Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers

2026-10-02

AI Summary

This study addresses the limited generalization of neural PDE surrogate models on unstructured 3D geometries and the prohibitive cost of generating large-scale training data. We propose a disk-dataset-free pretraining framework that leverages intrinsic shape descriptors to learn 3D domain representations, integrating geometry-driven steady-state strategies with physics-informed transient online data synthesis. This establishes a novel data-independent pretraining paradigm encompassing both steady-state and transient scenarios, overcoming conventional bottlenecks in computational and data efficiency. Experimental results demonstrate that the proposed framework achieves faster convergence, superior data efficiency, and enhanced fine-tuning accuracy in low-data regimes, offering an efficient and practical pathway for large-scale scientific simulations.

Abstract

Neural surrogate models for Partial Differential Equations (PDEs) on unstructured 3D geometries are often limited by poor generalization and the high cost of generating large-scale training datasets. Consequently, pre-training on massive datasets of related PDE dynamics has emerged as a critical alternative to enhance the robustness and scalability of these models. However, this strategy is neither compute- nor data-efficient, as it relies on massive pre-computed data that is very costly to generate. In this work, we introduce a disk-data-free pre-training framework tailored to both steady-state and transient regimes. For steady-state problems, we propose a geometry-driven strategy that leverages intrinsic shape descriptors to learn representations of complex 3D domains. For transient problems, we introduce a physics-driven approach based on online generation of synthetic PDE data, enabling scalable pre-training without reliance on expensive datasets. Across multiple experiments, our approach achieves faster convergence, greater data efficiency, and higher accuracy during fine-tuning, particularly under realistic low-data regimes. This methodology provides a practical pathway toward data-efficient neural emulators for large-scale simulations.

Problem

• Partial Differential Equations
• Neural Surrogate Models
• Pre-training
• Unstructured 3D Geometries
• Data Efficiency

Innovation

• Neural PDE Solvers
• Data-Efficient Pre-Training
• Unstructured 3D Geometries
• Physics-Informed Learning
• Synthetic Data Generation