SPADE: Structure-Prior Adaptive Decision Estimation

SPADE (Structure-Prior Adaptive Decision Estimation) is a new framework that incorporates physical-structure priors in scientific machine learning while addressing the risks of misspecification. It employs a closed-form approach that utilizes a specification test to determine the appropriateness of priors and applies Stein-unbiased James-Stein shrinkage for adaptive enforcement, achieving significant improvements over traditional neural network methods. SPADE demonstrates high accuracy in structure selection and reduced prediction error, making it a valuable tool for practitioners aiming to integrate structure priors effectively in their models.