Use multiple forward diff trials to generate approximate Jacobian sparsity pattern

Project.toml

@@ -1,7 +1,7 @@
 name = "SparseDiffTools"
 uuid = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
 authors = ["Pankaj Mishra <[email protected]>", "Chris Rackauckas <[email protected]>"]
-version = "2.6.0"
+version = "2.7.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -14,6 +14,7 @@ ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 PackageExtensionCompat = "65ce6f38-6b18-4e1d-a461-8949797d7930"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"

src/SparseDiffTools.jl

@@ -17,7 +17,7 @@ using ArrayInterface, SparseArrays
 import ArrayInterface: matrix_colors
 import StaticArrays
 # Others
-using SciMLOperators, LinearAlgebra
+using SciMLOperators, LinearAlgebra, Random
 import DataStructures: DisjointSets, find_root!, union!
 import SciMLOperators: update_coefficients, update_coefficients!
 import Setfield: @set!
@@ -89,7 +89,7 @@ export update_coefficients, update_coefficients!, value!
 export AutoSparseEnzyme
 
 export NoSparsityDetection, SymbolicsSparsityDetection, JacPrototypeSparsityDetection,
-    PrecomputedJacobianColorvec, AutoSparsityDetection
+    PrecomputedJacobianColorvec, ApproximateJacobianSparsity, AutoSparsityDetection
 export sparse_jacobian, sparse_jacobian_cache, sparse_jacobian!
 export init_jacobian
 

src/highlevel/coloring.jl

@@ -30,5 +30,35 @@ function (alg::PrecomputedJacobianColorvec)(ad::AbstractSparseADType, args...; k
     return MatrixColoringResult(colorvec, J, nz_rows, nz_cols)
 end
 
+# Approximate Jacobian Sparsity Detection
+## Right now we hardcode it to use `ForwardDiff`
+function (alg::ApproximateJacobianSparsity)(ad::AbstractSparseADType, f, x; fx = nothing,
+    kwargs...)
+    @unpack ntrials, rng = alg
+    fx = fx === nothing ? f(x) : fx
+    J = fill!(similar(fx, length(fx), length(x)), 0)
+    cfg = ForwardDiff.JacobianConfig(f, x)
+    for _ in 1:ntrials
+        x_ = similar(x)
+        randn!(rng, x_)
+        J .+= abs.(ForwardDiff.jacobian(f, x_, cfg))
+    end
+    return (JacPrototypeSparsityDetection(; jac_prototype = sparse(J), alg.alg))(ad, f, x;
+        fx, kwargs...)
+end
+
+function (alg::ApproximateJacobianSparsity)(ad::AbstractSparseADType, f!, fx, x; kwargs...)
+    @unpack ntrials, rng = alg
+    cfg = ForwardDiff.JacobianConfig(f!, fx, x)
+    J = fill!(similar(fx, length(fx), length(x)), 0)
+    for _ in 1:ntrials
+        x_ = similar(x)
+        randn!(rng, x_)
+        J .+= abs.(ForwardDiff.jacobian(f!, fx, x_, cfg))
+    end
+    return (JacPrototypeSparsityDetection(; jac_prototype = sparse(J), alg.alg))(ad, f!, fx,
+        x; kwargs...)
+end
+
 # TODO: Heuristics to decide whether to use Sparse Differentiation or not
 #       Simple Idea: Check min(max(colorvec_cols), max(colorvec_rows))

src/highlevel/common.jl

@@ -112,6 +112,31 @@ function _get_colorvec(alg::PrecomputedJacobianColorvec, ::AbstractReverseMode)
     return cvec
 end
 
+"""
+    ApproximateJacobianSparsity(; ntrials = 5, rng = Random.default_rng(),
+        alg = GreedyD1Color())
+
+Use `ntrials` random vectors to compute the sparsity pattern of the Jacobian. This is an
+approximate method and the sparsity pattern may not be exact.
+
+## Keyword Arguments
+
+    - `ntrials`: The number of random vectors to use for computing the sparsity pattern
+    - `rng`: The random number generator used for generating the random vectors
+    - `alg`: The algorithm used for computing the matrix colors
+"""
+struct ApproximateJacobianSparsity{R <: AbstractRNG,
+    A <: ArrayInterface.ColoringAlgorithm} <: AbstractSparsityDetection
+    ntrials::Int
+    rng::R
+    alg::A
+end
+
+function ApproximateJacobianSparsity(; ntrials::Int = 3,
+    rng::AbstractRNG = Random.default_rng(), alg = GreedyD1Color())
+    return ApproximateJacobianSparsity(ntrials, rng, alg)
+end
+
 # No one should be using this currently
 Base.@kwdef struct AutoSparsityDetection{A <: ArrayInterface.ColoringAlgorithm} <:
                    AbstractSparsityDetection

test/test_sparse_jacobian.jl

@@ -30,7 +30,7 @@ row_colorvec = SparseDiffTools.matrix_colors(J_sparsity; partition_by_rows = tru
 col_colorvec = SparseDiffTools.matrix_colors(J_sparsity; partition_by_rows = false)
 
 SPARSITY_DETECTION_ALGS = [JacPrototypeSparsityDetection(; jac_prototype = J_sparsity),
-    SymbolicsSparsityDetection(), NoSparsityDetection(),
+    SymbolicsSparsityDetection(), NoSparsityDetection(), ApproximateJacobianSparsity(),
     PrecomputedJacobianColorvec(; jac_prototype = J_sparsity, row_colorvec, col_colorvec)]
 
 @testset "High-Level API" begin