# Sensitivity Algorithms for Nonlinear Problems with Automatic Differentiation (AD)

DiffEqSensitivity.SteadyStateAdjointType

An implementation of the adjoint differentiation of a nonlinear solve. Uses the implicit function theorem to directly compute the derivative of the solution to $f(u,p) = 0$ with respect to p.

Constructor

SteadyStateAdjoint(;chunk_size = 0, autodiff = true,
diff_type = Val{:central},
autojacvec = autodiff, linsolve = nothing)

Keyword Arguments

• autodiff: Use automatic differentiation for constructing the Jacobian if the Jacobian needs to be constructed. Defaults to true.
• chunk_size: Chunk size for forward-mode differentiation if full Jacobians are built (autojacvec=false and autodiff=true). Default is 0 for automatic choice of chunk size.
• diff_type: The method used by FiniteDiff.jl for constructing the Jacobian if the full Jacobian is required with autodiff=false.
• autojacvec: Calculate the vector-Jacobian product (J'*v) via automatic differentiation with special seeding. The default is nothing. The total set of choices are:
• false: the Jacobian is constructed via FiniteDiff.jl
• true: the Jacobian is constructed via ForwardDiff.jl
• TrackerVJP: Uses Tracker.jl for the vjp.
• ZygoteVJP: Uses Zygote.jl for the vjp.
• EnzymeVJP: Uses Enzyme.jl for the vjp.
• ReverseDiffVJP(compile=false): Uses ReverseDiff.jl for the vjp. compile is a boolean for whether to precompile the tape, which should only be done if there are no branches (if or while statements) in the f function.
• linsolve: the linear solver used in the adjoint solve. Defaults to nothing, which uses a polyalgorithm to attempt to automatically choose an efficient algorithm.

For more details on the vjp choices, please consult the sensitivity algorithms documentation page or the docstrings of the vjp types.

References

Johnson, S. G., Notes on Adjoint Methods for 18.336, Online at http://math.mit.edu/stevenj/18.336/adjoint.pdf (2007)