## 4 Discussion  
A FE-based CNN regression network method was used for predicting the effective mechanical properties of BG-COL composite hydrogel. From the microstructure images, we can efficiently and accurately predict the mechanical properties of BG-COL, by considering various BG numbers, sizes, and _Vf_. In total, 2000 2D RVE microstructural images were generated with various circular shapes of BG and _Vf_. This RVE of BG-COL was then imported into the FE simulation software to calculate its effective mechanical properties. Subsequently, a python script in Abaqus was developed to extract the effective mechanical properties, including [PERSON]'s modulus and Poisson's ratio. Finally, a CNN regression network was trained and tuned to predict the mechanical properties of the composite with 95% and 83% accuracy for [PERSON]'s modulus and Poisson's ratio, respectively. The FE input (imaging) and outputs ([PERSON]'s modulus and Poisson's ratio) are used to train the ML models and then predict the FE outputs in 400 test cases. A sufficiently large number of BG-COL images were generated to represent various composite configurations based on our experimental observations. Specifically, we effectively developed a framework to generate geometries, solve the FE computations, and then create a substantial database of input-output pairs. Similarly, [PERSON] et al. [22] used three common two-phase materials (UD-CRTS [36], UHP mortar [37; 38], and MPR paste [39]), including fibers of circular shape with the same diameter, but they used different fiber _Vf_, median sizes, and particles in a robust cementitious matrix and a metallic particulate-reinforced (MPR) cement mortar. They used artificial neural network (ANN) and forest ensemble MLs methods to predict [PERSON]'s modulus and Poisson's ratio of materials by using geometrical features of particles and _Vf_ inputs. CNN regression was chosen in this work considering that our dataset is 200 \(\times\) 200 gray images with corresponding mechanical properties. The FE-based CNN method to predict the mechanical properties of the composite hydrogel is still lacking in the literature [22; 36; 40]. The prediction of BG-COL properties herein was motivated by the work of [PERSON] et al. [20]. They used a CNN regression method to predict the mechanical properties of an artificial composite consisting of two different components (matrix and inclusions). The uniqueness of our dataset is that it is based on the observations of the microstructural images of the BG-COL composites (Figure 1). In addi  
Figure 5: The prediction error of [PERSON]’s modulus and [PERSON]’s ratio for two representative cases with _Vf_ at (a) 27.73% and (b) 47.85%. tion, we adopted the \(\forall f\) ranging from 17% to 59% based on the published experiments [3]. The range of our \(\forall f\) is wider than the one by [PERSON] et al. [28]. Our results have shown that a larger \(\forall f\) significantly increased [PERSON]'s modulus and reduced the Poisson's ratio. Subjected to the same deformation, a larger \(\forall f\) is associated with a larger force load and a higher peak stress in the BG-COL (Figure 5). This trend was also observed by [PERSON] et al. [9]. The most critical parameters to achieve the prediction accuracy of 95% and 83% for Young's modulus and Poisson's ratio, respectively, were the number of feature maps in the convolutional layers and the number of units in the fully connected layer. A total of nine ML architectures with different layers (number of convolutional layers and feature maps in these layers, and fully connected layers and units in each layer), and different activation functions, including ReLU, sigmoid, and linear, were picked and trained. In the first architecture, our network was created by three convolutional layers with 256, 128, and 32 feature maps in each layer, respectively. The last convolutional layer was then connected to the first fully connected layer as the input in the vector form. Additionally, three fully connected layers with 500, 100, and 10 units were considered.