Geometry-to-Sound Prediction

Updated 2 December 2025

Geometry-to-sound prediction is a multidisciplinary field that infers acoustic properties from geometric and physical data using physics-based models, statistical methods, and machine learning.
Recent advances include FEM modal analysis, geometric acoustics, and hybrid CFD/CAA methods to achieve high-performance surrogate modeling and real-time applications.
Applications range from urban noise mapping and ear canal modeling to aeroacoustic noise reduction and immersive sound design in AR/VR.

Geometry-to-sound prediction refers to the task of inferring acoustic properties, signals, or maps from geometric and physical information. This field spans a range of physical scales and domains, including material-induced vibration, architectural or urban propagation, aeroacoustic generation, and individualized biological conduction. Prediction approaches draw from physics-based models (e.g., wave or ray equations), modal decompositions, statistical and machine learning frameworks, and hybrid techniques tailored to the physical regime and scale of interest. Recent research emphasizes causal and physically consistent pipelines, multimodal representation learning with geometry-acoustics alignment, and high-performance surrogate modeling for real-time applications.

1. Foundations and Core Physical Principles

At the heart of geometry-to-sound prediction lies physical modeling of how structure and material properties dictate acoustic behavior. In solid objects, vibrations arising from interactions (such as impact) are determined by the eigenspectrum of the mass and stiffness matrices as obtained by finite element modal analysis. The basic relation is:

$K u = \omega^2 M u$

where $K$ is the assembled stiffness matrix, $M$ is the mass matrix, and the eigenpairs $(\omega_i, u_i)$ define the modal frequencies and mode shapes of the object. In wave propagation settings (architectural, urban, or atmospheric), the Helmholtz equation

$\Delta u(x) + \frac{\omega^2}{c(x)^2} u(x) = 0$

governs sound fields, with $c(x)$ the local speed of sound. At high frequencies, the WKB/geometric approximation leads to the eikonal equation for phase propagation and an associated transport equation for amplitude, aligning sound prediction with ray-based geometric optics (Potter et al., 2022).

In flow-induced aeroacoustics, such as trailing-edge noise, the geometric and material microstructure of solid bodies modifies both source generation (via turbulence statistics) and propagation (via attenuation and impedance in porous or structured materials), typically modeled by extended Acoustic Perturbation Equations (APE) with Darcy and Forchheimer terms (Fassmann et al., 2018).

2. Geometric Inputs: Representations and Parameterizations

Geometry-to-sound pipelines rely on explicit and physically meaningful geometric descriptors:

CAD triangle meshes (surface) and tetrahedral volume meshes for solid objects, as input to eigenmode solvers or wave propagation engines (Pang et al., 25 Nov 2025).
2D/3D binary masks for built environments or urban layouts, encoding occluders, reflectors, and diffractors, often gridded at map-scale as in urban noise studies (Eckerle et al., 6 Oct 2025).
Parameter fields (e.g., porosity φ, pore size $D_p$ , permeability κ, Young’s modulus $E$ , Poisson’s ratio ν, density ρ), directly specifying local material-acoustic relationships.
Functional geometry (such as the area function $A(x)$ in horn models) reconstructed from impedance or reflectance measurements, as in individualized ear canal modeling (Roden et al., 16 Nov 2025).

Preprocessing pipelines may involve automated mesh generation (e.g., fTetWild for volumetric discretization of 3D objects (Pang et al., 25 Nov 2025)), supervised or contrastive learning for modality fusion (geometry–material–image–sound embedding), and geometric graph constructions to enforce spatial structure for statistical smoothing (Tavakoli et al., 2016).

3. Computational and Predictive Frameworks

Approaches to geometry-to-sound prediction are dictated by the task domain and desired output. A representative selection includes:

Modal Analysis for Impact Sounds in Solids

FEM modal analysis discretizes the object into global mass $M$ , stiffness $K$ , and computes the smallest $N$ eigenfrequencies and vectors (Pang et al., 25 Nov 2025). Given geometry and material, the pipeline directly yields the modal frequencies, which drive waveform synthesis through superposed damped sinusoids.

High-frequency Propagation via Geometric Acoustics

Eikonal-based approaches compute the travel-time phase $\tau(x)$ and amplitude $\alpha(x)$ fields recursively using the Jet Marching Method on unstructured tetrahedral meshes (Potter et al., 2022). These methods support unified modeling of direct, reflected, and edge-diffracted components (Uniform Theory of Diffraction).
For scenarios with wind or stratified atmospheres, ray paths are predicted by extremizing travel-time functionals, producing either Riemannian or Finsler (Randers) geodesics depending on wind structure (Gibbons et al., 2011).

Hybrid Aeroacoustic Noise Prediction

Hybrid CFD/CAA methods combine RANS-generated mean flows and turbulence statistics with fast stochastic source modeling (FRPM). Acoustic perturbation equations are then solved in physical space with explicit geometry-informed source layers and anisotropic attenuation (Fassmann et al., 2018).
The porous or structured trailing-edge geometry is parameterized directly into PDE terms, connecting material/architectural design to spectral output.

Learning-based Models for Urban and Multimodal Scenarios

Conditioned Normalizing Flows (“Full-Glow”) are used to map multi-channel urban geometric tensors (building masks, source positions, boundary conditions) to full sound-level maps, learning to reproduce diffraction and reflection effects at high speed for interactive applications (Eckerle et al., 6 Oct 2025).
Cross-modal learning on datasets like VibraVerse leverages geometry (O-CNN), material vectors, and modal eigenspectra, aligning them in a shared space with contrastive losses (CLASP) for physically consistent retrieval and multimodal tasks (Pang et al., 25 Nov 2025).

