{
  "annotation_id": "e3fda830-594a-48fb-a296-18ed1f6f78c5",
  "date_created": "2026-02-17T05:53:16.240000Z",
  "date_modified": "2026-02-17T05:53:16.240000Z",
  "file_hash": "4ae60c4a586fac5ba667b9fe258af8184586bc7d7bb4f962eef81afa6faeb292",
  "private": false,
  "record": {
    "abstract": "Partial differential equations (PDEs) are a central tool for modeling the dynamics of physical, engineering, and materials systems, but high-fidelity simulations are often computationally expensive. At the same time, many scientific applications can be viewed as the evolution of spatially distributed fields, making data-driven forecasting of such fields a core task in scientific machine learning. In this work we study autoregressive deep-learning surrogates for two-dimensional PDE dynamics on periodic domains, focusing on generalization to out-of-distribution initial conditions within a fixed PDE and parameter regime and on strict small-data settings with at most $\\mathcal{O}(10^2)$ simulated trajectories per system. We introduce a multi-channel U-Net [...], evaluate it on five qualitatively different PDE families and compare it to ViT, AFNO, PDE-Transformer, and KAN-UNet under a common training setup. Across all datasets, me-UNet matches or outperforms these more complex architectures in terms of field-space error, spectral similarity, and physics-based metrics for in-distribution rollouts, while requiring substantially less training time. It also generalizes qualitatively to unseen initial conditions with as few as $\\approx 20$ training simulations. A data-efficiency study and Grad-CAM analysis further suggest that, in small-data periodic 2D PDE settings, convolutional architectures with inductive biases aligned to locality and periodic boundary conditions remain strong contenders for accurate and moderately out-of-distribution-robust surrogate modeling.",
    "arxiv_id": "2601.08404",
    "authors": [
      "Binh Duong Nguyen",
      "Stefan Sandfeld"
    ],
    "categories": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Out-of-distribution generalization of deep-learning surrogates for 2D PDE-generated dynamics in the small-data regime",
    "url": "https://arxiv.org/abs/2601.08404",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1a408d25-049b-4085-b28a-1fa1bb15fe99",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}