Before revision:  Finally we introduce a new loss function that takes into account bid and ask prices and offers a solution to calibration in illiquid markets . A key issue discovered is that the trained neural network might be non-injective, which could potentially lead to poor accuracy in calibrating the forward curve parameters, even when showing a high degree of accuracy in recovering the prices . This reveals that the original meaning of the parameters gets somehow lost in the approximation  .
After revision:  Finally we introduce a new loss function that takes into account bid and ask prices and offers a solution to calibration in illiquid markets . A key issue discovered is that the trained neural network might be non-injective, which could potentially lead to poor accuracy in calibrating the forward curve parameters, even when showing a high degree of accuracy in recovering the prices after calibration, even if the original meaning of the parameters gets somehow lost in the approximation .