where g denotes the functional representation of the reorganized realizations obtained from the Questionnaire algorithm, represented by κ a and κ b , and u denotes the solution defined on the recovered space. The branch network consists of 3 fully connected hidden layers of 40 neurons each, with p = 500 output neurons. Because we maintained a two-dimensional parameter embedding, the input layer of the branch net consists of 2 neurons that consider κ a and κ b . The trunk net consists of 6 fully connected hidden layers (100 neurons each) with two inputs: ζ and τ . The Leaky ReLU activation function follows each hidden layer; all weights are initialized with a normal distribution. The model is trained by minimizing a data-driven loss function expressed as: