+    iv = get_iv(sys)
+    sts = unknowns(sys)
+    ps = parameters(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]
+
+    conssys = get_constraintsystem(sys)
+    cons = Any[]
+    if !isnothing(conssys)
+        cons = [con.lhs - con.rhs for con in constraints(conssys)]
+
+        for st in get_unknowns(conssys)
+            x = operation(st)
+            t = only(arguments(st))
+            idx = stidxmap[x(iv)]
+
+            cons = map(c -> Symbolics.substitute(c, Dict(x(t) => sol(t)[idx])), cons)
+        end
+    end
+
+    init_conds = Any[]
+    for i in u0_idxs
+        expr = sol(tspan[1])[i] - u0[i]
+        push!(init_conds, expr)
+    end
+
+    exprs = vcat(init_conds, cons)
+    _p = reorder_parameters(sys, ps)
+
+    build_function_wrapper(sys, exprs, sol, _p..., t; output_type = Array, kwargs...)
+end
+
 """
 ```julia
 DiffEqBase.DAEProblem{iip}(sys::AbstractODESystem, du0map, u0map, tspan,

src/systems/diffeqs/odesystem.jl

@@ -49,6 +49,8 @@ struct ODESystem <: AbstractODESystem
     ctrls::Vector
     """Observed variables."""
     observed::Vector{Equation}
+    """System of constraints that must be satisfied by the solution to the system."""
+    constraintsystem::Union{Nothing, ConstraintsSystem}
     """
     Time-derivative matrix. Note: this field will not be defined until
     [`calculate_tgrad`](@ref) is called on the system.
@@ -191,7 +193,7 @@ struct ODESystem <: AbstractODESystem
     """
     parent::Any
 
-    function ODESystem(tag, deqs, iv, dvs, ps, tspan, var_to_name, ctrls, observed, tgrad,
+    function ODESystem(tag, deqs, iv, dvs, ps, tspan, var_to_name, ctrls, observed, constraints, tgrad,
             jac, ctrl_jac, Wfact, Wfact_t, name, description, systems, defaults, guesses,
             torn_matching, initializesystem, initialization_eqs, schedule,
             connector_type, preface, cevents,
@@ -212,7 +214,7 @@ struct ODESystem <: AbstractODESystem
             u = __get_unit_type(dvs, ps, iv)
             check_units(u, deqs)
         end
-        new(tag, deqs, iv, dvs, ps, tspan, var_to_name, ctrls, observed, tgrad, jac,
+        new(tag, deqs, iv, dvs, ps, tspan, var_to_name, ctrls, observed, constraints, tgrad, jac,
             ctrl_jac, Wfact, Wfact_t, name, description, systems, defaults, guesses, torn_matching,
             initializesystem, initialization_eqs, schedule, connector_type, preface,
             cevents, devents, parameter_dependencies, assertions, metadata,
@@ -224,6 +226,7 @@ end
 function ODESystem(deqs::AbstractVector{<:Equation}, iv, dvs, ps;
         controls = Num[],
         observed = Equation[],
+        constraintsystem = nothing,
         systems = ODESystem[],
         tspan = nothing,
         name = nothing,
@@ -297,17 +300,29 @@ function ODESystem(deqs::AbstractVector{<:Equation}, iv, dvs, ps;
     if is_dde === nothing
         is_dde = _check_if_dde(deqs, iv′, systems)
     end
+            
+    if !isempty(systems) && !isnothing(constraintsystem)
+        conssystems = ConstraintsSystem[]
+        for sys in systems
+            cons = get_constraintsystem(sys)
+            cons !== nothing && push!(conssystems, cons) 
+        end
+        @show conssystems
+        @set! constraintsystem.systems = conssystems
+    end        
+
     assertions = Dict{BasicSymbolic, Any}(unwrap(k) => v for (k, v) in assertions)
+
     ODESystem(Threads.atomic_add!(SYSTEM_COUNT, UInt(1)),
-        deqs, iv′, dvs′, ps′, tspan, var_to_name, ctrl′, observed, tgrad, jac,
+        deqs, iv′, dvs′, ps′, tspan, var_to_name, ctrl′, observed, constraintsystem, tgrad, jac,
         ctrl_jac, Wfact, Wfact_t, name, description, systems,
         defaults, guesses, nothing, initializesystem,
         initialization_eqs, schedule, connector_type, preface, cont_callbacks,
         disc_callbacks, parameter_dependencies, assertions,
         metadata, gui_metadata, is_dde, tstops, checks = checks)
 end
 
-function ODESystem(eqs, iv; kwargs...)
