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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.25788 |
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| _version_ | 1866918151472545792 |
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| author | Zhang, Zhizhou Wu, Youjia Zhang, Kaixuan Wang, Yanjia |
| author_facet | Zhang, Zhizhou Wu, Youjia Zhang, Kaixuan Wang, Yanjia |
| contents | Industrial design evaluation often relies on high-fidelity simulations of governing partial differential equations (PDEs). While accurate, these simulations are computationally expensive, making dense exploration of design spaces impractical. Operator learning has emerged as a promising approach to accelerate PDE solution prediction; however, its effectiveness is often limited by the scarcity of labeled physics-based data. At the same time, large numbers of geometry-only candidate designs are readily available but remain largely untapped. We propose a two-stage framework to better exploit this abundant, physics-agnostic resource and improve supervised operator learning under limited labeled data. In Stage 1, we pretrain an autoencoder on a geometry reconstruction task to learn an expressive latent representation without PDE labels. In Stage 2, the neural operator is trained in a standard supervised manner to predict PDE solutions, using the pretrained latent embeddings as inputs instead of raw point clouds. Transformer-based architectures are adopted for both the autoencoder and the neural operator to handle point cloud data and integrate both stages seamlessly. Across four PDE datasets and three state-of-the-art transformer-based neural operators, our approach consistently improves prediction accuracy compared to models trained directly on raw point cloud inputs. These results demonstrate that representations from physics-agnostic pretraining provide a powerful foundation for data-efficient operator learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Cheap Geometry to Expensive Physics: Elevating Neural Operators via Latent Shape Pretraining Zhang, Zhizhou Wu, Youjia Zhang, Kaixuan Wang, Yanjia Machine Learning Industrial design evaluation often relies on high-fidelity simulations of governing partial differential equations (PDEs). While accurate, these simulations are computationally expensive, making dense exploration of design spaces impractical. Operator learning has emerged as a promising approach to accelerate PDE solution prediction; however, its effectiveness is often limited by the scarcity of labeled physics-based data. At the same time, large numbers of geometry-only candidate designs are readily available but remain largely untapped. We propose a two-stage framework to better exploit this abundant, physics-agnostic resource and improve supervised operator learning under limited labeled data. In Stage 1, we pretrain an autoencoder on a geometry reconstruction task to learn an expressive latent representation without PDE labels. In Stage 2, the neural operator is trained in a standard supervised manner to predict PDE solutions, using the pretrained latent embeddings as inputs instead of raw point clouds. Transformer-based architectures are adopted for both the autoencoder and the neural operator to handle point cloud data and integrate both stages seamlessly. Across four PDE datasets and three state-of-the-art transformer-based neural operators, our approach consistently improves prediction accuracy compared to models trained directly on raw point cloud inputs. These results demonstrate that representations from physics-agnostic pretraining provide a powerful foundation for data-efficient operator learning. |
| title | From Cheap Geometry to Expensive Physics: Elevating Neural Operators via Latent Shape Pretraining |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.25788 |