Neural models gain new data-efficient training for complex 3d simulations
Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers
Artificial Intelligence
Summary
Simulating physical systems in 3D is usually slow and needs many examples for training AI models to predict solutions. The authors introduce a new way to train these AI models without relying on huge datasets. For static problems, they use the shape of the 3D space itself to teach the model, and for changing problems, they create simulated examples on the fly. This approach helps the AI learn faster and perform better, especially when few examples are available.
What this means in practice
- •For simulation engineers: Improve predictive accuracy and reduce data needs when fine-tuning neural models for complex 3D simulations.
- •For computational fluid dynamics teams: Generate synthetic PDE data online to enhance model pre-training without expensive dataset creation.
Authors
Luis Medrano-Navarro, Giacomo Baldan, Qiang Liu, Benjamin Holzschuh, Jan Hagnberger, Mathias Niepert, Nils Thuerey
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.