## 1 Introduction  
The main reservoir spaces of typical fractured-cavity reservoirs consist of karst caves, high-angle fracture networks, and many dissolved pores [1, 2]. The reservoir heterogeneity is extremely important, mainly because the distribution is random, the internal structure is very uneven, the spatial configuration pattern of caverns and cracks is complex, and oil-water relationship and flow dynamics are complicated [3, 4]. In the early development stage of a fractured-cavity carbonate reservoir, oil production typically depends on natural or bottom water energy. Water injection is one of the more widely used strategies to increase oil production and slow down its decline. However, as the oil-water interface gradually rises, the increase of oil production usually diminishes after water huff-n-puff; a large portion of crude oil remains underground and cannot be produced [5]. Many pilot tests demonstrate that after N2 gas is injected into a cavity it will move up due to gravity segregation, and gradually occupy the upper space of the cavity, thus displacing crude oil down into the producing wells. N2 can also be used to replenish reservoir energy, slow down the decline of oil production, and improve oil recovery [6, 7]. It is of great importance to make an accurate prediction about N2 huff-n-puff in order to explore its potential in fractured-cavity carbonate reservoirs. The artificial neural network-improved fuzzy inference system (ANFIS), firstly developed by [PERSON] (1993) [8], was proven to be an effective tool for exploring inherent behaviors in different areas of study (e.g., water drought, sediment transport, PCP-based NMDA receptor antagonists, elastic constants of rocks, hepatitis C Virus, hydrologic modelling, and hydropower stream flow [9; 10; 11; 12; 13; 14; 15]). In recent decades, the ANFIS model has appealed great attentions to improve its predictive ability. By integrating advantages of grey wolf optimization and adaptive neuro-fuzzy inference system, an improved ANFIS is proposed by [PERSON] et al. [16], showing better prediction capability. [PERSON] and [PERSON] [17] studied the feasibility of principal component analysis to design an adaptive neuro-fuzzy inference. By selecting the grid partition (GP), fuzzy c-means (FCM), and subtractive clustering (SC) as three fuzzy inference system structures, [PERSON] [18] developed novel ANFIS models to predict the cetane number of biodiesel. [PERSON] et al. [19] applied the artificial neural network (ANN) and ANFIS models to reconstruct missing flow data. Some other self-adaptive methods were also developed in previous oil and gas studies [20; 21]. [PERSON] et al. [22; 23; 24] concluded that the ANFIS system can serve as an excellent model with relatively few errors. The ANFIS model has a strong training capability, which is akin to the ANN. Using the back-propagation algorithm, the parameters involved in the ANFIS model were adjusted until an expected error was reached. The goal of grey prediction is to construct differential equations for prediction, so it can be regarded as one form of differential simulation prediction. There may be multiple controlling factors of the forecasting indicator. [PERSON] et al. [25] presented a novel fractional grey prediction model by substituting the fractional differential equations with their first-order forms. The model is highly accurate and can overcome the class ratio test restrictions of the conventional grey model (GM) (1,1). It demonstrated that the fractional differential simulation (FDS) can greatly improve the prediction ability of differential simulation [26]. [PERSON] and [PERSON] [27] developed a novel GM model originating from a dynamic background-value coefficient. [PERSON] et al. [28] attempted to build a nonlinear grey Bernoulli multivariate prediction model. The GM (1, _n_) model was widely applied in various fields [29; 30; 31; 32; 33; 34].