PDE-OBS：跨观测模式的受控评估
PDE-OBS: Controlled Evaluation Across Observation Patterns
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中文总结 AI 辅助
PDE-OBS是一个集成基准平台，用于系统评估物理场重建与预测对观测模式的敏感性，通过多PDE数据、可配置观测算子和大量模型评估，揭示了跨模式误差普遍高于匹配模式误差的现象。
中文摘要 AI 辅助
物理场重建与预测依赖于测量密度和空间布局，然而在单一观测模式下进行评估，无法刻画当该模式发生变化时的性能表现。我们提出了PDE-OBS，一个集成的基准测试平台，涵盖数值数据生成、模型训练以及在不同观测条件下的推理与评估。该平台结合了来自七个偏微分方程族的560,000个场和轨迹，配备了可配置的观测算子，以及七种适用于静态重建和短期预测的适配基线方法。将观测构建与物理记录分离，使用户能够为训练和测试指定参数化模式和确定性混合，同时保留预测目标和数据划分。评估协议使用为每个测试模式训练得到的参考模型，在相同的测试观测和目标上比较各模型，并通过等计数分组进行空间布局比较。在一个包含14,000条记录的子集上，我们在九种测试模式下评估了441个训练模型，共产生3,969次评估。在所有49个PDE-方法组合中，跨模式平均误差均大于匹配模式平均误差，且这一发现在一个配置匹配的117个模型子集中依然成立。对于固定模型，更密集的测试观测并不总能一致地降低误差。在五个已完成组合上的混合模式训练减少了单一模式迁移的大误差，尽管目标训练参考模型通常仍更准确。综合来看，该基准和发现支持对观测模式敏感性进行系统评估，并为在不断变化的测量条件下开发方法提供了可复用的工作流程。代码：此HTTPS URL。
英文摘要
Physical-field reconstruction and forecasting depend on both measurement density and spatial layout, yet evaluation under a single observation pattern does not characterize performance when that pattern changes. We introduce PDE-OBS, an integrated benchmarking platform spanning numerical data generation, model training, and inference and evaluation under varying observation conditions. It combines 560,000 fields and trajectories from seven partial differential equation families with configurable observation operators and seven adapted baseline methods for stationary reconstruction and short-horizon forecasting. Separating observation construction from physical records allows users to specify parameterized patterns and deterministic mixtures for training and testing while preserving prediction targets and data splits. The evaluation protocol uses references trained for each test pattern to compare models on identical test observations and targets, alongside equal-count groups for spatial-layout comparisons. On a 14,000-record subset, we evaluate 441 trained models under nine test patterns, yielding 3,969 evaluations. Mean cross-pattern error exceeds mean matched-pattern error in all 49 PDE-method pairs, and this finding persists in a configuration-matched subset of 117 models. Denser test observations do not consistently reduce error for a fixed model. Mixed-pattern training on five completed pairs reduces large single-pattern transfer errors, although destination-trained references usually remain more accurate. Together, the benchmark and findings support systematic evaluation of observation-pattern sensitivity and provide a reusable workflow for developing methods under changing measurement conditions. Code: https://github.com/ru1ch3n/PDE-OBS.
发表机构
- Stony Brook University（石溪大学）
- University of California, Davis（加州大学戴维斯分校）
- TikTok
- PayPal
- New York University（纽约大学）
- Northeastern University（东北大学）
机构由 AI 辅助整理，请以论文原文为准。
