Split leaf and root dynamics optimization notebooks

[SarahAlidoost]

closes #66
closes #68

🔴 After merging #61, I will update the docs.

[SarahAlidoost]

@michielkallenberg @ronvree @SCiarella @fnattino in this pull request, STE method is used for the sigmoid approximation for the parameter SPAN in leaf_dynamics, see the issue #68. Please let me know what you think about this approach, or any other ideas/suggestions. Thanks!

[sonarqubecloud]

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[SCiarella]

Thanks @SarahAlidoost, I really prefer this new approach to the sigmoid because the gradient now is much more controlled.

Later, we could even allow the user to set a lower sharpness to have a better gradient for parameter optimization, but right now the value of 1000 that you have chosen looks ok.

I approve this PR for merge 👍

[ronvree]

I also think this is a really good idea! During the development it's much better to remove the ambiguity of whether some sigmoid approximates the original model well enough. Great suggestion!

Although the soft threshold might in some case have a more realistic biophysical interpretation (as also mentioned by Francesco in issue #68), I feel these discussions should be separated from the initial model development.

If I understand correctly the sharpness should ideally still be set based on the magnitude of the input if we want to guarantee there are no issues during optimization?

Would it make sense to implement the thresholds as nn.Module instances so it's easier to inspect their behavior and see the impact of any potential adjustments?

Thanks @SarahAlidoost! I also approve the PR for merge