+function ODESystem(eqs, iv; constraints = Equation[], kwargs...)
     diffvars, allunknowns, ps, eqs = process_equations(eqs, iv)
 
     for eq in get(kwargs, :parameter_dependencies, Equation[])
@@ -339,8 +354,22 @@ function ODESystem(eqs, iv; kwargs...)
     end
     algevars = setdiff(allunknowns, diffvars)
 
-    return ODESystem(eqs, iv, collect(Iterators.flatten((diffvars, algevars))),
-        collect(new_ps); kwargs...)
+    consvars = OrderedSet()
+    constraintsystem = nothing
+    if !isempty(constraints)
+        constraintsystem = process_constraint_system(constraints, allunknowns, new_ps, iv)
+        for st in get_unknowns(constraintsystem)
+            iscall(st) ? 
+                !in(operation(st)(iv), allunknowns) && push!(consvars, st) :
+                !in(st, allunknowns) && push!(consvars, st)
+        end
+        for p in parameters(constraintsystem)
+            !in(p, new_ps) && push!(new_ps, p)
+        end
+    end
+
+    return ODESystem(eqs, iv, collect(Iterators.flatten((diffvars, algevars, consvars))),
+        collect(new_ps); constraintsystem, kwargs...)
 end
 
 # NOTE: equality does not check cached Jacobian
@@ -668,3 +697,39 @@ function Base.show(io::IO, mime::MIME"text/plain", sys::ODESystem; hint = true,
 
     return nothing
 end
+
+# Validate that all the variables in the BVP constraints are well-formed states or parameters.
+#  - Callable/delay variables (e.g. of the form x(0.6) should be unknowns of the system (and have one arg, etc.)
+#  - Callable/delay parameters should be parameters of the system (and have one arg, etc.)
+function process_constraint_system(constraints::Vector{Equation}, sts, ps, iv; consname = :cons)
+    isempty(constraints) && return nothing
+
+    constraintsts = OrderedSet()
+    constraintps = OrderedSet()
+
+    for cons in constraints
+        collect_vars!(constraintsts, constraintps, cons, iv)
+    end
+
+    # Validate the states.
+    for var in constraintsts
+        if !iscall(var)
+            occursin(iv, var) && (var ∈ sts || throw(ArgumentError("Time-dependent variable $var is not an unknown of the system.")))
+        elseif length(arguments(var)) > 1
+            throw(ArgumentError("Too many arguments for variable $var."))
+        elseif length(arguments(var)) == 1
+            arg = only(arguments(var))
+            operation(var)(iv) ∈ sts || 
+                throw(ArgumentError("Variable $var is not a variable of the ODESystem. Called variables must be variables of the ODESystem."))
+
+            isequal(arg, iv) || isparameter(arg) || arg isa Integer || arg isa AbstractFloat || 
+                throw(ArgumentError("Invalid argument specified for variable $var. The argument of the variable should be either $iv, a parameter, or a value specifying the time that the constraint holds."))
+
+            isparameter(arg) && push!(constraintps, arg)
+        else
+            var ∈ sts && @warn "Variable $var has no argument. It will be interpreted as $var($iv), and the constraint will apply to the entire interval."
+        end
+    end
+
+    ConstraintsSystem(constraints, collect(constraintsts), collect(constraintps); name = consname)
+end

src/systems/optimization/constraints_system.jl

@@ -123,7 +123,7 @@ function ConstraintsSystem(constraints, unknowns, ps;
     name === nothing &&
         throw(ArgumentError("The `name` keyword must be provided. Please consider using the `@named` macro"))
 
-    cstr = value.(Symbolics.canonical_form.(scalarize(constraints)))
+    cstr = value.(Symbolics.canonical_form.(vcat(scalarize(constraints)...)))
     unknowns′ = value.(scalarize(unknowns))
     ps′ = value.(ps)