SciMLOperators.jl

July 31, 2025 · View on GitHub

Unified operator interface for SciML.ai and beyond

SciMLOperators is a package for managing linear, nonlinear, time-dependent, and parameter dependent operators acting on vectors, (or column-vectors of matrices). We provide wrappers for matrix-free operators, fast tensor-product evaluations, pre-cached mutating evaluations, as well as Zygote-compatible non-mutating evaluations.

The lazily implemented operator algebra allows the user to update the operator state by passing in an update function that accepts arbitrary parameter objects. Further, our operators behave like AbstractMatrix types thanks to overloads defined for methods in Base, and LinearAlgebra.

Therefore, an AbstractSciMLOperator can be passed to LinearSolve.jl, or NonlinearSolve.jl as a linear/nonlinear operator, or to OrdinaryDiffEq.jl as an ODEFunction. Examples of usage within the SciML ecosystem are provided in the documentation.

Installation

SciMLOperators.jl is a registered package and can be installed via

julia> import Pkg
julia> Pkg.add("SciMLOperators")

Examples

Let M, D, F be matrix-based, diagonal-matrix-based, and function-based SciMLOperators respectively.

using SciMLOperators, LinearAlgebra
N = 4
function f(v, u, p, t)
    u .* v
end
function f(w, v, u, p, t)
    w .= u .* v
end

u = rand(4)
p = nothing # parameter struct
t = 0.0     # time

M = MatrixOperator(rand(N, N))
D = DiagonalOperator(rand(N))
F = FunctionOperator(f, zeros(N), zeros(N); u, p, t)

Then, the following codes just work.

L1 = 2M + 3F + LinearAlgebra.I + rand(N, N)
L2 = D * F * M'
L3 = kron(M, D, F)
L4 = lu(M) \ D
L5 = [M; D]' * [M F; F D] * [F; D]

Each L# can be applied to AbstractVectors of appropriate sizes:

v = rand(N)
w = L1(v, u, p, t) # == L1 * v

v_kron = rand(N^3)
w_kron = L3(v_kron, u, p, t) # == L3 * v_kron

For mutating operator evaluations, call cache_operator to generate an in-place cache, so the operation is nonallocating.

α, β = rand(2)

# allocate cache
L2 = cache_operator(L2, u)
L4 = cache_operator(L4, u)

# allocation-free evaluation
L2(w, v, u, p, t) # == mul!(w, L2, v)
L4(w, v, u, p, t, α, β) # == mul!(w, L4, v, α, β)

Installation

Examples

Roadmap