We generalize the pre-orthogonal adaptive Fourier approximation developed by T. Qian et al. [9,7,10] to functions in the Bergman space on the unit disc and the unit ball to the Bergman space A(D) on the irreducible bounded symmetric domain D. We show that A(D) satisfies the boundary vanishing property, so that the maximum selection principle allows us to give an adaptive expansion of any function f∈A(D) in terms of linear combinations of generalized kernel functions in an optimal way.