{"ID":2862522,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.25788","arxiv_id":"2509.25788","title":"From Cheap Geometry to Expensive Physics: Elevating Neural Operators via Latent Shape Pretraining","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.","short_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 solut...","url_abs":"https://arxiv.org/abs/2509.25788","url_pdf":"https://arxiv.org/pdf/2509.25788v1","authors":"[\"Zhizhou Zhang\",\"Youjia Wu\",\"Kaixuan Zhang\",\"Yanjia Wang\"]","published":"2025-09-30T05:01:31Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Transformer\",\"LoRA\"]","has_code":false}