Passive Multi-Channel Room Characterization

Passive Multi-Channel Room Characterization Using Physics-Informed Neural Networks on Resource-Constrained Edge Devices This white paper presents EquoraVault -- a novel system for autonomous indoor environment characterization that combines classical thermodynamic models with physics-informed Kolmogorov-Arnold Networks (KAN) running entirely on ESP32-S3 microcontrollers (240 MHz, 8 MB PSRAM), with no cloud dependency. What the system does:Using only commodity environmental sensors (BME280, ENS160, PM sensor -- total BOM under 15 EUR), the system passively estimates room volume (within 10-15%), air change rate, thermal time constants, and condensation risk from four independent sensor channels: temperature, CO2, absolute humidity, and particulate matter. Key contributions: Four-channel cross-validation -- each physical parameter is estimated from multiple independent sensor channels governed by distinct transport physics, enabling self-consistency checks without external references. Regime-based state machine -- distinguishes closed-room, internally-connected, and externally-ventilated air mass configurations, maintaining separate physical models per regime. Passive condensation detection -- a novel algorithm exploiting the divergence between CO2-derived and humidity-derived air change rates to quantify moisture removal by surface condensation, requiring no additional hardware. Physics-informed KAN on edge -- a 5,000-parameter Kolmogorov-Arnold Network operating as a residual corrector on top of physics-based estimates, with under 10 ms inference and self-supervised training from SD-stored event data. Federated mesh learning -- ESP-NOW-based multi-room protocol enabling building-level thermal characterization from distributed edge inference without centralized data collection. Core insight: Different pollutants decay at rates governed by distinct physical mechanisms (dilution, settling, conduction, condensation). The ratios of their time constants are characteristic of room geometry and independent of the unknown ventilation rate, enabling passive volume estimation without tracer gas injection or active perturbation. Part of the EQUORA Institute White Paper Series. Status: Preprint (v1.0) -- subject to revision. Please cite the DOI and version number.