It remains challenging to design lightweight metamaterials with superior sound-absorbing and load-bearing capacities. One promising approach is using multiple coherently coupled resonators to serve as sound absorbers and reinforced grid cores of sandwich panels. However, with too many design parameters each requiring careful tuning to reach the stringent critical coupling condition, achieving an optimal design based on experience alone is challenging. An autoencoder-like neural network is constructed that, once well trained, significantly promote the inverse design process thanks to the highly efficient computational speed. Particularly, a probabilistic model is inserted into the network to tackle ill-posed inverse problems requiring man-made and probably unreal spectrum as an input, and can provide multiple ultra-thin (32 mm) and broadband designs. We have fabricated and tested the optimized metallic sandwich structures, showing broadband capacity of using solely nine resonators to achieve quasi-perfect sound absorption (over 0.9) from 399 to 675 Hz. The static compression and dynamic impact testing also verify the superior mechanical performance with high yield strength (21.2 MPa) and large normalized energy absorption (0.29) at lower relative density (13.5%). We believe this work is encouraging to accelerate the design of multifunctional absorbers targeted especially for low-frequency noise control in engineering.