The high mapping efficiency between various structures and electromagnetic (EM) properties on frequency selective surfaces (FSSs) is the state-of-the-art in EM community. The most straightforward approaches for beams analysis depend on the measurements and conventional EM calculation methods, which are inefficient and time-consuming. Equivalent circuit model (ECM) with excellent intuitiveness and simplicity is put forward extensively. Despite of several applications, the bottlenecks of ECM still exist, i.e., the application scope is restricted in narrow band and specific structure, which is triggered by the ignorance of EM nonlinear coupling. In this work, a lightweight physic model based on neural network (ECM-NN) is proposed for the first time, which exhibits a great physical interpretability and spatial generalization ability. The nonlinear mapping relationship between structures and beams behaviors is interpreted by corresponding simulations. Specially, two deep parametric factors obtained by multi-layer perceptron (MLP) network are introduced to serve as the core of lightweight strategy and compensate for the absence of nonlinearity. Experimental results of single square loop (SL) and double SL indicate that compared with related works, better agreements of the frequency responses and resonant frequencies are achieved by ECM-NN in broadband (0-30 GHz) as well as oblique incident angles (0-60°). The average accuracy of mapping is higher than 98.6%. The discoveries of this work provide a novel strategy for further studies of complex FSSs.