refactor(notebooks): use internal adam and optimize helper - batch 4

[marcorudolphflex]

follow-up from #463

Replaces the optax Adam with our Adam and makes use of the optimize helper where easily possible. This is the fourth batch, reduced to the 9 notebooks from #465 where develop still had real optax usage. Metalens.ipynb, Autograd27Smatrix.ipynb, and Autograd25WaveguideCrossing.ipynb are intentionally left out for separate discussion.

Results are roughly unchanged overall. Relevant comparison notes copied from #465 are below.

Percent differences below use (branch - develop) / develop. For max objectives, positive is better; for min objectives/costs, negative is better.

Status	Notebook	Direction	develop	branch	diff	diff %	Note
❓	TidyFab0GC	max	3.0199e-01	5.1519e-01	+2.1320e-01	+70.60%	objective, unexpectedly better
	Autograd19ApodizedCoupler	max	4.799e-01	4.801e-01	+2.0e-04	+0.04%	objective; coupling efficiency develop -1.98 dB vs. branch -1.99 dB
	Autograd7Metalens	max	2.2378e+01	2.3344e+01	+9.660e-01	+4.32%	objective, roughly unchanged
	Autograd26DiffractiveBeamSplitter	max	8.792e-01	8.790e-01	-2.0e-04	-0.02%	loss value; cost min changes by +0.02%; final efficiency 0.91 to 0.89
	Autograd28FiberLens	max	4.0488e-02	4.0460e-02	-2.8e-05	-0.07%	final flux, plot/result nearly unchanged
	BilayerSiNSiGC	max	8.134e-01	8.139e-01	+5.0e-04	+0.06%	objective, effectively unchanged
	RFAutograd1RectangularPatchAntenna	max	20.812315	20.717626	-9.4689e-02	-0.45%	final nonzero FOM, roughly unchanged
	Autograd13Metasurface	min	1.194e-01	1.185e-01	-9.0e-04	-0.75%	final loss, roughly unchanged
	Autograd23FabricationAwareInvdes	max	0.09930831775707324	0.09930831775707324	0	0.00%	initial objective check; no credits for full rerun

❓ TidyFab0GC.ipynb

Objective (max.): develop 3.0199e-01 vs. branch 5.1519e-01 (+70.60%)

Unexpectedly better. This may be from client/solver changes rather than the optimizer refactor.

Autograd19ApodizedCoupler.ipynb

Objective (max.): develop 4.799e-01 vs. branch 4.801e-01 (+0.04%)

Maximum coupling efficiency: develop -1.98 dB vs. branch -1.99 dB

Rerun is back in line with develop.

Autograd7Metalens.ipynb

Objective (max.): develop 2.2378e+01 vs. branch 2.3344e+01 (+4.32%)

Plot/result roughly unchanged.

Autograd26DiffractiveBeamSplitter.ipynb

develop:

Loss value (maximize): 0.8792
  Cost (minimize): 9.2696e-01
  Fab penalty: 9.9816e-01
  Efficiency: 0.9999

branch:

Loss value (maximize): 0.8790
  Cost (minimize): 9.2712e-01
  Fab penalty: 9.9816e-01
  Efficiency: 0.9999

Later final-efficiency output: develop 0.91 vs. branch 0.89.

Autograd28FiberLens.ipynb

Objective / final flux (max.): develop 4.0488e-02 vs. branch 4.0460e-02 (-0.07%)

Plot/result nearly unchanged.

BilayerSiNSiGC.ipynb

Objective (max.): develop 8.134e-01 vs. branch 8.139e-01 (+0.06%)

Effectively unchanged.

RFAutograd1RectangularPatchAntenna.ipynb

Final nonzero FOM: develop 20.812315 vs. branch 20.717626 (-0.45%).

Optimization a little less smooth now, result differs a bit:

Autograd13Metasurface.ipynb

Final loss (min.): develop 1.194e-01 vs. branch 1.185e-01 (-0.75%).

