Increase stellarator-helias epsfcn

[timothy-nunn]

At the moment stellarator-helias does not converge within its first 100 iterations. PROCESS then automatically revises the epsfcn (step length for calculating derivatives) from 1e-3 to 1e-2. Instead of waiting for this to happen automatically, I propose the input file is updated to reflect this.

@jjwalkowiak what do you think?

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 48.63%. Comparing base (c667257) to head (923c341).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #4440   +/-   ##
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  Coverage   48.63%   48.63%           
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  Files         151      151           
  Lines       29673    29673           
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  Hits        14432    14432           
  Misses      15241    15241           

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[jjwalkowiak]

My only concern would be that someone can try to use this regression test as template for other study and then start with 1e-2 as default option. But if you add a comment in the input file which explains that usually we start with 1e-3, then it is fine.
There might be also some issue with the results. I think it might be slightly different when you start directly from 1e-2 However I am not sure how it exactly works. Does the new epsfcn inherits the result from the last iteration of the previous epsfcn as a starting point, or it gets back to the defaults?

[timothy-nunn]

My only concern would be that someone can try to use this regression test as template for other study and then start with 1e-2 as default option. But if you add a comment in the input file which explains that usually we start with 1e-3, then it is fine. There might be also some issue with the results. I think it might be slightly different when you start directly from 1e-2 However I am not sure how it exactly works. Does the new epsfcn inherits the result from the last iteration of the previous epsfcn as a starting point, or it gets back to the defaults?

Thanks for the reply @jjwalkowiak. I will add a comment. I suspect that some of the state remains over from the previous failed optimisation hence why the regression tests have changed. However, this optima will be just as valid as the previous solution, it is probably just closer to the initial point.

Looking at the two solutions:
Old (main) objective value (cost of electricity): 1.21492798588871253e+02
New (this PR) objective value: 1.21493505404321311e+02

This is so small that it does not even show up in the 0.2% difference regression report.

The only large changes to the solution are constraint residuals. These changing indicate that a different solution is being found, however this solution has near identical objective value and all the constraints are being satisfied.

[clmould]

The reasoning for this change makes sense to me, so if @jjwalkowiak is happy I can merge it :)