## 2 Materials and Methods  
### Methodology  
In this section, a U-Net based framework (in Figure 1) is described for predicting the OT-like radiation distribution in the LPBF process using the contour information of a printed part in a supervised learning manner. Firstly, a U-Net based network structure is described. Afterwards, the training procedure of proposed U-Net Model, as well as the application procedure, are explained separately. The U-Net based network structure used in this work for predicting the radiation during the LPBF process is shown in Figure 2. This network structure is modified by the generator structure of Pix2 Pix algorithm [21], which is widely used in the image process for image implanting and style transfer by using conditional generative adversarial network (cGAN). The application of the Pix2 Pix algorithm in the AM field was introduced by [PERSON] [20], which showed the applicability of cGAN network for additive manufacturing to predict laser energy radiation. The U-Net-based generator in the Pix2 Pix network has a depth of 8 for the input resolution of 256 \(\times\) 256 pixels, where depth refers to the number of different spatially sized convolutional outputs. Figure 1: Framework for the prediction of the radiation. Figure 2: U-Net structure for energy distribution prediction via Net2 Vis [22]. Due to varying part design, the size of printed parts may vary and thus input images need to depict the whole building platform. So, the input resolution of this network needs to be enlarged. According to the requirement of this network structure, the resolution of inputs needs to be \(\left\{2^{k}|k\in Z\right\}\). Thus, the input data have a size of [2048, 2048, 5]. This includes the adjusted image size with a length and width of each 2048-pixel for the current layer and 4 layers below, namely layer n, n \(-\) 1, n \(-\) 2, n \(-\) 3, and n \(-\) 4. The network's output is the predicted OT-like radiation of the current layer. To adapt the resolution, this U-Net adapts the depth to 11 pairs of downscaling and upscaling steps, while the mean absolute error (MAE) is used to train the model. The input data are scaled down 11 times to the resolution 1 \(\times\) 1 at the bottleneck section and scaled up back to the output of 2048 \(\times\) 2048 pixels. Conv2D and Conv2 DTranspose layers use stride to downscale and upscale inputs by factor 2. The sequential layer for downscaling contains a Conv2D layer with activation function ReLU, while the upscaling layer contains a Conv2 DTranspose layer with activation function LeakyReLU. The pairs of downscaling and upscaling layers with identical size are concatenated to build up the U-shape of the network. The other hyperparameters remain the same in the original generator for the Pix2 Pix algorithm. The resolution and filter amount at each layer are marked in Figure 2. To evaluate the network performance with varied depth, a comparison between networks with depths 11, 9, 7, 5, and 3 is applied and shown in Section 3. In the meantime, this proposed network structure will be compared with the Pix2 Pix algorithm in Section 3. The training dataset is constructed from the monitoring data of an OT monitoring system, which is introduced in Section 2.2. The data are pre-processed to present the contour information of the printed parts via binarization and layer packaging. Considering mesh-based CAD files, it is difficult to use these designs to obtain the part contour as it lacks information of the part location on the building platform. Thus, the mesh-based design cannot be aligned and used with the bitmap-based monitoring data. On monitoring images, the laser exposure area has a high contrast to the background area (in Figure 3a). These areas can be binarized using the Ostu binarization algorithm [23], according to a histogram (in Figure 3b). The binarized monitoring data are shown in Figure 3c using a grey value of 5000 as the threshold, which show the separation of the background and laser exposure area.