The decomposition of a sound field into incoming plane waves is a versatile tool in acoustics. Underlying is an ill-conditioned inverse problem whose solution is numerically challenging especially when considering full audio bandwidth. Based on measurements from rigid spherical microphone arrays, various model-based beamforming techniques have traditionally been applied to address this problem. In room acoustics, the plane wave decomposition is often derived from multichannel room impulse responses. Recently, significant advances have been achieved in the solution of ill-conditioned inverse problems by using data-driven methods. In this contribution, we discuss the application of data-driven methods to compute the plane wave decomposition from multichannel room impulses responses. The influence of practical limitations, like the number of microphones and their self-noise, is investigated to assess the robustness of the approach.