###### Abstract
Based on all these considerations, we have presented a novel approach, as outlined in [PERSON] et al. (2016); [PERSON] et al. (2016), for formulating flow laws. This approach leverages the capacity of artificial neural networks (ANNs) to act as universal approximators, a concept established by [PERSON] et al. (2016) and [PERSON] et al. (2016). With this innovative method, there is no longer a prerequisite to predefine a mathematical form for the constitutive equation before its use in a finite element simulation. Artificial neural networks have been investigated in the field of thermomechanical plasticity modeling as reported by [PERSON] et al. (2019) or [PERSON] et al. (2018). These studies explore the application of ANNs in FE investigation of metal forming processes and their characterization of meta-materials. [PERSON] et al. (2018) successfully applied an ANN to predict the yield stress of 42 CrMo4 steel in hot compression, and ANNs have demonstrated success in predicting the flow stress behavior under hot working conditions ([PERSON] and [PERSON], 2016; [PERSON] et al., 2017). They have also been applied recently in micromechanics for polycrystalline metals by [PERSON] et al. (2016). The domain of application has been extended to dynamic recrystallization of metal alloys by [PERSON] et al. (2016). Some approaches mix analytical and ANN flow laws such as, for example, the work proposed by [PERSON] et al. (2017), where the authors use a combination of an ANN with the Arrhenius equation to model the behavior of a GH4169 superalloy. ANN behavior laws can also include chemical composition of materials in their formulation to increase the performance during simulation hot deformation for high-Mn steels with different concentrations, as proposed by [PERSON] et al. (2017). In the majority of the works presented in the previous paragraph, the authors work either on the proposal of a neural network model and its identification in relation to experimental tests, or on the use of ANNs within the framework of a numerical simulation of a process. The approach proposed here is more complete in that we identify a neural network from experimental tests (in our case, cylinder compression tests performed on a Gleeble device), then identify the network parameters. We then implement this ANN in Abaqus as a user subroutine in Fortran, and subsequently validate and use this network in numerical simulations. This can be performed for either Abaqus explicit or Abaqus standard since we can generate the Fortran subroutines for both versions of the code. We therefore work on the entire calculation chain, from experimental data acquisition, through network formulation and learning, to implementation and use. In this study, we will focus only on the use of the explicit version of Abaqus, since the computation of the flow stress in an explicit integration scheme becomes very CPU intensive due to the integration method, and variations in the performance of this implementation have a significant impact on the total CPU time. On the other hand, in an implicit integration scheme, as used in the Abaqus standard, most of the time is spent in inverting the linear system of equations, therefore variations in the performance of the stress computation has no influence on the final result, hoping that the stress is calculated correctly.