From Cheap Geometry to Expensive Physics: Elevating Neural Operators via Latent Shape Pretraining

• URL: http://arxiv.org/abs/2509.25788v1
• Date: Tue, 30 Sep 2025 05:01:31 GMT
• Title: From Cheap Geometry to Expensive Physics: Elevating Neural Operators via Latent Shape Pretraining
• Authors: Zhizhou Zhang, Youjia Wu, Kaixuan Zhang, Yanjia Wang,
• Abstract summary: Industrial design evaluation often relies on simulations of governing partial differential equations (PDEs)<n> Operator learning has emerged as a promising approach to accelerate PDE solution prediction.<n>We propose a two-stage framework to better exploit this abundant, physics-agnostic resource.
• Score: 4.838293051443775
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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