## 1 Introduction
At the same time, with the development of computer science and technology, new methods of machine learning and neural networks are widely used in the field of computer vision (image recognition, object detection, etc. ), natural language processing (speech recognition, sentiment analysis), and industries such as finance and transportation. A notable feature of these new methods is that they can learn the features of the given datasets well and make precise predictions, to a certain extent, and a more detailed introduction to neural networks, and the development of the whole methodology may be found in [4]. Scientists have keenly discovered the good prospects of these new technologies in the field of materials and have discussed them extensively. [PERSON] used machine learning to homogenize the inelastic behavior of materials and trained intelligent constitutive laws using recurrent neural networks [5]. The strains generated by the materials created by the Terzaghi principle in a porous medium in the context of tunnel works have been resolved with the use of FEM implemented with Matlab [6]. [PERSON] used an ANN to identify the properties of uncertain materials in unidirectional layers and used plug-ins in ABAQUS to generate virtual data to verify that the ANN could clearly and accurately parameterize the relationship between fiber mechanical properties on a microscopic scale and fiber/matrix interface parameters and mechanical properties on a macroscopic scale [7]. [PERSON] discusses the latest technologies, applications and opportunities of combining machine learning and multiscale modeling and raises some open questions and potential challenges and limitations in their article [8]. [PERSON] compared several data-driven, machine learning tools to predict the dynamic modulus of asphalt mixtures with high accuracy [9]. [PERSON] employed data-driven homogenization approaches to predict the mechanical response of oligocrystals composed of multiple crystals [10]. The application of neural networks and machine learning techniques in the field of material science can effectively handle the relationship between material properties and relevant parameters [11]. [PERSON] predicted the hydraulic conductivity of sandy soils using machine learning methods and gave a detailed introduction to AI optimization methods utilized in geotechnical engineering [12; 13; 14]. The existing research in the field of homogenization has two notable drawbacks. Firstly, both analytical and numerical homogenization methods, including the previously proposed asymptotic homogenization method, tend to primarily focus on solving elastic homogenization problems. In other words, there is a lack of sufficient research addressing inelastic homogenization problems. This lack of attention hampers the ability of engineers and researchers to effectively predict and analyze the behavior of complex geotechnical systems involving inelastic materials. Traditional analytical and numerical approaches require substantial computational resources and time-consuming iterations to achieve accurate results. This can be challenging when dealing with complex geotechnical problems that require efficient and practical solutions. However, one potential solution to address this issue is the utilization of neural network models. Neural networks offer a promising alternative due to their ability to provide rapid predictions through a single forward pass, resulting in negligible time costs. Once trained, a neural network can quickly generate homogenized results for a given set of inputs. This computational efficiency makes neural networks an attractive option for homogenization, potentially reducing the time and resources required for analysis. In this work, a Bayesian Optimized BP-ANN for the homogenization of Mohr-Coulomb mechanical parameters, based on its excellent performance in predicting output values, is proposed [15].