Statistical Spatial Modeling for Linguistic and Perceptual Data

Functional predictive modeling over spatial domains leverages kernel smoothing with geodesic distances for mean and covariance estimation of acoustic features (e.g., MFCCs), enabling spatial interpolation and waveform synthesis across complex geographic regions (Tavakoli et al., 2016).

4. Inverse and Surrogate Approaches

Certain pipelines invert from measured acoustic response back to geometry or parameter fields, or employ computational surrogates for rapid prediction:

Ear Canal Inverse Problem: The area function $A(x)$ of an ear canal is recovered from frequency-domain input impedance by inverting Webster’s horn equation using finite-difference time-domain schemes. This enables accurate subject-specific prediction of eardrum sound pressure from geometric or acoustic data (Roden et al., 16 Nov 2025).
Closed-form Correction for SoS in Ultrasound: Image registration between frames with differing geometric transmission paths and assumed SoS is used to resolve a scalar correction parameter ( $\gamma$ ), enabling closed-form update of the mean SoS to sub-percent accuracy (Bezek et al., 2022).
Normalizing-flow Accelerators: Conditioned flows, being invertible and generative, allow “what-if” geometry edits and on-the-fly recomputation of acoustic fields, essential in regulatory and planning workflows (Eckerle et al., 6 Oct 2025).

A summary of key methods and their geometric input types is provided below.

Domain	Geometric Input	Core Methodology
Rigid-body sound	3D mesh + materials	FEM modal analysis, SIREN decoder
Urban acoustics	2D masks + BCs	Conditioned Normalizing Flow
Room acoustics	Faceted mesh	Eikonal-transport Jet Marching
Ear canal modeling	1D area function	Webster’s equation inversion, FDTD
Aeroacoustics	Mesh + porosity, κ, φ	Hybrid CFD/CAA + extended APE

5. Quantitative Results and Error Metrics

Recent geometry-to-sound pipelines are evaluated via physically grounded metrics:

Modal Frequency Prediction: MSE on Mel-scaled predicted vs. FEM-computed modal frequencies; end-to-end inference accelerates to ~40x faster than sparse eigenvalue solvers while achieving $6.06\times 10^{-4}$ test error (Pang et al., 25 Nov 2025).
SoS Estimation for Ultrasound: Closed-form correction methods achieve mean absolute error (MAE) < 0.3% for ±5% initial error setups, and improve tomographic map RMSE by 78.5%–87.0% relative to non-corrected workflows (Bezek et al., 2022).
Urban Sound-pressure Mapping: Real-time Full-Glow models attain $0.65$ dB mean absolute error (MAE) in non-line-of-sight regions, with structural (SSIM) scores $0.92$–$0.96$ and >2000x speedup vs. physics solvers (Eckerle et al., 6 Oct 2025).
Horn Equation Inverse Ear Modeling: 1D model errors remain within $<$ 0.6 dB and $<$ 2° phase vs. 3D FEM benchmarks for 1–10 kHz with spatial resolution $\Delta x = 0.1$ mm (Roden et al., 16 Nov 2025).
Statistical Linguistic Mapping: Integrated squared error in functional mean/covariance estimation is quantified, with cross-validation for kernel and neighborhood parameters (Tavakoli et al., 2016).

6. Physical Consistency, Limitations, and Scope

Emergent research directions seek to enforce causal, physically interpretable mappings rather than mere correlational fits. The VibraVerse dataset and CLASP framework directly tie each geometry–sound pair to causal FEM-governed physical parameters (Pang et al., 25 Nov 2025). This contrasts with purely data-driven pipelines, which may exhibit generalization failures when extrapolating to out-of-distribution geometries or materials.

Limitations are domain-dependent:

High-frequency approximations neglect diffraction or modal effects at low frequencies unless explicitly incorporated (e.g., UTD for edges in geometric acoustics (Potter et al., 2022)).
Homogeneous or straight-ray assumptions may fail in highly refractive, multilayered, or anisotropic domains (Bezek et al., 2022).
Learning-based surrogates require extensive and representative training datasets; physical consistency is enhanced but not guaranteed unless embedded at the architectural or loss-function level (Pang et al., 25 Nov 2025, Eckerle et al., 6 Oct 2025).

A plausible implication is that robust geometry-to-sound prediction pipelines must combine domain-specific physical modeling, geometric fidelity, and (where surrogacy is required) contrastive, physically regularized learning regimes.

7. Applications and Future Directions

Applications are diverse and rapidly broadening:

Material/shape sonification, classification, and retrieval: Physically grounded geometry–sound embeddings for robotics, AR/VR, material science, and computer graphics (Pang et al., 25 Nov 2025).
Regulatory urban noise mapping, “what-if” studies, and compliance workflows: Real-time surrogate flow models for environmental assessment and urban planning (Eckerle et al., 6 Oct 2025).
Medical and individualized sound modeling: Subject-specific acoustic transfer function estimation for audiology, prosthetics, and earphone equalization by inverting horn geometry from impedance (Roden et al., 16 Nov 2025).
Architectural and room acoustics: Fast, unified eikonal/UTD systems for precomputation in immersive environments (Potter et al., 2022).
Aeroacoustic noise reduction: Rational design of porous trailing edge geometries for turbine or airfoil noise mitigation (Fassmann et al., 2018).

The field is transitioning toward fully differentiable, physically consistent geometry-to-sound engines that can both predict and invert multimodal relationships for sound-guided perception, design, and interaction with the physical world.