Combined Deep Learning and Optimization for Hydrogen-Solubility\nPrediction in Aqueous Systems Appropriate for Underground Hydrogen\nStorage Reservoirs

The\nwidespread use of fossil fuels drives greenhouse gas emissions,\nprompting the need for cleaner energy alternatives like hydrogen.\nUnderground hydrogen storage (UHS) is a promising solution, but measuring\nthe hydrogen (H<sub>2</sub>) solubility in brine is complex and costly.\nMachine learning can provide accurate and reliable predictions of\n H<sub>2</sub> solubility by analyzing diverse input variables, surpassing\ntraditional methods. This advancement is crucial for improving UHS,\nmaking it a viable component of the sustainable energy infrastructure.\nGiven its importance, this study utilized convolutional neural network\n(CNN) and long–short-term memory (LSTM) deep learning algorithms\nin combination with growth optimization (GO) and grey wolf optimization\n(GWO) algorithms to predict H<sub>2</sub> solubility. A total of 1078\ndata points were collected from laboratory results, including the\nvariables temperature (<i>T</i>), pressure (<i>P</i>), salinity (<i>S</i>), and salt type (<i>ST</i>). After removing 97 data points, which were identified as outliers\nand duplicates, the remaining 981 data points were divided into training\nand testing sets using the best separation ratio selected based on\nsensitivity analysis. Standalone and hybrid forms of deep learning\nalgorithms were then applied to the training data to develop predictive\nmodels with optimized control parameters for both deep learning and\noptimization algorithms. Among the developed models, CNN-GO has the\nlowest root-mean-square error (RMSE, train: 0.00006 mole fraction\nand test: 0.00021 mole fraction) compared to other hybrid and standalone\ndeep learning models. The application of scoring and regression error\ncharacteristic (REC) curve analysis showed that this model generated\nthe best prediction performance. Shapley additive explanation analysis\nindicated that <i>P</i> was the most important factor influencing\nH<sub>2</sub> solubility, followed by <i>S</i>, <i>T</i>, and <i>ST</i>, in that order. Partial dependency\nanalysis for the CNN-GO model revealed its ability to capture complex\nnonlinear relationships between input features and the target variable.