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concrete_solve.jl
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concrete_solve.jl
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## High level
# Here is where we can add a default algorithm for computing sensitivities
# Based on problem information!
const have_not_warned_vjp = Ref(true)
const STACKTRACE_WITH_VJPWARN = Ref(false)
function inplace_vjp(prob, u0, p, verbose, repack)
du = zero(u0)
ez = try
f = unwrapped_f(prob.f)
function adfunc(out, u, _p, t)
f(out, u, repack(_p), t)
nothing
end
Enzyme.autodiff(Enzyme.Reverse, adfunc, Enzyme.Duplicated(du, copy(u0)),
Enzyme.Duplicated(copy(u0), zero(u0)), Enzyme.Duplicated(copy(p), zero(p)), Enzyme.Const(prob.tspan[1]))
true
catch e
if verbose && have_not_warned_vjp[]
@warn "Potential performance improvement omitted. EnzymeVJP tried and failed in the automated AD choice algorithm. To show the stack trace, set SciMLSensitivity.STACKTRACE_WITH_VJPWARN[] = true. To turn off this printing, add `verbose = false` to the `solve` call.\n"
STACKTRACE_WITH_VJPWARN[] && showerror(stderr, e)
println()
have_not_warned_vjp[] = false
end
false
end
if ez
return EnzymeVJP()
end
# Determine if we can compile ReverseDiff
compile = try
f = unwrapped_f(prob.f)
if DiffEqBase.isinplace(prob)
!hasbranching(f, copy(u0), u0, repack(p), prob.tspan[1])
else
!hasbranching(f, u0, repack(p), prob.tspan[1])
end
catch
false
end
vjp = try
f = unwrapped_f(prob.f)
if p === nothing || p isa SciMLBase.NullParameters
ReverseDiff.GradientTape((copy(u0), [prob.tspan[1]])) do u, t
du1 = similar(u, size(u))
du1 .= 0
f(du1, u, p, first(t))
return vec(du1)
end
else
ReverseDiff.GradientTape((copy(u0), p, [prob.tspan[1]])) do u, p, t
du1 = similar(u, size(u))
du1 .= 0
f(du1, u, repack(p), first(t))
return vec(du1)
end
end
ReverseDiffVJP(compile)
catch e
if verbose
@warn "Potential performance improvement omitted. ReverseDiffVJP tried and failed in the automated AD choice algorithm. To show the stack trace, set SciMLSensitivity.STACKTRACE_WITH_VJPWARN[] = true. To turn off this printing, add `verbose = false` to the `solve` call.\n"
STACKTRACE_WITH_VJPWARN[] && showerror(stderr, e)
println()
have_not_warned_vjp[] = false
end
false
end
return vjp
end
function automatic_sensealg_choice(
prob::Union{SciMLBase.AbstractODEProblem,
SciMLBase.AbstractSDEProblem},
u0, p, verbose, repack)
if p === nothing || p isa SciMLBase.NullParameters
tunables, repack = p, identity
elseif isscimlstructure(p)
tunables, repack, _ = canonicalize(Tunable(), p)
else
throw(SciMLStructuresCompatibilityError())
end
default_sensealg = if p !== SciMLBase.NullParameters() &&
!(eltype(u0) <: ForwardDiff.Dual) &&
!(eltype(p) <: ForwardDiff.Dual) &&
!(eltype(u0) <: Complex) &&
!(eltype(p) <: Complex) &&
length(u0) + length(tunables) <= 100
ForwardDiffSensitivity()
elseif u0 isa GPUArraysCore.AbstractGPUArray || !DiffEqBase.isinplace(prob)
# only Zygote is GPU compatible and fast
# so if out-of-place, try Zygote
vjp = try
p = prob.p
y = prob.u0
f = prob.f
t = prob.tspan[1]
λ = zero(prob.u0)
if p === nothing || p isa SciMLBase.NullParameters
_dy, back = Zygote.pullback(y) do u
vec(f(u, p, t))
end
tmp1 = back(λ)
else
_dy, back = Zygote.pullback(y, p) do u, p
vec(f(u, p, t))
end
tmp1, tmp2 = back(λ)
end
ZygoteVJP()
catch e
if verbose
@warn "Potential performance improvement omitted. ZygoteVJP tried and failed in the automated AD choice algorithm. To show the stack trace, set SciMLSensitivity.STACKTRACE_WITH_VJPWARN[] = true. To turn off this printing, add `verbose = false` to the `solve` call.\n"
STACKTRACE_WITH_VJPWARN[] && showerror(stderr, e)
println()
end
false
end
if vjp == false
vjp = try
if p === nothing || p isa SciMLBase.NullParameters
ReverseDiff.gradient((u) -> sum(prob.f(u, p, prob.tspan[1])), u0)
else
ReverseDiff.gradient(
(u, _p) -> sum(prob.f(u, repack(_p), prob.tspan[1])), u0, tunables)
end
ReverseDiffVJP()
catch e
if verbose
@warn "Potential performance improvement omitted. ReverseDiffVJP tried and failed in the automated AD choice algorithm. To show the stack trace, set SciMLSensitivity.STACKTRACE_WITH_VJPWARN[] = true. To turn off this printing, add `verbose = false` to the `solve` call.\n"
STACKTRACE_WITH_VJPWARN[] && showerror(stderr, e)
println()
end
false
end
end
if vjp == false
vjp = try
p = prob.p
y = prob.u0
f = prob.f
t = prob.tspan[1]
λ = zero(prob.u0)
if p === nothing || p isa SciMLBase.NullParameters
_dy, back = Tracker.forward(y) do u
vec(f(u, p, t))
end
tmp1 = back(λ)
else
_dy, back = Tracker.forward(y, tunables) do u, tunables
vec(f(u, repack(tunables), t))
end
tmp1, tmp2 = back(λ)
end
TrackerVJP()
catch e
if verbose
@warn "Potential performance improvement omitted. TrackerVJP tried and failed in the automated AD choice algorithm. To show the stack trace, set SciMLSensitivity.STACKTRACE_WITH_VJPWARN[] = true. To turn off this printing, add `verbose = false` to the `solve` call.\n"
STACKTRACE_WITH_VJPWARN[] && showerror(stderr, e)
println()
end
false
end
end
if vjp isa Bool
if verbose
@warn "Reverse-Mode AD VJP choices all failed. Falling back to numerical VJPs"
end
if p === nothing || p === SciMLBase.NullParameters()
# QuadratureAdjoint skips all p calculations until the end
# So it's the fastest when there are no parameters
QuadratureAdjoint(autodiff = false, autojacvec = vjp)
elseif prob isa ODEProblem && !(vjp isa TrackerVJP)
GaussAdjoint(autodiff = false, autojacvec = vjp)
else
InterpolatingAdjoint(autodiff = false, autojacvec = vjp)
end
else
if p === nothing || p === SciMLBase.NullParameters()
# QuadratureAdjoint skips all p calculations until the end
# So it's the fastest when there are no parameters
QuadratureAdjoint(autojacvec = vjp)
elseif prob isa ODEProblem && !(vjp isa TrackerVJP)
GaussAdjoint(autojacvec = vjp)
else
InterpolatingAdjoint(autojacvec = vjp)
end
end
else
vjp = inplace_vjp(prob, u0, p, verbose, repack)
if vjp isa Bool
if verbose
@warn "Reverse-Mode AD VJP choices all failed. Falling back to numerical VJPs"
end
# If reverse-mode isn't working, just fallback to numerical vjps
if p === nothing || p === SciMLBase.NullParameters()
QuadratureAdjoint(autodiff = false, autojacvec = vjp)
elseif prob isa ODEProblem && !(vjp isa TrackerVJP)
GaussAdjoint(autodiff = false, autojacvec = vjp)
else
InterpolatingAdjoint(autodiff = false, autojacvec = vjp)
end
else
if p === nothing || p === SciMLBase.NullParameters()
QuadratureAdjoint(autojacvec = vjp)
elseif prob isa ODEProblem && !(vjp isa TrackerVJP)
GaussAdjoint(autojacvec = vjp)
else
InterpolatingAdjoint(autojacvec = vjp)
end
end
end
return default_sensealg
end
function automatic_sensealg_choice(
prob::AbstractNonlinearProblem, u0, p,
verbose, repack)
default_sensealg = if u0 isa GPUArraysCore.AbstractGPUArray ||
!DiffEqBase.isinplace(prob)
# autodiff = false because forwarddiff fails on many GPU kernels
# this only effects the Jacobian calculation and is same computation order
SteadyStateAdjoint(autodiff = false, autojacvec = ZygoteVJP())
else
vjp = inplace_vjp(prob, u0, p, verbose, repack)
SteadyStateAdjoint(autojacvec = vjp)
end
return default_sensealg
end
function DiffEqBase._concrete_solve_adjoint(
prob::Union{SciMLBase.AbstractODEProblem,
SciMLBase.AbstractSDEProblem,
SciMLBase.AbstractRODEProblem},
alg, sensealg::Nothing, u0, p,
originator::SciMLBase.ADOriginator, args...;
verbose = true, kwargs...)
