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

arXiv: https://arxiv.org/abs/2510.09657 · HTML: https://mlsanity.com/paper/2510.09657/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 7 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models](https://mlsanity.com/paper/2305.19836/) (2023)
- [Ship in Sight: Diffusion Models for Ship-Image Super Resolution](https://mlsanity.com/paper/2403.18370/) (2024)
- [Overview of the L3DAS23 Challenge on Audio-Visual Extended Reality](https://mlsanity.com/paper/2402.09245/) (2024)

## Abstract (arXiv)

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.