--- title: Frozen-source rapid smooth-boundary Q sprint --- # Frozen-source rapid smooth-boundary Q sprint ```{admonition} Live optimizer :class: tip This rollback-safe diagnostic fork freezes the evolved source from the thorough campaign, immediately uses the final binary projection, and replays into the smooth subpixel level-set boundary under unchanged temporal and pole-validity gates. ``` | State | Value | |---|---:| | Status | `running_shifted_lossless_temporal_level_set` | | Source | `frozen_evolved_fixed_norm_modal_electric_current` | | Source spatial profile | `freeform Ex/Ey/Ez on physical center plane` | | Source spatial profile trainable | `False` | | Active source degrees of freedom | 2700 | | Source coordinate shape | `(3, 1, 42, 42)` | | Ex / Ey / Ez coordinate norms | `0.1126, 0.9893, 0.0930` | | Source current norm ratio | 1 | | Source/reference overlap | 0.98556 | | Source angular trust radius | 8.958e-05 rad | | Detector / target trainable | `False / False` | | Temporal observable | `fixed_scale_reciprocal_mode_electric_coordinate` | | Phase | `shifted_lossless_temporal_level_set` | | Active coordinates | `subpixel_level_set_boundary` | | Completed updates | 286 | | Temporal objective | -0.96599 | | Whole-trace fixed-waveform fidelity | 0.50865 | | Source-off fixed-waveform fidelity | 0.50838 | | Fixed target source-off power (telemetry) | 0.50009 | | Fixed-target gain (ideal = 1) | 0.017215 | | Fixed-target normalized MSE | 0.96599 | | Normalized temporal residual | 0.98285 | | Full-field coherence | 0.99998 | | Shifted stationarity | 0.7681 | | Q telemetry | 779.93 | | Normalized V telemetry | 0.027609 | | Active pole tape | 1.5 ps | | Maxwell-step reduction vs 2 ps | 1.33× | | Material continuation stage | `frozen_source_final_binary_projection` | | Projection beta / eta | 64 / 0.50 | | Bulk gray fraction | 5.03% | | Initial guide density | 0.5 | | Initial guide permittivity | 3.0804 | | Design width in y | 1 µm | | Material optimizer | `adaptive_trust_region_lbfgs_subpixel_level_set_sprint_v1` | | Material coordinates | `topology-preserving subpixel level-set boundary` | | Material trust radius | 0.00030 µm | | L-BFGS memory pairs | 3 | | Forward-only rejected-step retries | 2 | | Source optimizer | `frozen at fork; no source solves or source trials` | | Boundary handoff | `replay_passed_level_set_active` | | Stable binary-topology states | 1 / 1 | | Boundary trust radius | 0.0003 µm | | Last candidate accepted | True | | Last pole trustworthy | True | | Latest update wall time | 122.6 s | | Last artifact write | 2026-08-29 14:53:16 UTC | The authoritative state is `benchmarks/artifacts/invdes_fryett_modal_temporal_modal_frozen_spline_sprint_v1.npz`. The thorough source-equilibrated checkpoint is the immutable rollback source for this diagnostic fork and is never written by the sprint. ## Geometry and exact material difference ![Initial, accepted, and difference geometry](../_static/generated/fryett_modal_source_frozen_sprint_geometry.png) ## Field used by the temporal objective ![Current windowed Ey field](../_static/generated/fryett_modal_source_frozen_sprint_fields.png) ## Exact temporal target response ![Simulated and projected target traces](../_static/generated/fryett_modal_source_frozen_sprint_temporal.png) 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. ## Frozen evolved source profile ![Area-whitened Ex, Ey, and Ez source coordinates](../_static/generated/fryett_modal_source_frozen_sprint_source_profile.png) ## Full-field temporal correlations ![Temporal Gram matrix and energies](../_static/generated/fryett_modal_source_frozen_sprint_gram.png) ## Objective, gradual beta continuation, and pole history ![Temporal campaign history](../_static/generated/fryett_modal_source_frozen_sprint_history.png) ## Q versus accepted material commit — linear scale ![Cavity Q versus accepted material commit on a linear scale](../_static/generated/fryett_modal_source_frozen_sprint_q_history.png) ## Exact methodology, target response, and moving components ## Purpose and rollback contract This campaign is a diagnostic fork of the accepted state in `modal_current_nested_midindex_v4`. It answers a deliberately narrower question: how much cavity Q can the already evolved source and dielectric produce after rapid binarization and smooth-boundary refinement? The source artifact is never overwritten. The fork records its source artifact, update, Q, source checksum, and material controller state, so stopping the sprint and resuming the thorough campaign is lossless. This is not mathematically equivalent to the nested source-envelope campaign. It freezes the source spatial coefficients at the fork and therefore measures the potential of that particular evolved excitation. The temporal waveform, reciprocal detector, target amplitude, target phase, and objective are also unchanged. ## One fixed temporal objective Let the frozen current be \[ \mathbf J(\mathbf r,t)=\mathbf u_f(\mathbf r)s(t), \qquad \|\mathbf u_f\|_2=1, \] where \(\mathbf u_f\) is copied exactly from the accepted thorough checkpoint. The ideal response is the causal convolution of the prescribed smooth burst with the impulse response of a lossless pole at the tracked frequency, \[ a_\star(t)=C\int_0^t s(\tau) \cos[\omega_0(t-\tau)]\,d\tau . \] The constant \(C\) is fixed once so that the ideal source-off carrier has unit amplitude. It is not fitted to each simulation. The optimized scalar is the same fixed-scale waveform objective as the thorough campaign, \[ F(\epsilon;\mathbf u_f)= -\frac{\sum_n w_n\,[a_n(\epsilon,\mathbf u_f)-a_{\star,n}]^2} {\sum_n w_n a_{\star,n}^2}. \] Thus the only moving quantity is the dielectric. Q, mode volume, overlap, and pole fits remain telemetry rather than extra objective terms. ## Rapid material continuation The copied raw density is evaluated immediately with projection \(\beta=64\), \(\eta=0.5\). There is no source inner loop and no further beta ramp. A material turn consists of one differentiated incumbent evaluation (one forward/adjoint pair) and one exact forward candidate replay. If a trial is rejected, the incumbent material gradient is cached, so the retry is forward-only rather than paying for another adjoint at the same coordinates. The material controller remains adaptive trust-region L-BFGS with eight curvature pairs. Its accepted material memory and trust radius are copied from the source campaign. No Q-dependent density cap or routine line search is introduced. Acceptance still requires positive actual improvement and the trust model controls contraction or expansion. ## Fail-closed smooth-boundary handoff After the first accepted, trustworthy \(\beta=64\) state with at most four percent bulk-gray cells and stable topology, the code fits a signed-distance level set and renders its smooth boundary with 6-by-6 cut-cell averaging. It performs a fresh Maxwell replay. The handoff is committed only if the replay passes the existing objective-retention, topology, pole-continuity, and Q-retention gates. Otherwise the accepted pixel state remains authoritative. Level-set coordinates are boundary displacements in micrometres. Crossing this coordinate chart intentionally resets material L-BFGS curvature because pixel density secants are not valid boundary-displacement secants. It does not alter the frozen source. Subsequent turns use the same fixed temporal objective and adaptive trust-region L-BFGS directly on the smooth boundary. ## Interpretation This sprint trades source re-equilibration for wall-clock throughput. A strong Q rise is evidence that the present cavity architecture has promising smooth-boundary potential. A weak result is evidence about this frozen-source branch, not a proof that the fully nested source/dielectric problem lacks a better solution. The preserved thorough checkpoint can be resumed at any time. ## Operations A bounded manual turn can be run with: ```bash FDTDX_FRYETT_MODAL_SOURCE_CO_DESIGN=1 FDTDX_FRYETT_MODAL_SOURCE_BILEVEL=1 FDTDX_FRYETT_MODAL_SOURCE_FROZEN_SPRINT=1 FDTDX_FRYETT_MODAL_TEMPORAL_ID=modal_frozen_spline_sprint_v1 uv run python -m benchmarks.cases.invdes_fryett_hybrid_scratch.modal_temporal --updates 1 ``` The persistent launcher is `scripts/start_fryett_modal_source_frozen_sprint_campaign.sh`.