if haskey(kwargs, :callback)
has_cb = kwargs[:callback] !== nothing
else
has_cb = false
end
if !(p === nothing || p isa SciMLBase.NullParameters)
if !isscimlstructure(p) && !isfunctor(p)
throw(SciMLStructuresCompatibilityError())
end
end
if p === nothing || p isa SciMLBase.NullParameters
tunables, repack = p, identity
elseif isscimlstructure(p)
tunables, repack, aliases = canonicalize(Tunable(), p)
elseif isfunctor(p)
tunables, repack = Functors.functor(p)
else
throw(SciMLStructuresCompatibilityError())
end
default_sensealg = automatic_sensealg_choice(prob, u0, tunables, verbose, repack)
if has_cb && default_sensealg isa AbstractAdjointSensitivityAlgorithm
default_sensealg = setvjp(default_sensealg, ReverseDiffVJP())
end
DiffEqBase._concrete_solve_adjoint(prob, alg, default_sensealg, u0, p,
originator, args...; verbose,
kwargs...)
end
function DiffEqBase._concrete_solve_adjoint(
prob::AbstractNonlinearProblem, alg,
sensealg::Nothing, u0, p,
originator::SciMLBase.ADOriginator, args...;
verbose = true, kwargs...)
if !(p === nothing || p isa SciMLBase.NullParameters)
if !isscimlstructure(p) && !isfunctor(p)
throw(SciMLStructuresCompatibilityError())
end
end
if p === nothing || p isa SciMLBase.NullParameters
tunables, repack = p, identity
elseif isscimlstructure(p)
tunables, repack, aliases = canonicalize(Tunable(), p)
else
tunables, repack = Functors.functor(p)
end
default_sensealg = automatic_sensealg_choice(prob, u0, tunables, verbose, repack)
DiffEqBase._concrete_solve_adjoint(prob, alg, default_sensealg, u0, p,
originator::SciMLBase.ADOriginator, args...; verbose,
kwargs...)
end
function DiffEqBase._concrete_solve_adjoint(
prob::Union{SciMLBase.AbstractDiscreteProblem,
SciMLBase.AbstractDDEProblem,
SciMLBase.AbstractSDDEProblem,
SciMLBase.AbstractDAEProblem},
alg, sensealg::Nothing,
u0, p, originator::SciMLBase.ADOriginator,
args...; kwargs...)
if length(u0) + length(p) > 100
default_sensealg = ReverseDiffAdjoint()
else
default_sensealg = ForwardDiffSensitivity()
end
DiffEqBase._concrete_solve_adjoint(prob, alg, default_sensealg, u0, p,
originator::SciMLBase.ADOriginator, args...;
kwargs...)
end
const ADJOINT_STEADY_PROBLEM_ERROR_MESSAGE = """
Chosen adjoint method is not compatible with the chosen problem. NonlinearProblem
and SteadyStateProblem require specific adjoint choices (like SteadyStateAdjoint)
and will not work with adjoints designed for time series models. For more details,
see https://docs.sciml.ai/SciMLSensitivity/stable/.
"""
struct AdjointSteadyProblemPairingError <: Exception
prob::Any
sensealg::Any
end
function Base.showerror(io::IO, e::AdjointSteadyProblemPairingError)
println(io, ADJOINT_STEADY_PROBLEM_ERROR_MESSAGE)
print(io, "Problem type: ")
println(io, e.prob)
print(io, "Sensitivity algorithm type: ")
println(io, e.sensealg)
end
# Also include AbstractForwardSensitivityAlgorithm until a dispatch is made!
function DiffEqBase._concrete_solve_adjoint(
prob::AbstractNonlinearProblem, alg,
sensealg::Union{
AbstractAdjointSensitivityAlgorithm,
AbstractForwardSensitivityAlgorithm,
TrackerAdjoint,
ReverseDiffAdjoint,
AbstractShadowingSensitivityAlgorithm
},
u0, p, originator::SciMLBase.ADOriginator,
args...; kwargs...)
throw(AdjointSteadyProblemPairingError(prob, sensealg))
end
function DiffEqBase._concrete_solve_adjoint(
prob::Union{SciMLBase.AbstractODEProblem,
SciMLBase.AbstractSDEProblem,
SciMLBase.AbstractRODEProblem},
alg,
sensealg::Union{BacksolveAdjoint,
QuadratureAdjoint,
InterpolatingAdjoint,
GaussAdjoint},
u0, p, originator::SciMLBase.ADOriginator,
args...; save_start = true, save_end = true,
saveat = eltype(prob.tspan)[],
save_idxs = nothing,
kwargs...)
