Unbinarized source-equilibrated cavity discovery

Live optimizer

This independent campaign starts from the midpoint-permittivity waveguide and keeps the dielectric as continuously filtered density for its entire lifetime: there is no projection, beta schedule, binary penalty, or boundary handoff. The freeform fixed-norm source is equilibrated at every incumbent and material candidate, while an agreement-controlled trust radius is free to grow from a small start up to the natural density-box diameter.

State	Value
Status	running_candidate_source_equilibration
Source	trainable_fixed_norm_modal_electric_current
Source spatial profile	freeform Ex/Ey/Ez on physical center plane
Source spatial profile trainable	True
Active source degrees of freedom	2700
Source coordinate shape	(3, 1, 42, 42)
Ex / Ey / Ez coordinate norms	0.0780, 0.9947, 0.0667
Source current norm ratio	1
Source/reference overlap	0.99186
Source angular trust radius	2.5e-05 rad
Detector / target trainable	False / False
Temporal observable	fixed_scale_reciprocal_mode_electric_coordinate
Phase	shifted_lossless_temporal
Active coordinates	unprojected_filtered_density_pixels
Completed updates	32
Temporal objective	-0.95732
Whole-trace fixed-waveform fidelity	0.5109
Source-off fixed-waveform fidelity	0.50991
Fixed target source-off power (telemetry)	0.49981
Fixed-target gain (ideal = 1)	0.021636
Fixed-target normalized MSE	0.95732
Normalized temporal residual	0.97843
Full-field coherence	1
Shifted stationarity	0.89801
Q telemetry	238.08
Normalized V telemetry	0.026653
Active pole tape	0.4 ps
Maxwell-step reduction vs 2 ps	5×
Material continuation stage	unprojected_filtered_density
Binarization / projection	disabled for entire campaign
Bulk gray fraction	48.66%
Initial guide density	0.5
Initial guide permittivity	3.0804
Design width in y	1 µm
Material optimizer	nested_source_unprojected_density_unbounded_trust_v1
Material coordinates	unprojected filtered density pixels indefinitely
Material trust radius	0.03200 maximum density change
L-BFGS memory pairs	5
Forward-only rejected-step retries	5
Source gradient transform	unit-sphere tangent and geodesic retraction
Source L-BFGS memory pairs	0
Active nested block	candidate_source
Nested Maxwell turns	322
Accepted material commits	32
Active source inner turn	0
Last source move accepted	False
Material commit rule	candidate source equilibrium before commit
Source projected 10 mrad gain	2.4041e-07
Material trust ceiling	1 maximum density change
Uncommitted material candidate active	True
Continuation clock	no continuation; density map is fixed
Boundary handoff	disabled; continuous density is terminal
Stable binary-topology states	not applicable
Boundary trust radius	not applicable
Last candidate accepted	False
Last pole trustworthy	True
Latest update wall time	35.73 s
Last artifact write	2026-08-29 17:45:38 UTC

The authoritative state is benchmarks/artifacts/invdes_fryett_modal_temporal_modal_unbinarized_nested_v1.npz. This is a fresh artifact initialized independently of both the stopped sprint and the preserved thorough nested checkpoint.

Geometry and exact material difference

Field used by the temporal objective

Exact temporal target response

The orange curve is the fixed causal convolution of the prescribed current waveform with the cosine Green function of one lossless pole. It is not the source waveform and is not fitted to the simulation. During the drive it contains the exact causal build-up; after turn-off its extrema are exactly -1 and +1. The blue simulation is plotted in those same absolute objective units, so a smaller blue envelope is a real amplitude error, not a display normalization. The current waveform appears only in the diagnostic panel on its own explicitly independent display scale. The former blue background bands were 4D field-snapshot windows; they were never objective weights and have been removed from this plot to make the absolute comparison unambiguous. Every temporal sample still enters the single normalized mean-square error equally.

Evolving freeform source profile

Live nested-source progress

The accepted-material and Q plots keep the same x coordinate while the inner source problem is being solved. This panel advances on every source forward/adjoint turn, so accepted source motion is visible before the next material commit.

Full-field temporal correlations

Objective, continuous density, adaptive trust, and pole history

Q versus accepted material commit — linear scale

Exact methodology, target response, and moving components

Question being tested

This campaign tests whether early projection sharpening was forcing the dielectric to commit before a high-Q collective structure could form. It is a fresh optimization, not a continuation of the stopped frozen-source sprint or the earlier gradual-beta campaign.

