tokens: them by 1000. For the labels, we normalize the total magnetic field strength by dividing it by 5000 and the inclination and azimuth angles by dividing them by π . The two numbers, 1000 and 5000, are used here because most of the Stokes measurements have values between −1000 and +1000, and their total magnetic field strengths range from −5000 to +5000 G. After obtaining the estimated vector magnetic field, which is inferred by our trained model, of a test data sample (pixel), we can derive the three Cartesian components of the magnetic field, namely, B x , B y , and B z , of the pixel as follows:where B total denotes the total magnetic field strength, φ is the inclination angle, and θ is the azimuth angle. 3. Methodology We use a CNN to infer vector magnetic fields from Stokes profiles of GST/NIRIS. Our CNN model helps in denoising inversions by exploiting the spatial information of the Stokes profiles. Figure 2 presents the architecture of our network. It contains an input layer, three convolutional blocks, two fully connected layers, and an output layer. The input layer receives a sequence of Stokes Q , U , and V components, each having 60 wavelength sampling points, with three channels. Each channel corresponds to a Stokes component. Figure 2. Architecture of our CNN. This network is comprised of an input layer, three convolutional blocks, two fully connected layers, and an output layer. The input of the CNN is a three-channel sequence of Stokes Q , U , and V components each having 60 wavelength sampling points. The intermediate outputs of the three convolutional blocks have 64, 128, and 256 channels, respectively. There are 1024 neurons activated by ReLUs in both of the two fully connected layers. The output layer has three neurons activated by the Tanh function, where each neuron produces a value in the range (−1, 1) representing the total magnetic field strength, inclination angle, and azimuth angle, respectively. After the input layer, there are three convolutional blocks with the following structures. The first convolutional block consists of two convolutional layers that take, as input, the output from the previous layer and filter it with 64 kernels of sizes 3 × 1 × 3 and 3 × 1 × 64, respectively, and a max-pooling layer with a pooling factor of 2. The second convolutional block consists of two convolutional layers with filters of 128 kernels of sizes 3 × 1 × 64 and 3 × 1 × 128, respectively, and a max-pooling layer with a pooling factor of 2. The third convolutional block consists of two convolutional layers with filters of 256 kernels of sizes 3 × 1 × 128 and 3 × 1 × 256, respectively. The third convolutional block does not contain a max-pooling layer. The activation functions used in both the convolutional and fully connected layers are rectified linear units (ReLUs; Goodfellow et al. 2016 ), defined asThe output of the three convolutional blocks is flattened into a sequence, which is then sent to the two fully connected layers
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