if !(sensealg isa GaussAdjoint) &&
!(p isa Union{Nothing, SciMLBase.NullParameters, AbstractArray}) ||
(p isa AbstractArray && !Base.isconcretetype(eltype(p)))
throw(AdjointSensitivityParameterCompatibilityError())
end
if p === nothing || p isa SciMLBase.NullParameters
tunables, repack = p, identity
elseif isscimlstructure(p)
tunables, repack, aliases = canonicalize(Tunable(), p)
elseif sensealg isa Union{QuadratureAdjoint, GaussAdjoint}
tunables, repack = Functors.functor(p)
else
throw(SciMLStructuresCompatibilityError())
end
# Remove saveat, etc. from kwargs since it's handled separately
# and letting it jump back in there can break the adjoint
kwargs_prob = NamedTuple(filter(
x -> x[1] != :saveat && x[1] != :save_start &&
x[1] != :save_end && x[1] != :save_idxs,
prob.kwargs))
if haskey(kwargs, :callback)
cb = track_callbacks(CallbackSet(kwargs[:callback]), current_time(prob),
state_values(prob), parameter_values(prob),
sensealg)
_prob = remake(prob; u0 = u0, p = p, kwargs = merge(kwargs_prob, (; callback = cb)))
else
cb = nothing
_prob = remake(prob; u0 = u0, p = p, kwargs = kwargs_prob)
end
# Remove callbacks, saveat, etc. from kwargs since it's handled separately
kwargs_fwd = NamedTuple{Base.diff_names(Base._nt_names(values(kwargs)), (:callback,))}(values(kwargs))
# Capture the callback_adj for the reverse pass and remove both callbacks
kwargs_adj = NamedTuple{
Base.diff_names(Base._nt_names(values(kwargs)),
(:callback_adj, :callback))}(values(kwargs))
isq = sensealg isa QuadratureAdjoint
if sensealg isa BacksolveAdjoint
sol = solve(_prob, alg, args...; save_noise = true,
save_start = save_start, save_end = save_end,
saveat = saveat, kwargs_fwd...)
elseif ischeckpointing(sensealg)
sol = solve(_prob, alg, args...; save_noise = true,
save_start = true, save_end = true,
saveat = saveat, kwargs_fwd...)
else
sol = solve(_prob, alg, args...; save_noise = true, save_start = true,
save_end = true, kwargs_fwd...)
end
# Force `save_start` and `save_end` in the forward pass This forces the
# solver to do the backsolve all the way back to `u0` Since the start aliases
# `_prob.u0`, this doesn't actually use more memory But it cleans up the
# implementation and makes `save_start` and `save_end` arg safe.
if sensealg isa BacksolveAdjoint
# Saving behavior unchanged
ts = current_time(sol)
only_end = length(ts) == 1 && ts[1] == _prob.tspan[2]
out = SciMLBase.sensitivity_solution(sol, state_values(sol), ts)
elseif saveat isa Number
if _prob.tspan[2] > _prob.tspan[1]
ts = _prob.tspan[1]:convert(typeof(_prob.tspan[2]), abs(saveat)):_prob.tspan[2]
else
ts = _prob.tspan[2]:convert(typeof(_prob.tspan[2]), abs(saveat)):_prob.tspan[1]
end
# if _prob.tspan[2]-_prob.tspan[1] is not a multiple of saveat, one looses the last ts value
last(current_time(sol)) !== ts[end] && (ts = fix_endpoints(sensealg, sol, ts))
if cb === nothing
_out = sol(ts)
else
_, duplicate_iterator_times = separate_nonunique(current_time(sol))
_out, ts = out_and_ts(ts, duplicate_iterator_times, sol)
end
out = if save_idxs === nothing
out = SciMLBase.sensitivity_solution(sol, state_values(_out), ts)
else
_outf = getu(_out, save_idxs)
out = SciMLBase.sensitivity_solution(sol, _outf(_out), ts)
end
only_end = length(ts) == 1 && ts[1] == _prob.tspan[2]
elseif isempty(saveat)
no_start = !save_start
no_end = !save_end
sol_idxs = 1:length(sol)
no_start && (sol_idxs = sol_idxs[2:end])
no_end && (sol_idxs = sol_idxs[1:(end - 1)])
only_end = length(sol_idxs) <= 1
_u = sol.u[sol_idxs]
u = save_idxs === nothing ? _u : [x[save_idxs] for x in _u]
ts = current_time(sol, sol_idxs)
out = SciMLBase.sensitivity_solution(sol, u, ts)
else
_saveat = saveat isa Array ? sort(saveat) : saveat # for minibatching
if cb === nothing
_saveat = eltype(_saveat) <: typeof(prob.tspan[2]) ?
convert.(typeof(_prob.tspan[2]), _saveat) : _saveat
ts = _saveat
_out = sol(ts)
else
_ts, duplicate_iterator_times = separate_nonunique(current_time(sol))
_out, ts = out_and_ts(_saveat, duplicate_iterator_times, sol)
end
out = if save_idxs === nothing
out = SciMLBase.sensitivity_solution(sol, state_values(_out), ts)
else
_outf = getu(_out, save_idxs)
out = SciMLBase.sensitivity_solution(sol, _outf(_out), ts)
end
only_end = length(ts) == 1 && ts[1] == _prob.tspan[2]
end
_save_idxs = save_idxs === nothing ? Colon() : save_idxs
function adjoint_sensitivity_backpass(Δ)
function df_iip(_out, u, p, t, i)
outtype = _out isa SubArray ?
