الملخص
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.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Medrano-Navarro, L., Baldan, G., Liu, Q., Holzschuh, B., Hagnberger, J., Niepert, M., & Thuerey, N. (2026). Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers. https://omanscience.com/ar/articles/geometry-meets-physics-data-efficient-pre-training-for-unstructured-neural-pde-solvers
MLA 9
Medrano-Navarro, Luis, et al. "Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers." https://omanscience.com/ar/articles/geometry-meets-physics-data-efficient-pre-training-for-unstructured-neural-pde-solvers.
شيكاغو (المؤلف–التاريخ)
Medrano-Navarro, Luis, Giacomo Baldan, Qiang Liu, Benjamin Holzschuh, Jan Hagnberger, Mathias Niepert, and Nils Thuerey. 2026. "Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers." https://omanscience.com/ar/articles/geometry-meets-physics-data-efficient-pre-training-for-unstructured-neural-pde-solvers.
هارفارد
Medrano-Navarro, L., Baldan, G., Liu, Q., Holzschuh, B., Hagnberger, J., Niepert, M. and Thuerey, N. (2026) 'Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers', Available at: https://omanscience.com/ar/articles/geometry-meets-physics-data-efficient-pre-training-for-unstructured-neural-pde-solvers.
فانكوفر
Medrano-Navarro L, Baldan G, Liu Q, Holzschuh B, Hagnberger J, Niepert M, et al. Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers. https://omanscience.com/ar/articles/geometry-meets-physics-data-efficient-pre-training-for-unstructured-neural-pde-solvers
IEEE
L. Medrano-Navarro, G. Baldan, Q. Liu, B. Holzschuh, J. Hagnberger, M. Niepert, and N. Thuerey, "Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers," https://omanscience.com/ar/articles/geometry-meets-physics-data-efficient-pre-training-for-unstructured-neural-pde-solvers.