Open gszep opened 3 years ago
problems with adjoints https://arxiv.org/abs/2103.15341
The continuation steps through it most likely. This solver is well described here: Keller, Herbert B. “The Bordering Algorithm and Path Following Near Singular Points of Higher Nullity.” SIAM Journal on Scientific and Statistical Computing 4, no. 4 (December 1983): 573–82. https://doi.org/10.1137/0904039.
The implicit layers approach to calculating gradients requires solving a linear system with
A::Matrix \ x::Vector
whereA
is the JacobiandG/d(u,p)
whereG = [ F, det(J) ]
. Let's make a plot of the percentage error between finite difference and autodiff as the condition number forA
is increased. @rveltz I use the same linear solvers as you, do you know what happens when your matrixJ = dF/du
is ill-conditioned?