ArrayInterface.parameterless_type(_out.parent) :
ArrayInterface.parameterless_type(_out)
if only_end
eltype(Δ) <: NoTangent && return
if (Δ isa AbstractArray{<:AbstractArray} || Δ isa AbstractVectorOfArray) &&
length(Δ) == 1 && i == 1
# user did sol[end] on only_end
x = Δ isa AbstractVectorOfArray ? Δ.u[1] : Δ[1]
if _save_idxs isa Number
vx = vec(x)
_out[_save_idxs] .= vx[_save_idxs]
elseif _save_idxs isa Colon
vec(_out) .= vec(adapt(outtype, x))
else
vec(@view(_out[_save_idxs])) .= adapt(outtype,
vec(x)[_save_idxs])
end
else
Δ isa NoTangent && return
if _save_idxs isa Number
x = vec(Δ)
_out[_save_idxs] .= adapt(outtype, @view(x[_save_idxs]))
elseif _save_idxs isa Colon
vec(_out) .= vec(adapt(outtype, Δ))
else
x = vec(Δ)
vec(@view(_out[_save_idxs])) .= adapt(outtype, @view(x[_save_idxs]))
end
end
else
Δu = Δ isa Tangent ? Δ.u : Δ
!Base.isconcretetype(eltype(Δ)) &&
(Δu[i] isa NoTangent || eltype(Δu) <: NoTangent) && return
if Δ isa AbstractArray{<:AbstractArray} || Δ isa AbstractVectorOfArray ||
Δ isa Tangent
x = (Δ isa AbstractVectorOfArray || Δ isa Tangent) ? Δ.u[i] : Δ[i]
if _save_idxs isa Number
_out[_save_idxs] = x[_save_idxs]
elseif _save_idxs isa Colon
vec(_out) .= (x isa NoTangent || x isa ZeroTangent) ? vec(zero(u)) :
vec(x)
else
vec(@view(_out[_save_idxs])) .= vec(@view(x[_save_idxs]))
end
else
if _save_idxs isa Number
_out[_save_idxs] = adapt(outtype,
reshape(Δ, prod(size(Δ)[1:(end - 1)]),
size(Δ)[end])[_save_idxs,
i])
elseif _save_idxs isa Colon
vec(_out) .= vec(adapt(outtype,
reshape(Δ, prod(size(Δ)[1:(end - 1)]),
size(Δ)[end])[:, i]))
else
vec(@view(_out[_save_idxs])) .= vec(adapt(outtype,
reshape(Δ,
prod(size(Δ)[1:(end - 1)]),
size(Δ)[end])[:,
i]))
end
end
end
end
function df_oop(u, p, t, i; outtype = nothing)
if only_end
eltype(Δ) <: NoTangent && return
if (Δ isa AbstractArray{<:AbstractArray} || Δ isa AbstractVectorOfArray) &&
length(Δ) == 1 && i == 1
# user did sol[end] on only_end
x = Δ isa AbstractVectorOfArray ? Δ.u[1] : Δ[1]
if _save_idxs isa Number
vx = vec(x)
_out = adapt(outtype, @view(vx[_save_idxs]))
elseif _save_idxs isa Colon
_out = adapt(outtype, x)
else
_out = adapt(outtype, vec(x)[_save_idxs])
end
else
Δ isa NoTangent && return
if _save_idxs isa Number
x = vec(Δ)
_out = adapt(outtype, @view(x[_save_idxs]))
elseif _save_idxs isa Colon
_out = adapt(outtype, vec(Δ))
else
x = vec(Δ)
_out = adapt(outtype, @view(x[_save_idxs]))
end
end
else
!Base.isconcretetype(eltype(Δ)) &&
(Δ[i] isa NoTangent || eltype(Δ) <: NoTangent) && return
if Δ isa AbstractArray{<:AbstractArray} || Δ isa AbstractVectorOfArray
x = Δ isa AbstractVectorOfArray ? Δ.u[i] : Δ[i]
if _save_idxs isa Number
_out = @view(x[_save_idxs])
elseif _save_idxs isa Colon
_out = vec(x)
else
_out = vec(@view(x[_save_idxs]))
end
else
if _save_idxs isa Number
_out = adapt(outtype,
reshape(Δ, prod(size(Δ)[1:(end - 1)]),
size(Δ)[end])[_save_idxs,
i])
elseif _save_idxs isa Colon
_out = vec(adapt(outtype,
reshape(Δ, prod(size(Δ)[1:(end - 1)]),
size(Δ)[end])[:, i]))
else
_out = vec(adapt(outtype,
reshape(Δ,
prod(size(Δ)[1:(end - 1)]),
size(Δ)[end])[:, i]))
end
end
end
return _out
end
if haskey(kwargs_adj, :callback_adj)
cb2 = CallbackSet(cb, kwargs[:callback_adj])
else
cb2 = cb
end
if ArrayInterface.ismutable(eltype(state_values(sol)))
du0, dp = adjoint_sensitivities(sol, alg, args...; t = ts,
dgdu_discrete = df_iip,
sensealg = sensealg,
callback = cb2,
kwargs_adj...)
