Dictionary‐based weak‐form training for noise‐robust series hybrid models with multiplicative unknowns

ABSTRACT Hybrid modeling combines first‐principles equations with a data‐driven subcomponent. Training for the data‐driven part is sensitive to measurement noise when training targets are constructed using pointwise time derivatives. Beyond differentiation errors, hybrid models involve solving an inverse problem to estimate the data‐driven term, which may further amplify noise effects. This effect is pronounced when a model parameter is described by a data‐driven terms and becomes algebraically coupled with the first‐principles model, a configuration referred to as a series‐type hybrid model. To address this structural sensitivity to noise, we build upon recently developed system identification frameworks based on the weak (integral) reformulation of differential equations, thereby avoiding the explicit computation of time derivatives. Our framework is developed for series‐type hybrid models with a multiplicative parameter and implemented using dictionary‐based regression. A case study on a continuous stirred tank reactor demonstrates improved noise robustness compared with conventional pointwise training approaches.