Generative Models for Helmholtz Equation Solutions: A Dataset of Acoustic Materials

TL;DR

This work tackles the computational load of solving the Helmholtz equation for acoustic wave propagation in complex materials by introducing HA30K, a dataset of 31,000 2D configurations with corresponding pressure fields computed via FreeFEM. It demonstrates a diffusion-based surrogate, Stable Diffusion with ControlNet, that maps material-domain images and global acoustic parameters to pressure-field predictions, enabling fast, parallelizable inference with adjustable diffusion steps. Objective metrics (MSE, FID, SSIM) and hardware-accelerated experiments show that the method achieves high fidelity while delivering significant speedups compared to sequential solvers. By providing a public benchmark and a scalable baseline, the work facilitates data-driven exploration and inverse-design for acoustic materials.

Abstract

Accurate simulation of wave propagation in complex acoustic materials is crucial for applications in sound design, noise control, and material engineering. Traditional numerical solvers, such as finite element methods, are computationally expensive, especially when dealing with large-scale or real-time scenarios. In this work, we introduce a dataset of 31,000 acoustic materials, named HA30K, designed and simulated solving the Helmholtz equations. For each material, we provide the geometric configuration and the corresponding pressure field solution, enabling data-driven approaches to learn Helmholtz equation solutions. As a baseline, we explore a deep learning approach based on Stable Diffusion with ControlNet, a state-of-the-art model for image generation. Unlike classical solvers, our approach leverages GPU parallelization to process multiple simulations simultaneously, drastically reducing computation time. By representing solutions as images, we bypass the need for complex simulation software and explicit equation-solving. Additionally, the number of diffusion steps can be adjusted at inference time, balancing speed and quality. We aim to demonstrate that deep learning-based methods are particularly useful in early-stage research, where rapid exploration is more critical than absolute accuracy.

Figures (4)

• Figure 1: Samples from the HA30K dataset. The red dot represents the sound source location. Black squares represent the obstacles.
• Figure 2: An example showing the possible locations of the sound source given the position of obstacles (in blue).
• Figure 3: Baseline architecture: The baseline architecture takes the topological structure of the domain along with a textual description of the acoustic properties and outputs an estimate of the pressure field. The target is the pressure field obtained by solving the Helmholtz equation.
• Figure 4: Speedup obtained using parallel calculation with our baseline compared to sequential simulations with FreeFEM.