feat: add doc example for implementing the interface

Author: AayushSabharwal

Diff for: docs/Project.toml

@@ -1,7 +1,13 @@
 [deps]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+OrdinaryDiffEqTsit5 = "b1df2697-797e-41e3-8120-5422d3b24e4a"
+SciMLSensitivity = "1ed8b502-d754-442c-8d5d-10ac956f44a1"
 SciMLStructures = "53ae85a6-f571-4167-b2af-e1d143709226"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [compat]
 Documenter = "1"
+OrdinaryDiffEqTsit5 = "1.1.0"
+SciMLSensitivity = "7.69"
 SciMLStructures = "1"
+Zygote = "0.6.72"

Diff for: docs/make.jl

@@ -6,6 +6,7 @@ cp("./docs/Project.toml", "./docs/src/assets/Project.toml", force = true)
 pages = [
     "Home" => "index.md",
     "interface.md",
+    "example.md",
     "api.md"
 ]
 

Diff for: docs/src/example.md

@@ -0,0 +1,121 @@
+# An example implementation of the interface
+
+In this tutorial we will implement the SciMLStructures.jl interface for a parameter
+object. This is useful when differentiating through ODE solves using SciMLSensitivity.jl
+and only part of the parameters are differentiable.
+
+```@example
+using OrdinaryDiffEqTsit5
+using LinearAlgebra
+
+mutable struct SubproblemParameters{P, Q, R}
+  p::P # tunable
+  q::Q
+  r::R
+end
+
+mutable struct Parameters{P, C}
+  subparams::P
+  coeffs::C # tunable matrix
+end
+
+# the rhs is `du[i] = p[i] * u[i]^2 + q[i] * u[i] + r[i] * t` for i in 1:length(subparams)
+# and `du[length(subparams)+1:end] .= coeffs * u`
+function rhs!(du, u, p::Parameters, t)
+  for (i, subpars) in enumerate(p.subparams)
+    du[i] = subpars.p * u[i]^2 + subpars.q * u[i] + subpars.r * t
+  end
+  N = length(p.subparams)
+  mul!(view(du, (N+1):(length(du))), p.coeffs, u)
+  return nothing
+end
+
+u = sin.(0.1:0.1:1.0)
+subparams = [SubproblemParameters(0.1i, 0.2i, 0.3i) for i in 1:5]
+p = Parameters(subparams, cos.([0.1i+0.33j for i in 1:5, j in 1:10]))
+tspan = (0.0, 1.0)
+
+prob = ODEProblem(rhs!, u, tspan, p)
+solve(prob, Tsit5())
+```
+
+The ODE solves fine. Now let's try to differentiate with respect to the tunable parameters.
+
+```@example
+using Zygote
+using SciMLSensitivity
+
+# 5 subparams[i].p, 50 elements in coeffs
+Zygote.gradient(0.1ones(55)) do tunables
+  subpars = [SubproblemParameters(tunables[i], subpar.q, subpar.r) for (i, subpar) in enumerate(p.subparams)]
+  coeffs = reshape(tunables[6:end], size(p.coeffs))
+  newp = Parameters(subpars, coeffs)
+  newprob = remake(prob; p = newp)
+  sol = solve(prob, Tsit5())
+  return sum(sol.u[end])
+end
+```
+
+SciMLSensitivity does not know how to handle the parameter object, because it does not
+implement the SciMLStructures interface.
+
+```@example
+import SciMLStructures as SS
+
+# Mark the struct as a SciMLStructure
+SS.isscimlstructure(::Parameters) = true
+# It is mutable
+SS.ismutablescimlstructure(::Parameters) = true
+
+# Only contains `Tunable` portion
+# We could also add a `Constants` portion to contain the values that are
+# not tunable. The implementation would be similar to this one.
+SS.hasportion(::SS.Tunable, ::Parameters) = true
+
+function SS.canonicalize(::SS.Tunable, p::Parameters)
+  # concatenate all tunable values into a single vector
+  buffer = vcat([subpar.p for subpar in p.subparams], vec(p.coeffs))
+
+  # repack takes a new vector of the same length as `buffer`, and constructs
+  # a new `Parameters` object using the values from the new vector for tunables
+  # and retaining old values for other parameters. This is exactly what replace does,
+  # so we can use that instead.
+  repack = let p = p
+    function repack(newbuffer)
+      SS.replace(SS.Tunable(), p, newbuffer)
+    end
+  end
+  # the canonicalized vector, the repack function, and a boolean indicating
+  # whether the buffer aliases values in the parameter object (here, it doesn't)
+  return buffer, repack, false
+end
+
+function SS.replace(::SS.Tunable, p::Parameters, newbuffer)
+  N = length(p.subparams) + length(p.coeffs)
+  @assert length(newbuffer) == N
+  subparams = [SubproblemParameters(newbuffer[i], subpar.q, subpar.r) for (i, subpar) in enumerate(p.subparams)]
+  coeffs = reshape(view(newbuffer, (length(p.subparams)+1):length(newbuffer)), size(p.coeffs))
+  return Parameters(subparams, coeffs)
+end
+
+function SS.replace!(::SS.Tunable, p::Parameters, newbuffer)
+  N = length(p.subparams) + length(p.coeffs)
+  @assert length(newbuffer) == N
+  for (subpar, val) in zip(p.subparams, newbuffer)
+    subpar.p = val
+  end
+  copyto!(coeffs, view(newbuffer, (length(p.subparams)+1):length(newbuffer)))
+  return p
+end
+```
+
+Now, we should be able to differentiate through the ODE solve.
+
+```@example
+Zygote.gradient(0.1ones(length(SS.canonicalize(SS.Tunable(), p)[1]))) do tunables
+  newp = SS.replace(SS.Tunable(), p, tunables)
+  newprob = remake(prob; p = newp)
+  sol = solve(newprob, Tsit5())
+  return sum(sol.u[end])
+end
+```