Synthetic Continuity-Residual Fusion Sandbox: JuPedSim + Sionna + BLE Co-Simulation

Current assessment (2026-09-15)

Superseded design retained for provenance, reviewed September 15, 2026. No primary data are attributed to this card. The later continuity-prior campaign found practical equivalence to smoothing in both tested flow regimes. That scoped in-silico negative supersedes the original expectation of a physics-specific gain.

The later continuity-prior campaign found practical equivalence to smoothing in both tested flow regimes. That scoped in-silico negative supersedes the original expectation of a physics-specific gain.

Next evidence needed: Use EXP-S1 for the current protocol and evidence. The earlier plan below is not an instruction to reopen this experiment.

Basis: Thesis Narrative, the September 10 synthesis, and the September 15 register review. See the review record for evidence sources and outstanding checks.

Earlier protocol and dated results

The methods and observations below retain their original scope. Read their readiness statements and proposed next steps as historical. The current assessment above records what has changed; frozen thresholds have not been retrospectively revised.

The problem, in plain words

Wi-Fi crowd counting turns radio measurements into a headcount. Indoors, that inverse problem is under-determined: a handful of transmitter–receiver links carry far less information than a full per-cell density map contains, so many different crowds could explain the same radio reading. When a problem is under-determined, you need a prior — an extra assumption that tells the model which of the many possible answers is more plausible.

The thesis proposed a beautiful prior: crowds obey physics. If you know density and velocity, mass-conservation says how the density field must evolve — no teleporting people, no crowds condensing out of nowhere. Enforce that as a training penalty and, the argument goes, the model should reject physically-impossible reconstructions and land closer to the truth. This is exactly the physics-informed-learning recipe that works in traffic-flow estimation (di2023_285b ↗, shi2022_1e5b ↗).

But there is a trap. A physics penalty is also a smoothing penalty — it discourages sharp, jittery density fields. So if the "physics" model does better, you have to ask a sceptical question: is it the physics, or is it just the smoothing? A wrong physics law that still smooths could look like a win for the wrong reason. Answering that cleanly is the whole game.

What we are trying to prove

• Original EXP-006 hypothesis (falsifiable): the continuity-residual penalty \lambda\lVert \partial\rho/\partial t + \nabla\cdot(\rho\mathbf{v})\rVert_2^2 lowers per-cell occupancy error across every architecture in a nine-model zoo, and the lift is separable from the architecture — validating the mechanism independently of the network. A built-in falsification test was written in from the start: replace the true conservation law with a random one; if the random law helps as much, the penalty is generic regularisation, not physics.
• What a null means: if a wrong physics law regularises as well as the right one, or if plain smoothing beats both, then the "crowd-as-liquid" prior earns no specific support — it is a smoother wearing a physics costume. That is a real, publishable negative: it tells the thesis not to build its central chapter on this mechanism.
• The sharpened test that actually ran: campaign c-continuity-prior-csi-density distilled the zoo down to the one comparison that matters — identical MLP with vs. without the penalty, plus a smoothing control and mismatched velocity closures — on coupled JuPedSim-density + synthetic-CSI data. Small, controlled, decisive.

How the experiment works (plain method)

The designed sandbox (EXP-006 as written). JuPedSim generates crowd trajectories on two synthetic geometries; Sionna RT (fidelity tier) and a fast statistical channel (headline tier) turn agent positions into per-subcarrier CSI; a log-distance model turns them into BLE RSSI; PedPy computes per-cell Voronoi density, the fundamental diagram, and the continuity residual that is the ground-truth signal the penalty regularises toward. Nine models each train with the loss \mathcal{L} = \mathrm{MSE}(\hat n, n) + \lambda\cdot\mathrm{MSE}(\partial\hat\rho/\partial t + \nabla\cdot(\hat\rho\hat{\mathbf v}), 0) across \lambda \in \{0, 0.01, 0.1, 0.3, 1.0\}.

What the campaign actually ran (the sharpened core). On the test-lab-synth corridor floor with a deliberately sparse CSI link layout (the under-determined regime a prior should help most), a crowd-size sweep {12, 24, 36, 60} was ray-traced through the coupled exp-csi-crowd chain to drive density up to a peak of ~5 ped/m². Then two identical small MLPs f(CSI links)(t) → density field were trained — one plain (data loss only), one with the 1D continuity penalty — and compared against a plain-smoothing control and against continuity variants using matched, constant, and anti-physical velocity closures. Density RMSE was read out per regime (low / mid / high) over ~105–110 high-density cell-frames.

What we've found so far (honest, across sessions)

Three sessions of c-continuity-prior-csi-density tell one arc: a promising win, a confound, and a clean negative.

Reading it plainly:

1. The physics is not doing the work. In session 2, feeding the model the correct Weidmann velocity law, a constant law, and an anti-physical increasing law all produced the same high-density RMSE (~1.23–1.24). If the continuity physics were the active ingredient, a wrong law should have hurt — it didn't. The prior is FD-agnostic.
2. A plain smoother beats it. A generic smoothness penalty with no velocity model at all scored 0.91, better than every physics variant. So the modest gain over the raw model is generic regularisation of an under-determined inverse — and not even the best available version of it.
3. Session 1's −11 % was the confound the critic feared. The penalty's Weidmann closure was the same velocity law JuPedSim used to generate the crowd, so "physics wins" could not be separated from "we leaked the simulator's own recipe into the loss." Sessions 2 and 3 removed the leak and the win evaporated.

Campaign outcome: across both low- and strong-directed-flow regimes, the 1D continuity prior (FD-closure and measured-velocity divergence) is a generic smoother in disguise on the sparse CSI→density inverse. The "crowd-as-liquid" prior is not warranted as the thesis's central claim; hypothesis continuity-prior-regularizes-density moved candidate → deferred.

Key references

• di2023_285b ↗ — the PINN recipe and λ-range EXP-006 borrowed; also the source of "a wrong prior should hurt" (which, tellingly, it did not here).
• shi2022_1e5b ↗ — PINN with a fundamental-diagram closure; the closest positive precedent, in traffic not crowds.
• hughes2002_57b4 ↗, corbetta2023_bcb7 ↗ — the continuum/mass-conservation prior the penalty enforces, and when it does (and does not) apply.
• santos2023_97b5 ↗, isufi2024_148d ↗ — why a smoothing prior and a divergence penalty are nearly indistinguishable on an under-determined inverse.
• zhou2020_6173 ↗, liu2022_3454 ↗, liu2022_8a7a ↗ — the CSI crowd-density task this mechanism was meant to improve.
• wang2026_2758 ↗, guarino2026_e72c ↗, zhang2026_ccac ↗ — the sim-to-real horizon and the reproducibility bar the red-team and SWE voices invoke.
• liddle2022_ee2c ↗ — the directed-flow bottleneck regime where the prior had its last, still-unsuccessful, chance.
• chaudhari2024_6efc ↗, zou2018_1590 ↗, demrozi2021_bf55 ↗ — the building-occupancy deployment target the practitioner and facilities voices speak for.
• sun2026_2f5e ↗ — channel-realism critique behind the field scientist's caveat.