## 1 Introduction  
Inconel 718 is a typical nickel-based superalloy extensively applied in aero engines and gas turbines due to its superior corrosion resistance, oxidation resistance, heat resistance and high strength, creep strength [1; 2; 3]. Exactly because of its high strength and outstanding heat-resistance, it is a hard issue to process Inconel 718 superalloy under low temperature. However, the flow behaviors of Inconel 718 superalloy become extremely complicated under elevated temperature not only due to concomitant hardening and softening behaviors, which mainly include three metallurgical phenomena: work hardening (WH) as well as the subsequent dynamic recovery (DRV) and dynamic recrystallization (DRX) [4; 5; 6; 7] but also due to the precipitation and dissolution of the three different intermetallic precipitation phases, namely \(\gamma^{\prime}\), \(\gamma^{\prime\prime}\) and \(\delta\) phases [2]. The flow behaviors of materials are generally described by constitutive relationship: the intrinsic relationship among the process variables such as stress, strain rate and temperature. Constitutive relationship is usually applied to the numerical computation to predict the deformation behaviors of materials [8]. Accurate constitutive relationship is the premise of reliable numerical computation results. Therefore, how to accurately construct constitutive relationship has been a problem attracting more and more attention. For decades, numerous researchers have contributed to three types of constitutive models including phenomenological, analytical and semi-empirical or empirical ones [9]. However, in recent years, a more adaptable and easier modeling approach, artificial neural network (ANN) has been developed and applied in the characterizing and prediction of material flow behaviors. ANN, which emulates the structures, mechanisms and functions of biological neural networks, has a data-driven black-box structure [10] and can automatically learn and grasp the laws of data, even conducted accurate prediction beyond the data already existing. Explicit professional knowledge is not particularly important for the researchers using ANN model, and the critical work is collecting the data of some typical examples. Due to such superiority, the ANN was widely used in various fields, such as the classification of olive farms [11], and the segmentation of the visual object [12], ANN contains a 'learning rule' to modify the weights of the connections on the basis of the input patterns. The commonly used learning rules mainly include Hebbian rule, delta rule, competitive learning rule, and anti-Hebbian rule [13], in which delta rule is often applied in the most widely and successfully used ANN called 'back-propagation artificial neural network'. In back-propagation ANN, 'learning' is a supervised process which follows with each cycle through the feed-forward computation of activations and the backward propagation of error signals for weight adjustments via the generalized delta rule [14]. Recently, considerable efforts have been spent on the constitutive description of several alloys by back-propagation ANN model. [PERSON] et al. [15], [PERSON] et al. [16], [PERSON] et al. [17], [PERSON] [18] et al. employed back-propagation artificial neural network models to predict the flow behaviors of high-speed steel, carbon steels, type 304L stainless steel, AZ81 magnesium alloy, etc. These reports revealed that back-propagation ANN is an effective tool to predict the complex non-linear hot flow behaviors by self-training. Despite the fact that plenty of researchers have developed ANN models to describe the constitutive relationships of various materials, further researches with greater depth have been rarely implemented. On the other side, some researchers combined ANN with finite element method (FEM) to handle actual engineering problems. For instance, [PERSON] et al. [19] and [PERSON] et al.