Amortised neural acoustic tomography: domain-specific encoder design and topology-dependent Eikonal analysis
We present an amortised neural framework for three-dimensional acoustic diffraction tomography that reconstructs scene geometry as signed distance functions from boundary element method (BEM) pressure observations. Our central finding is that domain-specific encoder design, rather than physics-informed loss terms, drives reconstruction accuracy. Building on a transfer function decomposition that separates scattering from free-space propagation, we introduce an encoder that maps complex pressure measurements to latent geometry codes through magnitude–phase input representation and frequency-selective attention pooling. Across 100 synthetic scenes spanning 12 shape categories (3 random seeds), this encoder attains 0.644±0.015 mean intersection over union, a 51.0% improvement over a domain-agnostic baseline ( p=0.0015), while the physics losses evaluated in this amortised setting provide zero or negative benefit. Inference is a single forward pass ( ∼127 ms, a ∼950× speedup over per-scene optimisation). A systematic Eikonal regularisation ablation reveals a topology- and architecture-dependent asymmetry: any benefit is confined to specific convex shapes with reconstruction headroom in the per-scene auto-decoder and vanishes under encoder amortisation, whereas the harm—a flattening of topological features—is universal across architectures. Combined with Helmholtz partial differential equation failure and Laplacian supervision dead-ends, these findings challenge the assumption that physics losses universally benefit neural acoustic surrogates and suggest that architectural physics integration is more effective than loss-based approaches. We will release a 100-scene 3D BEM benchmark dataset, deterministically regenerable from the accompanying code, for reproducibility.