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 .
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 with a large bid-ask spread. The experiments reveal a high degree of accuracy in recovering the prices .