[
    {
        "id": "osp-19502",
        "type": "article-journal",
        "title": "Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solvers",
        "author": [
            {
                "family": "Medrano-Navarro",
                "given": "Luis"
            },
            {
                "family": "Baldan",
                "given": "Giacomo"
            },
            {
                "family": "Liu",
                "given": "Qiang"
            },
            {
                "family": "Holzschuh",
                "given": "Benjamin"
            },
            {
                "family": "Hagnberger",
                "given": "Jan"
            },
            {
                "family": "Niepert",
                "given": "Mathias"
            },
            {
                "family": "Thuerey",
                "given": "Nils"
            }
        ],
        "URL": "https://omanscience.com/ar/articles/geometry-meets-physics-data-efficient-pre-training-for-unstructured-neural-pde-solvers",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "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."
    }
]