else
du0, dp = adjoint_sensitivities(sol, alg, args...; t = ts,
dgdu_discrete = df_oop,
sensealg = sensealg,
callback = cb2,
kwargs_adj...)
end
du0 = reshape(du0, size(u0))
dp = p === nothing || p === DiffEqBase.NullParameters() ? nothing :
dp isa AbstractArray ? reshape(dp', size(tunables)) : dp
_, repack_adjoint = if p === nothing || p === DiffEqBase.NullParameters() ||
!isscimlstructure(p)
nothing, x -> (x,)
else
Zygote.pullback(p) do p
t, _, _ = canonicalize(Tunable(), p)
t
end
end
if originator isa SciMLBase.TrackerOriginator ||
originator isa SciMLBase.ReverseDiffOriginator
(NoTangent(), NoTangent(), du0, repack_adjoint(dp)[1], NoTangent(),
ntuple(_ -> NoTangent(), length(args))...)
else
(NoTangent(), NoTangent(), NoTangent(),
du0, repack_adjoint(dp)[1], NoTangent(),
ntuple(_ -> NoTangent(), length(args))...)
end
end
out, adjoint_sensitivity_backpass
end
# Prefer this route since it works better with callback AD
function DiffEqBase._concrete_solve_adjoint(prob::SciMLBase.AbstractODEProblem, alg,
sensealg::ForwardSensitivity,
u0, p, originator::SciMLBase.ADOriginator,
args...;
save_idxs = nothing,
kwargs...)
if p === nothing || p isa SciMLBase.NullParameters
tunables, repack = p, identity
elseif isscimlstructure(p)
tunables, repack, _ = canonicalize(Tunable(), p)
else
throw(SciMLStructuresCompatibilityError())
end
if tunables isa AbstractArray && eltype(tunables) <: ForwardDiff.Dual &&
!(eltype(u0) <: ForwardDiff.Dual)
# Handle double differentiation case
u0 = eltype(p).(u0)
end
## Force recompile mode until jvps are specialized to handle this!!!
_f = if prob.f isa ODEFunction &&
(prob.f.f isa FunctionWrappersWrappers.FunctionWrappersWrapper ||
SciMLBase.specialization(prob.f) === SciMLBase.AutoSpecialize)
ODEFunction{isinplace(prob), SciMLBase.FullSpecialize}(unwrapped_f(prob.f))
else
prob.f
end
# callback = nothing ensures only the callback in kwargs is used
_prob = ODEForwardSensitivityProblem(
_f, u0, prob.tspan, p; sensealg = sensealg, callback = nothing)
sol = solve(_prob, alg, args...; kwargs...)
_, du = extract_local_sensitivities(sol, sensealg, Val(true))
ts = current_time(sol)
u = if save_idxs === nothing
uf = getu(sol, 1:length(u0))
reshape.(uf(sol), Ref(size(u0)))
else
uf = getu(sol, _save_idxs)
uf(sol)
end
out = SciMLBase.sensitivity_solution(sol, u, ts)
if originator isa SciMLBase.EnzymeOriginator
@reset out.prob = prob
end
function forward_sensitivity_backpass(Δ)
adj = sum(eachindex(du)) do i
J = du[i]
if Δ isa AbstractVector
v = Δ[i]
elseif Δ isa DESolution || Δ isa AbstractVectorOfArray
v = Δ.u[i]
elseif Δ isa AbstractMatrix
v = @view Δ[:, i]
else
v = @view Δ[.., i]
end
J'vec(v)
end
du0 = @not_implemented("ForwardSensitivity does not differentiate with respect to u0. Change your sensealg.")
if originator isa SciMLBase.TrackerOriginator ||
originator isa SciMLBase.ReverseDiffOriginator
(NoTangent(), NoTangent(), du0, adj, NoTangent(),
ntuple(_ -> NoTangent(), length(args))...)
else
(NoTangent(), NoTangent(), NoTangent(), du0, adj, NoTangent(),
ntuple(_ -> NoTangent(), length(args))...)
end
end
out, forward_sensitivity_backpass
end
function DiffEqBase._concrete_solve_forward(prob::SciMLBase.AbstractODEProblem, alg,
sensealg::AbstractForwardSensitivityAlgorithm,
u0, p, originator::SciMLBase.ADOriginator,
args...; save_idxs = nothing,
kwargs...)
