# Inverse-design fidelity audit

```{admonition} Fail-closed parity
:class: important

A high optimizer scalar is not equivalence when the local scene changes the
initialization, controls, symmetry, constraints, frequency samples, or FOM.
The suite fails closed on those differences. Independent Tidy3D forward solves
of the final binary artifacts withdrew two apparent local passes and confirmed
only the S-matrix crossing within the user's 10% trust target. Its 93.75%
published-performance ratio still misses the repository's 95% gate. Two
unsupported large problems remain explicit exclusions instead of being
replaced with easier compact surrogates.
```

## Current disposition

| Tidy3D notebook | Published controls and start | Required symmetry / constraints | Current status |
|---|---|---|---|
| Autograd24 digital splitter | 20×10 shallow-hole permittivities; uniform ε=6.5 | electric y symmetry; published update and fabrication-radius sweep; upper-port five-wavelength FOM | **Fails external validation:** local 0.43253, but Tidy3D scores the same binary geometry 0.31384 versus 0.47210 published |
| Autograd8 bend | 60 angular width controls; midpoint-width start | minimum-curvature penalty | **Invalid:** local adapter used unrelated 16×16 topology density |
| Autograd25 crossing | 300×300 at 10 nm; published plus-cross start | one-eighth material symmetry; `(0,-1,1)` field symmetry; β=∞ | **Invalid:** local adapter used 16×16, β=4, and no field symmetry |
| Autograd27 S-matrix | 451×451 at 10 nm; published plus-cross start | exact D4 material symmetry; β=30; binary final projection | **Passes 10%, misses 95%:** Tidy3D same-geometry 0.91920 versus 0.98044 published (93.75%) |
| Autograd9 WDM | 300×300; uniform 0.5; 20 frequency samples | 100 nm conic filter; β 1→50; erosion/dilation; binary final projection | **Invalidated:** local 0.93813, but Tidy3D scores the same artifact 0.02938 |
| Autograd17 bandpass | 640×320; uniform 0.5; 51 frequency samples | 120 nm conic filter; β 1→50; erosion/dilation; binary final projection | **Fails strict parity:** local 0.91277; Tidy3D same-geometry 0.73536 versus 0.82519 published |
| Autograd6 compact grating coupler | 216×108 half-domain at 20 nm; random Gaussian-smoothed cold start | electric y symmetry; double constant-padded 80 nm filter; erosion/dilation; β 1→30; binary final projection | **Fails:** FDTDX 0.57728; Tidy3D same-geometry 0.53388 versus 0.66374 published |

The detailed evidence, normalization derivation, and GPU memory measurements
are maintained in [`docs/INVDES_AUDIT.md`](https://github.itap.purdue.edu/hoodlabpurdue/fdtdx-hoodlab/blob/main/docs/INVDES_AUDIT.md).

The executed [Autograd24 splitter](../examples/notebooks/digital_splitter.ipynb)
and [Autograd6 grating-coupler](../examples/notebooks/grating_coupler.ipynb)
audit notebooks show the full parameter → geometry → optimization → fresh
validation → field-profile workflow. Their plots show the realized binary
geometry and actual Yee-grid material, not merely optimizer controls.

## Separate local fitted-Q validation

The [high-Q nanobeam notebook](../examples/notebooks/high_q_nanobeam_optimization.ipynb)
is not entered in the table above because it does not claim parity with a
published Tidy3D inverse-design notebook. It validates a solver capability:
automatic mirror completion, a JAX multi-window pole fit, exact-checkpointed
FDTD gradients, bounded symmetric cylinder controls, and independent long-run
validation of the final literal geometry. One cold-start adjoint update reaches
Q=187,133, which is 5.33× the unchanged cavity and 2.02× the unoptimized
mirror-completed control, with zero fabrication violation. A separately billed
matched Tidy3D pair uses 20 literal holes for both the control and final shape:
Q increases from 84,247 to 146,678, or 1.741×. This confirms a real shape-only
gain while showing that the 25 nm FDTDX model overpredicts its magnitude.

## Independent forward sign-off

The final-design checks use no Tidy3D optimization. Each FDTDX binary artifact
is inserted into the source notebook's exact Tidy3D forward scene and scored
with the published observable.

| design | FDTDX claim | Tidy3D same geometry | published Tidy3D | disposition |
|---|---:|---:|---:|---|
| WDM | 0.93813 | 0.02938 | 0.82566 | invalid local objective/normalization |
| bandpass | 0.91277 | 0.73536 | 0.82519 | 10.9% below published; strict gate fails |
| digital splitter | 0.43253 | 0.31384 | 0.47210 | 33.5% below published |
| S-matrix crossing | 0.96945 | 0.91920 | 0.98044 | 10% trust check passes; 95% gate fails |
| compact grating coupler | 0.57728 | 0.53388 | 0.66374 | within 8.1% cross-solver, but 19.6% below published |

The grating comparison uses the executed notebook result of −1.78 dB
(0.663743). The nearby prose still says 150 iterations and −1.48 dB, but that
text is stale relative to the retained 75-step execution and final spectrum.

## The splitter FOM error

The Autograd24 notebook's upper-port objective is bounded by 0.5. Tidy3D
multiplies it by two only for total insertion loss. Because FDTDX normalizes the
source on the reduced half-plane, the physical upper-port value is

$$
T_\mathrm{upper}=\frac{1}{2}\frac{P_\mathrm{upper,reduced}}{P_\mathrm{source,reduced}}.
$$

The old adapter omitted the factor $1/2$ and called 0.752 a win. It was about
0.376 under the notebook convention, below the 0.4485 requirement. The
corrected benchmark also records total transmission and source drift, so this
mistake cannot silently return.

## Why the refined mesh is still coarse

The notebook's automatic mesh targets roughly 22.4 nm inside silicon. On the
local RTX 3080 12 GB, the selected 45 nm xy / 50 nm z grid has an 8.70 GiB raw
PML tape before reverse workspace. The automatic recorder chooses float16
storage with every-fourth-step reconstruction, reducing the tape to 1.09 GiB
inside its 1.22 GiB budget; the complete adjoint uses about 9.2 GB on device.
Eight-by-eight hole quadrature and exact planar-interface alignment give a cold
start of 0.12245 versus Tidy3D's 0.1113.

This is a real device-memory limitation, not a justification for comparing a
different optimization problem. Feature-aware spacing, physical-PML retention,
interface alignment, and recorder-memory planning are now automatic. Local
refinement around the slab and holes remains the next memory-efficiency step.

## Memory-feasible scope

The digital splitter, WDM, bandpass, S-matrix crossing, and compact grating
coupler are memory-feasible on this machine. The grating retains all 216×108
20 nm controls; its 125×63×94 reduced Yee grid uses about 9.2 GiB on the GPU,
with a 0.96 GiB planned reversible tape. Autograd8's published 10×10×3.7 µm bend would require an
approximately 30 GiB raw reverse tape plus a differentiable polygon/curvature
rasterizer that FDTDX does not yet have. Autograd25's 10 nm, 1.67 ps crossing
would require hundreds of GiB even after its y/z field symmetries. Those two
cases therefore stay excluded instead of being represented by unrelated 16×16
topology problems.

## Restore criteria

- the same start—never an unpublished warm start;
- the same parameters, filter/projection schedule, symmetries, and fabrication
  constraints;
- the same physical FOM and normalization, with separate passivity checks;
- geometry plus multi-wavelength field profiles before and after optimization;
- a complete target run and a fresh forward validation of the best design.