feat(adjoint): Adaptively sample fields along slab height and polygon edges

- Implement adaptive field sampling for PolySlab and Cylinder for shape
  derivatives
- Replace fixed grid with Gauss-Legendre quadrature
- Sample fields along all surface boundaries (edges and faces)
- Handle edge cases: slabs outside simulation, faces at ±inf, 2D simulations
- Add analytical tests for gradient computation
- Remove `DerivativeSurfaceMesh` abstraction in favor of direct evaluation
- Convert `DerivativeInfo` from Pydantic model to dataclass for efficiency
- Implement interpolator sharing at `GeometryGroup` level
- Add Gauss-Legendre quadrature caching
- Optimize memory allocation with pre-allocated arrays
- Ensure dtype consistency throughout gradient pipeline

Author: yaugenst-flex

CHANGELOG.md

@@ -31,6 +31,8 @@ with fewer layers than recommended.
 - Warnings are now generated (instead of errors) when instantiating `PML`, `StablePML`, or `Absorber` classes (or when invoking `pml()`, `stable_pml()`, or `absorber()` functions) with fewer layers than recommended.
 - `Simulation.subsection` can no longer take `symmetry` as an argument - the symmetry is always taken from the original simulation.
 - If a mode simulation is crossing a symmetry plane of the larger simulation domain, but the mode plane is not symmetric, a warning is issued that it will be expanded symmetrically. Previously this warning only happened during the solver run.
+- Enhanced `PolySlab` and `Cylinder` gradient computation via adaptive field sampling along geometry boundaries instead of fixed-grid center sampling.
+- Shape derivatives have been sped up significantly, especially for simulations containing many structures in a `GeometryGroup`.
 
 ### Fixed
 - Arrow lengths are now scaled consistently in the X and Y directions, and their lengths no longer exceed the height of the plot window.

tests/test_components/test_autograd.py

@@ -812,7 +812,7 @@ def test_autograd_async(use_emulated_run, structure_key, monitor_key):
     make_sim = fn_dict["sim"]
     postprocess = fn_dict["postprocess"]
 
-    task_names = {"test_a", "adjoint", "task1", "_test"}
+    task_names = {"test_a", "adjoint", "_test"}
 
     def objective(*args):
         sims = {task_name: make_sim(*args) for task_name in task_names}
@@ -912,7 +912,7 @@ def test_autograd_async_some_zero_grad(use_emulated_run, structure_key, monitor_
     make_sim = fn_dict["sim"]
     postprocess = fn_dict["postprocess"]
 
-    task_names = {"1", "2", "3", "4"}
+    task_names = {"1", "2"}
 
     def objective(*args):
         sims = {task_name: make_sim(*args) for task_name in task_names}
@@ -934,7 +934,7 @@ def test_autograd_async_all_zero_grad(use_emulated_run):
     make_sim = fn_dict["sim"]
     postprocess = fn_dict["postprocess"]
 
-    task_names = {"1", "2", "3", "4"}
+    task_names = {"1", "2"}
 
     def objective(*args):
         sims = {task_name: make_sim(*args) for task_name in task_names}
@@ -1927,11 +1927,6 @@ def postprocess(sim_data: td.SimulationData) -> float:
 def test_multi_freq_edge_cases(use_emulated_run, structure_key, label, check_fn, monkeypatch):
     # test multi-frequency adjoint handling
 
-    import tidy3d.components.data.sim_data as sd
-
-    monkeypatch.setattr(sd, "RESIDUAL_CUTOFF_ADJOINT", 1)
-    reload(td)
-
     postprocess_fn = check_fn(structure_key=structure_key)
 
     def objective(params):