SciML Structural Priors: When They Help and When They Harm Forecasting.

This research investigates the effectiveness of structural priors in Scientific Machine Learning (SciML) models, such as Neural Ordinary Differential Equations (NODEs) and Physics-Informed Neural Networks (PINNs), particularly when these priors might not accurately reflect the underlying data-generating process. Using macroeconomic forecasting as a challenging testbed with sparse annual data across 23 countries, the study compared five model families including traditional ARIMA and various SciML approaches. The findings indicate that models with less rigid structural constraints, specifically ARIMA and NODEs, generally outperformed more constrained models like PINNs and UDEs in forecasting. This suggests that when structural priors are misaligned with the data, they can hinder rather than help model performance, acting as "misregularizers." The paper identifies issues like prior misalignment, regime shifts, and optimization instability as key failure modes. The authors conclude that practitioners should rigorously validate whether incorporating structural knowledge genuinely improves performance before assuming its universal benefit. This diagnostic insight is crucial for the responsible and effective application of SciML in real-world scenarios, especially in domains with complex and evolving dynamics.