Optically transparent and structurally flexible metamaterial absorbers (MMAs) are widely used in many practical applications. However, the realization of such MMAs requires both thickness reduction and bandwidth enhancement, which remains a challenge task. As a multi-objective optimization problem, it is a time-consuming and resource-demanding process. Guided by prior-knowledge, two degrees of freedom are taken into account in the design, namely the structure of unit-cells and their spatial arrangement. In this way, the multi-objective optimization problem is simplified into a two-step problem. A general procedure based on machine-learning (ML) method is proposed to solve this problem. First, an artificial neural network (ANN) is used to map the configuration parameters of a type of meta-atom onto its reflection coefficients; then, a dynamic graph convolutional neural network (DGCNN) is trained to realize the synthesis of quasi-periodic distributed MMA array; finally, combined with the differential evolution (DE) algorithm, the optimized configuration of the meta-atoms and their optimum distribution are obtained. Based on the proposed procedure, an ultrathin optically transparent and flexible MMA is designed, fabricated and further verified by experiments. The designed MMA realizes 87% absorption bandwidth covering 6.22 GHz–19.42 GHz (103% relative bandwidth) with the thickness only 3. 3 mm (0. 068 λ L), which approaches the theoretical limit 1/17 λ L. And its averaged transparency is about 63% at the wavelength range 500–800 mm. The whole design process is achieved 50 times faster than the conventional full-wave simulation, which convincingly demonstrates the superiority of the proposed method.