## 4 ANN Modeling  
This section chronologically describes how to develop the ANN model for relief well optimization. In general, an ANN models consist of input, hidden, and output layers, based on a perceptron algorithm, which resembles human neurons [53]. Each layer consists of nodes, which are basic units of computation in a neural network. Each node is connected to each other using feed forward methodology that considers links for node computation. Figure 8 shows an example of a feed forward back propagation neural network with one input layer, one hidden layer, and one output layer. Each node in all layers is fully  
Figure 7: Storage security depends on a combination of physical and geochemical trapping. Over time, the physical process of residual CO2 trapping and geochemical process of solubility trapping and mineral trapping increase. Source from Figure 5.9 in [1], copyright permitted.  
connected with weights. When the datasets of inputs and outputs are provided to the ANN with a supervised learning algorithm, it learns in a way that repeats the output from the inputs by tuning the weights: this process is referred to as training [38]. In order to train the neural network model, multi-layer feed forward back propagation methodology was adopted with a non-linear relationship between inputs and outputs. The ANN model for relief well optimization was developed using Keras with Tensor Flow [54], which is an open source machine learning framework provided by Google [55]. We created a learning neural network and developed deep learning in a sequential model as the ANN model is defined in Python with Keras as a sequence of layers.  
For a better performance, it is very important to design the appropriate structure of the model, i.e., input layer, optimal number of hidden layers, optimal number of nodes in each hidden layer, appropriate activation functions, and the output layer. The ANN modeling process used in this study is schematically described in Figure 9. The seven parameters that have a significant effect on the optimal relief well design were determined for the input parameter of the model. Using the determined parameters, 1000 datasets were generated from the 10- and 30-year injection scenarios (500 datasets for each). A total of 300,000 samples with elapsed times of 300 years were extracted from the 1000 generated datasets. The generated samples were categorized into two groups, i.e., the 240,000 training and 60,000 testing datasets, which reflect 80% and 20% of the total samples, respectively. The training datasets were used to train the model by adjusting network weights and biases, and the testing datasets were used to test and to evaluate the final performance of the model. Data correlation analysis and a preprocessing process were performed to convert the optimized data into a training dataset and then an ANN model was developed while changing the hyperparameters (i.e., number of nodes and layers) of the ANN model. After the performance of the ANN model was tested, the injectivity, storage stability and storage efficiency were predicted at all points of the candidate sector of the relief well location. The predicted values at all points were verified by comparing with the simulation results. If the prediction was accurate, the calculated mass of cumulative CO\({}_{2}\) injection at all points of the candidate sector was analyzed and the relief well location with the maximum value was selected. The selected location was determined as the optimum position for the relief well within the candidate sector in Pohang Basin.  
Figure 8: Schematic of a fully connected feed forward back propagation neural network.