Best practices for optimization problems with ODE solves and eigen calls

General Usage Performance
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1

I am working on an optimization which has the following structure

  1. Build some Hamiltonian large matrices which are functions of the parameters I am optimizing over
  2. Project onto the lowest couple of energy levels
  3. Calculate some propagators (basically solve an ODE)
  4. Calculate some cost function based off the results

I am wondering if there are any recommendations for how do this well! Currently I am using SciML Optimization.jl with NelderMead but have also had some slightly better success with NonlinearSolve’s LevenbergMarquardt + AutoFiniteDiff.

I think the main questions are:

  1. Has anyone run into similar optimization problems and if so, what works? What are some other solvers / techniques that might be good for this type of problem.
  2. Ideally, I would be able to use Forward or Reverse autodiff. However, this does not work because of the eigen decomposition. Is there any way to get this to work?
2

Hi, could you provide a minimal example of the differentiation failures you’re running into? Ideally with vaguely realistic problem sizes and sparsities