Generative Models for Helmholtz Equation Solutions: A Dataset of Acoustic Materials
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912642218590208 |
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| author | Gramaccioni, Riccardo Fosco Marinoni, Christian Frezza, Fabrizio Uncini, Aurelio Comminiello, Danilo |
| author_facet | Gramaccioni, Riccardo Fosco Marinoni, Christian Frezza, Fabrizio Uncini, Aurelio Comminiello, Danilo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09657 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generative Models for Helmholtz Equation Solutions: A Dataset of Acoustic Materials Gramaccioni, Riccardo Fosco Marinoni, Christian Frezza, Fabrizio Uncini, Aurelio Comminiello, Danilo Machine Learning Artificial Intelligence Numerical Analysis Signal Processing 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. |
| title | Generative Models for Helmholtz Equation Solutions: A Dataset of Acoustic Materials |
| topic | Machine Learning Artificial Intelligence Numerical Analysis Signal Processing |
| url | https://arxiv.org/abs/2510.09657 |