fix(photonics2d): consistent simulate/optimize (v1)

[mkeeler43]

Description

simulate and optimize disagree in Photonics2D v0: the objective optimize reports for a design
is not reproduced when you simulate the design it returned. On the published v0 dataset,
re-simulating a stored optimal_design differs from its stored objective by a median of ~130% and
up to 37×. This PR fixes it by adding Photonics2D v1; v0 is unchanged and still importable.

Photonics background (what's specific to this problem)

Unlike the structural/thermal problems, a photonics design is a continuous density field
rho ∈ [0, 1] that is converted to a permittivity map and scored by an FDFD solve
(frequency-domain Maxwell). The device is a wavelength demultiplexer, and the objective
("total overlap") measures how well two wavelengths reach their respective output ports.

Gradient-based topology optimization here uses two operators (from the ceviche tutorial this problem
is refactored from), applied to rho before it becomes permittivity:

• blur (operator_blur) — a convolution imposing a minimum feature size; without it the optimizer
  produces unmanufacturable single-pixel features.
• projection (operator_proj) — a tanh smoothed-Heaviside that pushes rho toward 0/1 so the
  final design is near-binary. Its sharpness is beta; a continuation schedule ramps beta from
  soft to hard over the run so early-iteration gradients stay informative.

Both are optimization machinery — they only make sense while searching for a design, not while
scoring a finished one.

The bug (v0)

v0 ran blur + projection inside the shared epsr_parameterization, which was called by both
optimize and simulate — and simulate ran it at beta = max_beta while optimize ramped
beta. Two consequences:

• simulate(design) silently re-blurs and re-projects the design before scoring it, so it does not
  score the design it was handed.
• optimize returned a design that was projected once and then binarized with np.rint, which
  differs again from what its final recorded objective was computed on.

So the stored/returned design is not the one that produced the reported number, and the gap grows
with blur_radius (more projection → larger mismatch) — up to 37× on the dataset.

The fix (v1)

Blur + projection live only inside optimize; simulate scores designs as given.

• A design is a finished physical density rho ∈ [0, 1] (blur + projection already applied).
• simulate(design) validates rho ∈ [0, 1] (check_constraints) and converts it to permittivity by
  scaling only (design_to_epsr) — no blur, no projection — then runs FDFD.
• optimize(start):
  • Step 0 evaluates the raw start, so history[0] == simulate(start).
  • Steps 1..N apply blur + projection with beta ramping initial_beta → max_beta in an explicit
    Adam loop, clipping rho to [0, 1] each step. (The tanh projection only maps [0,1]→[0,1], so
    keeping rho bounded is what makes it well-behaved — this is why the projection does not need to
    be a sigmoid.)
  • Returns the projected density at max_beta, so simulate(optimize(x)[0]) == history[-1].
• epsr_parameterization is split into design_to_epsr (scale only, used by simulate) and
  filter_and_project (blur + projection, used by optimize). Both are additive in backend.py;
  no v0 function is modified.
• Optimizer knobs (penalty_weight, step_size, eta, initial_beta, max_beta) are now validated
  Config fields. The trailing np.rint binarization and the beta-scheduling adam_optimize
  callback are gone — the explicit loop updates beta directly.

Fixes # (simulate vs optimization-history inconsistency issue — please link)

Reverting to v0

• Default: from engibench.problems.photonics2d import Photonics2D → v1 (…_v1 dataset).
• Legacy: from engibench.problems.photonics2d.v0 import Photonics2D → v0 (…_v0, unchanged).

Dataset

Regenerated on Euler, reusing v0's exact conditions and train/val/test split (1594 / 199 / 200) so the
two are directly comparable; all 1993 optimizations succeeded. Published to
IDEALLab/photonics_2d_120_120_v1. Warm start is fixed across all rows
(random_design(noise=0.001), seed 0), documented on the problem page.

Validation

Re-simulate each stored optimal_design and compare to its stored objective:

Dataset	median	mean	max
v0	130%	430%	37×
v1	~3e-10	~1e-8	~2e-7

Type of change

• Bug fix, shipped as a new problem version (v1); v0 behavior preserved
• This change requires a documentation update (done — docs/problems/photonics2d.md)

The default Photonics2D now returns different numbers than before (it is v1), so the default import
is behavior-changing; handled by the version bump, with v0 kept importable for reproducibility.

Checklist

• ruff check and ruff format
• mypy
• Commented code (docstrings explain the photonics-specific blur/projection/continuation)
• Documentation updated
• Tests added (tests/test_photonics2d.py) plus reference values
• New and existing unit tests pass, including the dataset-backed generic tests