PDE-OBS: Controlled Evaluation Across Observation Patterns

2026-09-28

AI Summary

This study addresses the limitation that single observation mode evaluations fail to capture performance fluctuations in physical field reconstruction by proposing an integrated benchmark platform. The platform incorporates seven types of partial differential equation data with configurable observation operators, enabling parameterized mode definitions through the decoupling of observation construction from physical records, and establishes a standardized cross-mode evaluation protocol to quantify model sensitivity. Experiments reveal that cross-mode errors consistently exceed matched-mode errors, and dense observations do not necessarily reduce errors. Furthermore, mixed training strategies effectively mitigate transfer errors. This work provides a systematic tool and novel insights for the robustness evaluation of physical field reconstruction.

Abstract

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.

Problem

• Physical-field reconstruction
• Observation patterns
• PDE benchmarking
• Cross-pattern evaluation
• Measurement density

Innovation

• PDE-OBS
• observation patterns
• physical-field reconstruction
• benchmarking platform
• cross-pattern evaluation