_prob = ODEForwardSensitivityProblem(
prob.f, u0, prob.tspan, p; sensealg = sensealg, callback = nothing)
sol = solve(_prob, args...; kwargs...)
if originator isa SciMLBase.EnzymeOriginator
@reset sol.prob = prob
end
u, du = extract_local_sensitivities(sol, Val(true))
_save_idxs = save_idxs === nothing ? (1:length(u0)) : save_idxs
ts = current_time(sol)
uf = getu(sol, _save_idxs)
out = SciMLBase.sensitivity_solution(sol,
ForwardDiff.value.(uf(sol, 1:length(sol))), ts)
function _concrete_solve_pushforward(Δself, ::Nothing, ::Nothing, x3, Δp, args...)
x3 !== nothing && error("Pushforward currently requires no u0 derivatives")
du * Δp
end
out, _concrete_solve_pushforward
end
const FORWARDDIFF_SENSITIVITY_PARAMETER_COMPATIBILITY_MESSAGE = """
ForwardDiffSensitivity assumes the `AbstractArray` interface for `p`. Thus while
DifferentialEquations.jl can support any parameter struct type, usage
with ForwardDiffSensitivity requires that `p` could be a valid
type for being the initial condition `u0` of an array. This means that
many simple types, such as `Tuple`s and `NamedTuple`s, will work as
parameters in normal contexts but will fail during ForwardDiffSensitivity
construction. To work around this issue for complicated cases like nested structs,
look into defining `p` using `AbstractArray` libraries such as RecursiveArrayTools.jl
or ComponentArrays.jl.
"""
struct ForwardDiffSensitivityParameterCompatibilityError <: Exception end
function Base.showerror(io::IO, e::ForwardDiffSensitivityParameterCompatibilityError)
print(io, FORWARDDIFF_SENSITIVITY_PARAMETER_COMPATIBILITY_MESSAGE)
end
# Generic Fallback for ForwardDiff
function DiffEqBase._concrete_solve_adjoint(
prob::Union{SciMLBase.AbstractODEProblem,
SciMLBase.AbstractDAEProblem,
SciMLBase.AbstractDDEProblem,
SciMLBase.AbstractSDEProblem,
SciMLBase.AbstractSDDEProblem,
SciMLBase.AbstractRODEProblem},
alg,
sensealg::ForwardDiffSensitivity{CS, CTS},
u0, p, originator::SciMLBase.ADOriginator,
args...; saveat = eltype(prob.tspan)[],
kwargs...) where {CS, CTS}
if p === nothing || p isa SciMLBase.NullParameters
tunables, repack = p, identity
elseif isscimlstructure(p)
tunables, repack, _ = canonicalize(Tunable(), p)
else
throw(SciMLStructuresCompatibilityError())
end
if saveat isa Number
_saveat = prob.tspan[1]:saveat:prob.tspan[2]
else
_saveat = saveat
end
# use the callback in kwargs, not prob
sol = solve(remake(prob, p = p, u0 = u0, callback = nothing),
alg, args...; saveat = _saveat, kwargs...)
