Pulsed midpoint-guide direct-pixel source/material Adam discovery

Live optimizer

This fresh comparison starts from a 450 nm midpoint-permittivity waveguide (density 0.5 in its core) and its solved fundamental mode current. The drive is a broadband Gaussian pulse, and the fixed ideal-cavity target is recomputed as the exact discrete causal convolution of that pulse with a lossless cosine pole, normalized to unity after the pulse. Maxwell sees the 25 nm material pixels directly: there is no conic filter, projection, or binarization. One reverse pass returns both material and source gradients at the same incumbent; raw Adam moves both blocks simultaneously and unconditionally. The gentler learning rates halve every twenty steps so they descend slowly. One forward/adjoint pair is exactly one plotted step; there is no candidate replay, step rejection, rollback, trust region, beta, or boundary handoff.

State	Value
Status	running_simultaneous_joint_adam
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	0.0144, 0.9981, 0.0598
Source current norm ratio	1
Source/reference overlap	0.99968
Source Adam learning rate	0.0005
Detector / target trainable	False / False
Temporal observable	fixed_scale_reciprocal_mode_electric_coordinate
Phase	fixed_frequency_lossless_temporal
Active coordinates	unprojected_direct_25nm_density_pixels
Completed updates	2
Temporal objective	-0.99889
Whole-trace fixed-waveform fidelity	0.50028
Source-off fixed-waveform fidelity	0.5
Fixed target source-off power (telemetry)	0.50008
Fixed-target gain (ideal = 1)	0.00056261
Fixed-target normalized MSE	0.99889
Normalized temporal residual	0.99945
Full-field coherence	0.29958
Shifted stationarity	0.2412
Q telemetry	pending
Normalized V telemetry	pending
Active pole tape	pending ps
Maxwell-step reduction vs 2 ps	pending×
Material continuation stage	unprojected_direct_25nm_density_pixels
Binarization / projection	disabled for entire campaign
Bulk gray fraction	45.00%
Material initialization	450 nm waveguide core at density 0.5; cladding elsewhere
Initial density mean / standard deviation	0.225 / 0.24875
Source initialization	solved fundamental TE mode of midpoint-permittivity guide
Temporal source	broadband Gaussian pulse
Ideal target	exact discrete pulse ⊛ lossless cosine Green function; post-pulse amplitude 1
Material spatial filter	none; direct pixels
Material pixel pitch	25 nm
Design width in y	1 µm
Joint optimizer	raw simultaneous Adam ascent
Material coordinates	direct unprojected 25 nm density pixels indefinitely
Material Adam learning rate	0.005
Initial material / source learning rate	0.005 / 0.0005
Material / source learning-rate floor	1e-05 / 1e-06
Learning-rate descent	×0.5 every 20 steps
Adam beta1 / beta2 / epsilon	0.9 / 0.999 / 1e-08
Joint Adam steps	2
Joint gradient evaluations	2
Joint forward evaluations	2
Last material motion	0.0050053
Last source angular motion	0.021351 rad
Per plotted optimizer step	one forward trajectory + one reverse pass for both blocks
Candidate replay / line search	none / none
Acceptance / rollback	unconditional commit / none
Source inner iterations	0
Trust region / L-BFGS memory	disabled / none
Displayed objective/fields/source	evaluated input state 1
Updated coordinates	pending next FDTD evaluation
Boundary handoff	disabled; continuous density is terminal
Stable binary-topology states	not applicable
Boundary trust radius	not applicable
Latest Adam step	committed unconditionally; evaluated next step
Last pole trustworthy	False
Latest update wall time	22.5 s
Last artifact write	2026-08-29 19:47:12 UTC

The authoritative state is benchmarks/artifacts/invdes_fryett_modal_temporal_modal_unbinarized_joint_adam_v1.npz. This is an independently initialized Adam comparison artifact. Preparing it does not evaluate Maxwell, start a worker, or alter the running nested campaign.

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

Full-field temporal correlations

Objective, simultaneous Adam motion, continuous density, and pole history

Q versus raw joint Adam step — linear scale

Exact methodology, target response, and moving components

Purpose of the comparison

This campaign tests raw simultaneous Adam with a broadband pulse rather than the preceding resonant CW-like burst. The 8 um by 1 um design region begins as a continuous 450 nm waveguide: its core density is 0.5, corresponding to ((\epsilon_{\max}+\epsilon_{\min})/2), and the remaining design cells begin as cladding density zero. The initial fixed-norm real Ex/Ey/Ez current is the solved fundamental TE mode of that same midpoint-permittivity guide. Its 2,700 freeform coordinates remain trainable after initialization.

Raw density obeys

[ 0\leq\rho_{ij}\leq1, \qquad \bar\rho_{ij}=\rho_{ij}. ]

There is no conic filter or other spatial averaging: Maxwell receives each 25 nm density coordinate directly. There is also no projection, beta, gray or binary penalty, continuation schedule, topology gate, or smooth-boundary handoff. Thus single-pixel structure is allowed in this diagnostic campaign.