Autograd23FabricationAwareInvdes.ipynb

Did not rerun this notebook because I do not have credits for the prefab/fabrication-aware run path. No result shift is expected from this diff.

---

Note

Low Risk
Notebook-only optimizer wiring changes with no library API changes; numerical drift is minor except one flagged rerun outlier.

Overview
Fourth batch of inverse-design notebook cleanup: nine tutorials drop optax in favor of tidy3d.plugins.autograd adam, apply_updates, and optimize() where the loop is a straight min/max with bounds.

TidyFab0GC is refactored to call optimize(..., direction="max") with a step callback and min-feature bounds instead of hand-rolled Adam steps. Others (Autograd19ApodizedCoupler, Autograd13Metasurface, Autograd26DiffractiveBeamSplitter, etc.) keep explicit loops but swap optax.adam / optax.apply_updates for the internal Adam API; notebooks that still need custom iteration (e.g. beta ramping, live plots) are not forced onto optimize(). Metalens.ipynb, Autograd27Smatrix, and Autograd25WaveguideCrossing are out of scope for this batch.

Reruns vs. develop are mostly within ~1% on objectives; TidyFab0GC shows a large objective jump that may be environment/solver noise rather than the optimizer swap. Autograd23FabricationAwareInvdes was not fully rerun (prefab credits).

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[github-actions]

Spell Check Report

TidyFab0GC.ipynb:

Cell 65, Line 10: 'pre-update'
  > # The callback records pre-update iterates, so param_history

---

Checked 9 notebook(s). Found spelling errors in 1 file(s).
Generated by GitHub Action run: https://github.com/flexcompute/tidy3d-notebooks/actions/runs/27344014223

[groberts-flex]

thanks @marcorudolphflex! overall looks great! I'm a little curious about the RF one where the optimization curve looks less smooth. I wonder if that's some other changes since the last time develop was run or the alternate Adam optimizer behaves slightly differently than optax. Either way, the final performance looks good and I don't think this is a blocker at all!

One small other thing that I came across while going through this with codex was that in TidyFab0GC.ipynb, the best_params are taken from the param_history but those are updated in the callback before the device is stepped. So we could either use the final parameters that are returned or fill in the final device and figure of merit into the param_history.

[marcorudolphflex]

thanks @marcorudolphflex! overall looks great! I'm a little curious about the RF one where the optimization curve looks less smooth. I wonder if that's some other changes since the last time develop was run or the alternate Adam optimizer behaves slightly differently than optax. Either way, the final performance looks good and I don't think this is a blocker at all!

One small other thing that I came across while going through this with codex was that in TidyFab0GC.ipynb, the best_params are taken from the param_history but those are updated in the callback before the device is stepped. So we could either use the final parameters that are returned or fill in the final device and figure of merit into the param_history.

Thanks!
In the past, I reran many notebooks where I reverted optax changes to see if that was the cause and it never changed anything - which is why I skipped that here. Pretty sure some other changes caused that.

Good catch, went with the "final params" way here.

[groberts-flex]

thanks @marcorudolphflex! overall looks great! I'm a little curious about the RF one where the optimization curve looks less smooth. I wonder if that's some other changes since the last time develop was run or the alternate Adam optimizer behaves slightly differently than optax. Either way, the final performance looks good and I don't think this is a blocker at all!
One small other thing that I came across while going through this with codex was that in TidyFab0GC.ipynb, the best_params are taken from the param_history but those are updated in the callback before the device is stepped. So we could either use the final parameters that are returned or fill in the final device and figure of merit into the param_history.

Thanks! In the past, I reran many notebooks where I reverted optax changes to see if that was the cause and it never changed anything - which is why I skipped that here. Pretty sure some other changes caused that.

Good catch, went with the "final params" way here.

Makes sense, that's good to know! It does seem likely the changes are from somewhere else. This all looks good to me, thanks for doing these conversions