if originator isa SciMLBase.EnzymeOriginator
@reset sol.prob = prob
end
# saveat values
# need all values here. Not only unique ones.
# if a callback is saving two times in primal solution, we also need to get it at least
# two times in the solution using dual numbers.
ts = current_time(sol)
function forward_sensitivity_backpass(Δ)
if !(p === nothing || p === SciMLBase.NullParameters())
dp = @thunk begin
chunk_size = if CS === 0 && length(tunables) < 12
length(tunables)
elseif CS !== 0
CS
else
12
end
num_chunks = length(tunables) ÷ chunk_size
num_chunks * chunk_size != length(tunables) && (num_chunks += 1)
pparts = typeof(tunables[1:1])[]
for j in 0:(num_chunks - 1)
local chunk
if ((j + 1) * chunk_size) <= length(tunables)
chunk = ((j * chunk_size + 1):((j + 1) * chunk_size))
pchunk = vec(tunables)[chunk]
pdualpart = seed_duals(pchunk, prob.f,
ForwardDiff.Chunk{chunk_size}())
else
chunk = ((j * chunk_size + 1):length(tunables))
pchunk = vec(tunables)[chunk]
pdualpart = seed_duals(pchunk, prob.f,
ForwardDiff.Chunk{length(chunk)}())
end
pdualvec = if j == 0
vcat(pdualpart, tunables[((j + 1) * chunk_size + 1):end])
elseif j == num_chunks - 1
vcat(tunables[1:(j * chunk_size)], pdualpart)
else
vcat(tunables[1:(j * chunk_size)], pdualpart,
tunables[(((j + 1) * chunk_size) + 1):end])
end
pdual = SciMLStructures.replace(Tunable(), p, pdualvec)
u0dual = convert.(eltype(pdualvec), u0)
if (convert_tspan(sensealg) === nothing &&
((haskey(kwargs, :callback) &&
has_continuous_callback(kwargs[:callback])))) ||
(convert_tspan(sensealg) !== nothing && convert_tspan(sensealg))
tspandual = convert.(eltype(pdual), prob.tspan)
else
tspandual = prob.tspan
end
## Force recompile mode because it won't handle the duals
## Would require a manual tag to be applied
if prob.f isa ODEFunction
if prob.f.jac_prototype !== nothing
_f = ODEFunction{SciMLBase.isinplace(prob.f),
SciMLBase.FullSpecialize}(unwrapped_f(prob.f),
jac_prototype = convert.(eltype(u0dual),
prob.f.jac_prototype))
else
_f = ODEFunction{SciMLBase.isinplace(prob.f),
SciMLBase.FullSpecialize}(unwrapped_f(prob.f))
end
elseif prob.f isa SDEFunction && prob.f.jac_prototype !== nothing
_f = SDEFunction{SciMLBase.isinplace(prob.f),
SciMLBase.FullSpecialize}(unwrapped_f(prob.f),
jac_prototype = convert.(eltype(u0dual),
prob.f.jac_prototype))
else
_f = prob.f
end
# use the callback from kwargs, not prob
_prob = remake(prob, f = _f, u0 = u0dual, p = pdual,
tspan = tspandual, callback = nothing)
if _prob isa SDEProblem
_prob.noise_rate_prototype !== nothing && (_prob = remake(_prob,
noise_rate_prototype = convert.(eltype(pdual),
_prob.noise_rate_prototype)))
end
if saveat isa Number
_saveat = prob.tspan[1]:saveat:prob.tspan[2]
else
_saveat = saveat
end
_sol = solve(_prob, alg, args...; saveat = ts, kwargs...)
_, du = extract_local_sensitivities(_sol, sensealg, Val(true))
if haskey(kwargs, :callback)
# handle bounds errors: ForwardDiffSensitivity uses dual numbers, so there
# can be more or less time points in the primal solution
# than in the solution using dual numbers when adaptive solvers are used.
# First step: filter all values, so that only time steps that actually occur
# in the primal are left. This is for example necessary when `terminate!`
# is used.
indxs = findall(t -> t ∈ ts, current_time(_sol))
_ts = current_time(_sol, indxs)
# after this filtering step, we might end up with a too large amount of indices.
# For example, if a callback saved values in the primal, then we now potentially
# save it by `saveat` and by `save_positions` of the callback.
# Second step. Drop these duplicates values.
if length(indxs) != length(ts)
for i in (length(_ts) - 1):-1:2
if _ts[i] == _ts[i + 1] && _ts[i] == _ts[i - 1]
deleteat!(indxs, i)
end
end
end
_du = @view du[indxs]
else
_du = du
end
_dp = sum(eachindex(_du)) do i
J = _du[i]
if Δ isa AbstractVector
v = Δ[i]
elseif Δ isa AbstractVectorOfArray || Δ isa Tangent
v = Δ.u[i]
elseif Δ isa AbstractMatrix
v = @view Δ[:, i]
else
v = @view Δ[.., i]
end
if !(Δ isa NoTangent || v isa ZeroTangent)
if u0 isa Number
ForwardDiff.value.(J'v)
elseif v isa Tangent
ForwardDiff.value.(J'vec(v.x))
else
ForwardDiff.value.(J'vec(v))
end
else
zero(p)
end
end
push!(pparts, vec(_dp))
end
reduce(vcat, pparts)
end
else
dp = nothing
end
du0 = @thunk begin
chunk_size = if CS === 0 && length(u0) < 12
length(u0)
elseif CS !== 0
CS
else
12
end
num_chunks = length(u0) ÷ chunk_size
num_chunks * chunk_size != length(u0) && (num_chunks += 1)
du0parts = u0 isa Number ? typeof(u0)[] : typeof(u0[1:1])[]
local _du0
for j in 0:(num_chunks - 1)
local chunk
if u0 isa Number
u0dualpart = seed_duals(u0, prob.f,
ForwardDiff.Chunk{chunk_size}())
elseif ((j + 1) * chunk_size) <= length(u0)
chunk = ((j * chunk_size + 1):((j + 1) * chunk_size))
u0chunk = vec(u0)[chunk]