perf(autograd): optimize grey_dilation with striding

[yaugenst-flex]

The previous implementation of grey_dilation was based on convolution, which was slow for both the forward and backward passes.

This PR replaces it with a high-performance implementation that uses NumPy's sliding_window_view to create sliding window views of the input array. I also wrote a custom VJP that uses the same striding technique to make the backward pass faster too.

I also simplified the implementation of grey_erosion so that grey_dilation is now the only function that does the heavy lifting.

Benchmarks show speedups of 10-100x depending on the array and kernel size.

This should make these ops much more usable in topopt @groberts-flex

Greptile Summary

Significant performance optimization of the grey_dilation morphological operation by replacing convolution-based implementation with NumPy's sliding_window_view for strided array operations.

• Replaced convolution-based implementation with strided array approach in tidy3d/plugins/autograd/functions.py, achieving 10-100x speedup
• Added custom VJP (vector-Jacobian product) for efficient backpropagation using the same striding technique
• Simplified grey_erosion by expressing it through duality with grey_dilation
• Updated morphology test cases to use first-order gradients and include kernel structure testing
• Added comprehensive benchmarks showing performance improvements scaling with array and kernel sizes

[greptile-apps]

LGTM

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[github-actions]

Diff Coverage

Diff: origin/develop...HEAD, staged and unstaged changes

• tidy3d/plugins/autograd/functions.py (98.8%): Missing lines 67

Summary

• Total: 83 lines
• Missing: 1 line
• Coverage: 98%

tidy3d/plugins/autograd/functions.py

  63         The indices for padding along the axis.
  64     """
  65     total_pad = sum(pad_width)
  66     if n == 0:
! 67         return numpy_module.zeros(total_pad, dtype=int)
  68 
  69     idx = numpy_module.arange(-pad_width[0], n + pad_width[1])
  70 
  71     if mode == "constant":

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[groberts-flex]

thanks for this implementation, the speed up looks awesome especially for a function that will be in a lot of robust optimizations!

left some comments/questions, some just for my own understanding!

[groberts-flex]

thanks @yaugenst-flex this is great! I understand now much better the multiplicity/multiple maximum part reading through the updated comment. thanks for the clarifications and changes.