One fixed temporal objective

For material coordinates (\rho) and unit-norm source coordinates (u), the reciprocal modal response is (a(t;\rho,u)). The drive is the actual discretized Gaussian pulse (s_m) produced by FDTDX, centered at (f_0) with 35 THz spectral width. The ideal response is recomputed from that pulse, not reused from the resonant burst. For FDTD time step (\Delta t),

[ c_n=\sum_{m=0}^{n}s_m\cos[\omega_0(n-m)\Delta t], \qquad A=\left|\sum_m s_m e^{-i\omega_0m\Delta t}\right|. ]

Using the exact geometry-independent discrete modal impulse coupling (\kappa), the fixed target is

[ a_{\star,n}=-\frac{\kappa}{|\kappa|}\frac{c_n}{A}. ]

This includes the causal pulse-on transient sample by sample. After the pulse, it is a pure cosine at (\omega_0) with unity amplitude. Detector-cadence samples are taken only after forming the full-step convolution. Neither amplitude nor phase is fitted to the simulated trace. The sole optimized scalar, with every temporal sample weighted equally, is

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

Q, grayness, source overlap, and pole fits are telemetry or pole-tracking checks, not additional objective terms.

One reverse pass, two gradients

At Adam step (k), one FDTD trajectory and one reverse pass evaluate

[ F_k,\quad g_{\rho,k}=\frac{\partial F}{\partial\rho},\quad g_{u,k}=\frac{\partial F}{\partial u} ]

at the identical incumbent pair ((\rho_k,u_k)). In JAX this is one value_and_grad operation with both argument numbers. It is not two adjoint solves, and neither block sees the other block’s updated value.

The material and source maintain independent Adam first and second moments,

[ m_k=\beta_1m_{k-1}+(1-\beta_1)g_k, \qquad v_k=\beta_2v_{k-1}+(1-\beta_2)g_k^2, ]

with bias corrections and ascent direction

[ d_k=\frac{m_k/(1-\beta_1^k)} {\sqrt{v_k/(1-\beta_2^k)}+\epsilon}. ]

The slower, longer-lived descending learning-rate schedule is

• initial material learning rate (\alpha_{\rho,0}=5\times10^{-3});

• initial source-coordinate learning rate (\alpha_{u,0}=5\times10^{-4});

• both rates are multiplied by (1/2) after every twenty steps;

• the material and source floors are (10^{-5}) and (10^{-6}), respectively;

• (\beta_1=0.9), (\beta_2=0.999), and (\epsilon=10^{-8}).

This is ten times gentler than the preceding fast random-pixel run at startup, and the four-times-longer plateau prevents both rates from prematurely reaching their floors. There is no controller that increases a rate, adapts a trust radius, or suppresses a proposal.

The material step is

[ \rho_{k+1}=\operatorname{clip}{[0,1]} (\rho_k+\alpha\rho d_{\rho,k}). ]

The source has all 2,700 real Ex/Ey/Ez center-plane coordinates and begins from the midpoint-guide mode described above, while its total current norm remains fixed. The raw source gradient and preconditioned direction are projected into the tangent plane of the unit sphere. The source then moves and retracts,

[ \tilde u_{k+1}=u_k+\alpha_u (I-u_ku_k^T)d_{u,k}, \qquad u_{k+1}=\frac{\tilde u_{k+1}}{|\tilde u_{k+1}|_2}. ]

The source first moment is projected into the new tangent plane after the step. Its elementwise second moment remains the ordinary ambient-coordinate Adam accumulator. Thus this is a practical constrained Adam comparison, not a claim of coordinate-invariant Riemannian Adam.

Step and solve accounting

Material and source are committed simultaneously and unconditionally. There is no source inner iteration, alternating block solve, L-BFGS memory, trust radius, line search, gain-ratio acceptance test, finite-candidate gate, rejected-step retry, rollback, or candidate replay. Overshoot and oscillation are observable optimizer dynamics rather than events hidden by a controller.

One optimizer step is exactly one forward trajectory and its one reverse pass. The objective, fields, Q telemetry, geometry, and source shown for step (k) are those evaluated at ((\rho_k,u_k)) to obtain that step’s gradient. The resulting ((\rho_{k+1},u_{k+1})) is committed without another solve and is evaluated at the next dashboard step. This standard one-step timing is shown explicitly; the dashboard never presents an unevaluated proposal as if it already had an objective value.

Every fourth committed step retains the existing pole audit. Once a trustworthy Q above 100 is found, the carrier and minimum viable ringdown tape track that pole while the same simultaneous Adam rule and fixed lossless target continue.

Prepared-state contract

Preparation creates only a CPU-initialized ready_not_started artifact and static dashboard. It does not evaluate Maxwell, acquire the GPU lock, stop the running nested campaign, or start optimizer/dashboard services. A later explicit launch evaluates the baseline first and then starts an indefinite worker.

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_SOURCE_JOINT_ADAM=1 FDTDX_FRYETT_MODAL_TEMPORAL_ID=modal_unbinarized_joint_adam_v1 uv run python -m benchmarks.cases.invdes_fryett_hybrid_scratch.modal_temporal --updates 1

The persistent launcher is scripts/start_fryett_modal_source_joint_adam_campaign.sh.