) is a differentiable message-passing function where W (l) is a matrix of learnable weights, φe is single hidden layer neural network with the ReLU activation function. Finally, a global pooling operation is performed to get a vectorial representation of the DES, which again is concatenated with the molar ratios, temperature, and pressure information to establish the DES representation at the corresponding state conditions. This representation is then passed to an MLP of three hidden layers with the sigmoid activation function to regress the CO 2 solubility value.