The Encoding-Learning Tradeoff in Scientific Machine Learning: A Risk-Asymmetric Study of Brusselator Reaction-Diffusion Forecasting

Hybrid modeling blends physics and data, but the risks of this balance are rarely quantified. Data-driven models struggle to extrapolate, while physics-informed models can fail catastrophically when the encoded science is wrong.This trade-off is evaluated using 270 models on a chemical reaction–diffusion system under multiple noise and data regimes. Hard-coded equations are contrasted with flexible surrogates learned from observations. Incorrect physics inflates forecast error by up to 6,400×, whereas learning the same term from data incurs only a 1.7× penalty. These results show that misspecifying physics is far riskier than allowing the model to learn.