arXiv:2607.09684cs.LGcs.AI2026-07

结构先验未必有用,错配反而拖累模型性能。

SciML in the Wild: A Diagnostic Study of When Structural Priors Help and When They Hurt

论文配图:SciML in the Wild: A Diagnostic Study of When Structural Priors Help and When They Hurt
图 1 · 摘自论文原文
  • 用宏观经济数据测试五类模型,检验结构先验有效性
  • 无约束模型(如ARIMA、NODE)普遍优于强约束模型(如PINN、UDE)
  • 提醒研究者:先验证结构是否匹配,再加先验

科学机器学习(SciML)方法如神经常微分方程(NODE)、物理信息神经网络(PINN)和通用微分方程(UDE),在结构先验反映真实动力学时最有效。本文探究当这一假设不成立时会发生什么。以宏观经济预测为压力测试场景,我们在23个国家、稀疏年度数据、多时间切分和五次随机种子下评估了五类模型:ARIMA、LSTM、NODE、PINN、UDE。结果表明,所有模型均未实现稳定优异的预测表现,凸显低频宏观经济预测的困难。然而,清晰的相对性能层级显现:较弱约束模型(如ARIMA、NODE)始终优于强约束启发式先验模型(如PINN、UDE)。这并非否定SciML,而是一个诊断性发现:当先验与数据生成过程不一致时,结构先验可能成为误正则化项。我们识别出包括先验错配、制度变迁、结构性断裂和优化不稳定性在内的失败模式,主张SciML从业者应在假设更多结构有益前,先验证其是否真的有帮助。

原文摘要 · Abstract (English)

Scientific Machine Learning (SciML) methods such as Neural Ordinary Differential Equations (NODEs), Physics-Informed Neural Networks (PINNs), and Universal Differential Equations (UDEs) are most effective when structural priors reflect reliable governing dynamics. We ask what happens when this assumption is violated. Using macroeconomic forecasting as a stress-test domain, we evaluate five model families, ARIMA, LSTM, NODE, PINN, and UDE, across 23 countries using sparse annual data, multiple temporal splits, and five random seeds. Our results show that none of the evaluated models achieve consistently strong forecasting performance, highlighting the difficulty of low-frequency macroeconomic prediction. However, a clear relative hierarchy emerges: less-constrained models, particularly ARIMA and NODE, consistently outperform more-constrained heuristic-prior models such as PINN and UDE. Rather than treating this as a rejection of SciML, we interpret it as a diagnostic result: structural priors can act as misregularizers when they do not match the data-generating process. We identify failure modes including prior misalignment, regime shifts, structural breaks, and optimization instability, and argue that SciML practitioners should test whether structure helps before assuming that more structure is beneficial.

SciML结构先验模型诊断

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