Non-deterministic behaviour

[theo-brown]

I can run an inverse solve with the same constraints and initial conditions and get two different equilibria, or a forward solve with the same coil currents and get two different equilibria. This can result in a limited plasma and the failure to form secondary X points.

Is there secretly some randomness in the solver that isn't being seeded correctly? Or is there numerical instability that is causing this behaviour?

Example inverse solve:

Will replicate the forward solve when I have a spare mo

[nicamo]

Hi @theo-brown, starting from the forward, which is easier to diagnose. Are both equilibria successful GS solutions? Or just "the last iteration for psi_plasma" after an unsuccessful static solve? If the former, you may have found a case of multiple GS solutions, like identified by Kamran: https://iopscience.iop.org/article/10.1088/1741-4326/adf3cc
In general, non-deterministic behaviour is introduced in the forward static solve when encountering stagnation, and repeating simple iterations would not determine improvement.

[theo-brown]

In general, non-deterministic behaviour is introduced in the forward static solve when encountering stagnation, and repeating simple iterations would not determine improvement.

What's the method for this? Is it something that could be seeded for reproducibility?

Edit: Ah, I see, it's here:

freegsnke/freegsnke/GSstaticsolver.py

Lines 554 to 564 in ca47ed9

	if (residual_collinearity > 0.9) and (picard_flag is False):
	log.append(
	"New starting_direction used due to collinear residuals."
	)
	# Generate a random Krylov vector to continue the exploration
	# This is arbitrary and can be improved
	starting_direction = np.sin(
	np.linspace(0, 2 * np.pi, self.nx)
	* 1.5
	* np.random.random()
	)[:, np.newaxis]

Maybe I could PR to replace this with a seeded RNG?