What are some of the common forward vol specifications under HJM framework used in the industry. I guess most common would be 2 and 3 factor models, but any pointers to more details would be very useful. An example would be - parametric instantaneous forward rate vol as sum of two exponential decaying vols (same as G2++ model).
PS: could you please also point to any references on the model calibration as well.
Thanks for your help!