The complete 8 µm by 1 µm design region begins as a 450 nm-wide waveguide. Its raw core density is 0.5, corresponding to ((\epsilon_{\max}+\epsilon_{\min})/2), and the initial current is the fundamental TE mode of that midpoint-permittivity guide. The temporal drive is the same finite smooth resonant burst followed by source-free ringdown.

No binarization or moving material objective

The raw material variables obey only the natural box constraint

[ 0\leq \rho_{ij}\leq 1. ]

A fixed 75 nm conic filter supplies a minimum spatial scale,

[ \bar\rho = K_{75,\mathrm{nm}} * \rho, ]

and (\bar\rho) is sent directly to Maxwell. There is no tanh projection, beta, erosion/dilation threshold, binary penalty, grayness penalty, scheduled decoder change, or smooth-boundary handoff. Continuous filtered density is the terminal parameterization for as long as the campaign runs. Gray fraction is diagnostic only.

Fixed temporal objective

For a dielectric (\rho) and fixed-norm source coordinate (u), the measured reciprocal modal coordinate is (a(t;\rho,u)). The target is the fixed causal response of one lossless pole to the prescribed current waveform,

[ a_\star(t)=C\int_0^t s(\tau) \cos[\omega_0(t-\tau)],d\tau, ]

where (C) is chosen once so the ideal source-off carrier has amplitude one. Neither amplitude nor phase is fitted to a simulated trace. The only optimized scalar is

[ F(\rho,u)=-\frac{\sum_n w_n [a(t_n;\rho,u)-a_\star(t_n)]^2} {\sum_n w_n a_\star(t_n)^2}. ]

Q, mode volume, grayness, and source/reference overlap are telemetry, not additional objective terms. Once a trustworthy Q above 100 exists, the usual pole tracking and minimum viable ringdown tape remain active.

Nested source/material optimization

The source has all 2,700 real Ex/Ey/Ez electric-current coordinates on the physical center plane. Its physical norm is fixed, so source steps are tangent rotations followed by unit-sphere geodesic retraction. The temporal waveform, detector, target, and source norm never move.

At every material decision the controller:

1. locally equilibrates the source at the accepted dielectric;

2. computes one material gradient at that source equilibrium;

3. creates one uncommitted material trust-region proposal;

4. locally equilibrates an independent source copy at the candidate; and

5. commits both only if the exact source-optimized candidate improves the exact source-optimized incumbent and passes the unchanged field/pole gates.

Source equilibrium requires two consecutive projected-tangent checks. The 10 mrad predicted gain must be below both an absolute (10^{-7}) objective threshold and 0.1% of the source block’s initial projected gain. The float32 resolution and bounded trust-floor exits remain as numerical safeguards. This is a local fixed-norm source optimum, not a global-optimality claim.

At a stationary source, the envelope theorem gives

[ \frac{d}{d\rho}F(\rho,u^\star(\rho)) =\left.\frac{\partial F}{\partial\rho}\right|_{u=u^\star}, ]

so one material forward/adjoint evaluation supplies the correct local outer gradient without differentiating through all source iterations.

Adaptive trust regions without scheduled release

Material trust starts at a maximum raw-density change of 0.001. Source trust starts at 0.01 radians. Each block uses independent eight-pair L-BFGS memory and the same standard agreement ratio

[ r=\frac{F_{\mathrm{trial}}-F_{\mathrm{current}}} {\nabla F^T\Delta x}. ]

A successful step using at least 80% of its radius grows the radius by 2 when (r\geq0.75). A rejected step or (r<0.05) halves it. There is no Q-based, iteration-based, beta-based, or manually released material ceiling. The only upper material limit is 1.0, the diameter of the raw density box; the source limit is (\pi/2), the natural useful hemisphere of a real fixed-norm source. There is no routine line search, DCT preconditioner, density-motion cap, or cumulative-motion cap.

L-BFGS memory is retained across accepted updates and pole recentering when the coordinate chart is unchanged. Three consecutive rejected trials clear stale curvature. All accepted state, source-inner state, and uncommitted candidate state are checkpointed atomically, and the persistent worker runs indefinitely until explicitly stopped.

Operations

A bounded manual turn can be run with:

FDTDX_FRYETT_MODAL_SOURCE_CO_DESIGN=1 FDTDX_FRYETT_MODAL_SOURCE_BILEVEL=1 FDTDX_FRYETT_MODAL_SOURCE_UNBINARIZED=1 FDTDX_FRYETT_MODAL_TEMPORAL_ID=modal_unbinarized_nested_v1 uv run python -m benchmarks.cases.invdes_fryett_hybrid_scratch.modal_temporal --updates 1

The persistent launcher is scripts/start_fryett_modal_source_unbinarized_campaign.sh.