A state-space representation of the boundary integral equation for room acoustic modelling

Machine-learnt models are increasingly used to predict ISO 3382-1 room acoustic parameters at unmeasured seats from sparse measurements, with reported coefficients of determination frequently above 0.85. This paper shows that such figures are often determined by the evaluation protocol rather than by the model. Using a multi-condition measurement campaign in a 264-seat conference hall and a 180-seat concert hall, three model families were evaluated under a factorial protocol ablation: validation splits either row-based or grouped by receiver position, and inputs either including measured-at-test quantities (the target position's impulse response, co-located parameter measurements, position identifiers) or restricted to source-receiver geometry and environmental state. Row-based splits with measured-at-test inputs reproduce the high reported accuracies (mean R^2 of 0.81 for the core parameters); grouped splits with deployment-consistent inputs reduce these to 0.09-0.60 and reorder the apparent difficulty of parameter classes. Access to the target's own impulse response at test time reproduces the high accuracy of the row-based folds but provides no benefit under grouped folds. The row-based figure reflects condition interpolation at the measured positions rather than transferable acoustic information. Under the deployment-consistent protocol the spread between Random Forest, the hybrid network, and inverse-distance weighting is several times smaller than the spread between protocols for a fixed model; the learnt models retain a measurable advantage for sound strength and reverberation time, and the high accuracy of the original pipelines re-emerges as condition interpolation at measured positions, a distinct and operationally useful task. A reporting checklist operationalises the findings.

Repeated prediction of acoustic fields from spatially distributed boundary excitation is computationally expensive when each source realization requires a new wave simulation. This work introduces a quadrature-aware complex-linear boundary operator (CLBO) that maps complex normal velocity on a vibrating surface to complex pressure at receiver locations. The model couples learned source and receiver basis functions through an explicit complex surface-quadrature contraction, so the boundary excitation enters linearly by construction. This preserves complex superposition, homogeneity, and zero response to zero excitation, while representing the source through coordinates, normals, and quadrature weights rather than a fixed flattened input vector. Reference data were generated using a verified three-dimensional multiple-relaxation-time (MRT) lattice Boltzmann solver and stored in a solver-agnostic boundary-to-field format. CLBO was compared with a fixed-sensor complex DeepONet under matched case splits and optimization settings, with additional tests of structural consistency, receiver-coordinate interpolation, source discretization, source-family holdout, label efficiency, physics-informed ablations, unseen source mixtures, and computational cost. Across five training seeds, CLBO achieved a mean complex relative field error of 0.184 +/- 0.00771, compared with 0.367 +/- 0.00742 for DeepONet. Its measured source-superposition error was 1.31 x 10^-7, and its mean error on newly simulated mixed-source cases was 0.237, compared with 0.415 for DeepONet. Inference was 1.83 x 10^4 faster than the reference calculation for the reported query size. These results show that enforcing the known complex-linear boundary-to-field structure improves physical consistency and generalization under distributed acoustic excitation.

Acoustic scene understanding in multi-room environments is a difficult task. Most existing systems use a single centralized microphone array, and they often fail because walls and doors block sound signals. To address this challenge, we propose a geometry-informed distributed acoustic scene understanding framework. Our system leverages distributed microphones and uses an audio spectrogram transformer and a topology-aware graph neural network to fuse spatio-temporal acoustic features. Then, these features are decoded into discrete semantic triplets. Finally, a frozen large language model combines these symbolic observations with the environmental geometry. This allows the system to perform spatial understanding, infer plausible missing transitions, and generate a physically consistent narrative of the scene. Experiments on a custom multi-room simulator demonstrate that our framework outperforms centralized baselines and improves spatial consistency under simulated occlusion.