## 2 Data and Methods
### Implementation of the Regression NN
The best performing model with the lowest MAE on the validation set was trained on the entire training set, and the resulting model was evaluated with the remaining test set. Although preliminary results of an unconstrained network revealed low MAE for the known training data, the validation and training loss were not converging in the same way and the network resulted in different performances on training and validation set. Therefore, several constraints on the model hyperparameters were introduced to prevent the model from overfitting and overgeneralization. Regularization is used to prevent the model from overfitting by constraining the model complexity by keeping many model parameters close to zero (L2-regularization) or zero (L1-regularization) [53]. Hereby, the terms L1 and L2 refer to the norm, i.e., the L1-norm being the sum of the absolute values and the L2-norm being the square root of the squared distances. Weak L1 and L2 regularization was applied to all of the hidden layers in the regression network and the penalty terms were added to the cost function. Secondly, an Early Stopping technique prevents the model from overfitting by interrupting the training at the respective epoch, at which the validation loss reaches a minimum or stops to improve, i.e., no progress is obtained within a predefined number of epochs (patience interval). To train the model more efficiently, a relatively high number of neurons per layer (64) was selected in combination with Early Stopping regularization [54; 55]. A sufficient amount of training data (\(\sim\)350,000 samples for thin ice and 60,000 samples for the full-range SIT) allowed to set the batch size up to 1024 to restrain the amplitude of fluctuations of the validation loss and to reduce the total training time. The two predictive neural networks were first trained in the Arctic. Subsequently, the network to estimate thin SIT was applied to the Arctic sea, and the network to estimate full-range SIT was applied to both Arctic and Antarctic seas. Prior to the training, the input features were processed to be treatable by the NN. Because the NN was trained using Gradient Descent method, it was required to scale and normalize the input features. This included normalization after filtering outliers to keep the variables within the reasonable ranges of values. Figure 4 shows the Kernel Density Estimation (KDE) charts of input features after defining their ranges of values, which were eventually used to train the thin and full-range SIT model, respectively. Figure 3: Principle architecture of the implemented neural networks (NN) consisting of a multiple-input normalization layer adapted to the number of input features, i.e., T\({}_{B}\), SIC, T\({}_{S}\), and Fb (in case of the full-range model), a number of non-linear hidden layers with a number of neurons per layer, and a linear single-output layer yielding continuous values of SIT. The final network architecture contains 2 or 3 hidden layers with 64 neurons per layer regarding the thin or full-range model, respectively. An ocean-land mask was applied to all maps to exclude land areas. Additionally, an ocean-ice mask was applied to preserve data points over areas with a SIC \(>\) 15 %, being the minimum value for which the OSI-401-b SIC product is defined. T\({}_{B}\) increases monotonically as a function of SIT and the interval of suitable values is defined between 100 K and 210 K, which is in agreement with the expected dynamic range of T\({}_{B}\) when considering a SIT up to 0.6 m in Figure 2a (also under cold conditions). Only a small amount of larger values was filtered (<0.1 % after applying the ocean-land and ocean-ice masks), which could be attributed to areas of possible land-sea contamination. For thin SIT prediction, a cutoff thickness (SIT\({}_{max}\) = 0.6 m) was defined as the limit beyond which the sensitivity of T\({}_{B}\) to SIT is assumed to be negligible. Regarding sea ice Pb, a threshold of 0.4 m is used as the upper limit for training the full-range model.