用物理约束选关键数据，大幅降低神经算子训练成本
PICore: Physics-Informed Unsupervised Coreset Selection for Data Efficient Neural Operator Training
- 基于物理损失函数无监督筛选最具信息量的输入数据
- 仅需对选中数据做少量仿真标注，训练效率提升78%
- 适合需要高效训练神经算子的研究者或工程应用
神经算子通过学习函数空间间的映射，为无法解析求解的偏微分方程（PDE）提供强大解决方案。然而，其训练面临两大瓶颈：需大量标注数据，而标签依赖昂贵数值模拟获得。为此，我们提出PICore，一种无需真实解即可选择最相关信息样本的无监督核心数据集选取框架。PICore利用物理信息损失，根据样本对算子学习的潜在贡献度筛选未标注输入。选定紧凑输入集后，仅对这些样本进行数值模拟生成标签，显著降低标注成本。随后在缩减后的有标签数据上训练神经算子，大幅缩短训练时间。在四个不同PDE基准测试中，多种核心集选择策略下，PICore相比监督方法平均训练效率提升78%，且精度损失极小。
原文摘要 · Abstract (English)
Neural operators offer a powerful paradigm for solving partial differential equations (PDEs) that cannot be solved analytically by learning mappings between function spaces. However, there are two main bottlenecks in training neural operators: they require a significant amount of training data to learn these mappings, and this data needs to be labeled, which can only be accessed via expensive simulations with numerical solvers. To alleviate both of these issues simultaneously, we propose PICore, an unsupervised coreset selection framework that identifies the most informative training samples without requiring access to ground-truth PDE solutions. PICore leverages a physics-informed loss to select unlabeled inputs by their potential contribution to operator learning. After selecting a compact subset of inputs, only those samples are simulated using numerical solvers to generate labels, reducing annotation costs. We then train the neural operator on the reduced labeled dataset, significantly decreasing training time as well. Across four diverse PDE benchmarks and multiple coreset selection strategies, PICore achieves up to 78% average increase in training efficiency relative to supervised coreset selection methods with minimal changes in accuracy. We provide code at https://github.com/Asatheesh6561/PICore.
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