The recently developed optoacoustic tomography systems have attained volumetric frame rates exceeding 100 Hz, thus opening up new venues for studying previously invisible biological dynamics. Further gains in temporal resolution can potentially be achieved via partial data acquisition, though a priori knowledge on the acquired data is essential for rendering accurate reconstructions using compressed sensing approaches. In this work, we suggest a machine learning method based on principal component analysis for high-frame-rate volumetric cardiac imaging using only a few tomographic optoacoustic projections. The method is particularly effective for discerning periodic motion, as demonstrated herein by non-invasive imaging of a beating mouse heart. A training phase enables efficiently compressing the heart motion information, which is subsequently used as prior information for image reconstruction from sparse sampling at a higher frame rate. It is shown that image quality is preserved with a 64-fold reduction in the data flow. We demonstrate that, under certain conditions, the volumetric motion could effectively be captured by relying on time-resolved data from a single optoacoustic detector. Feasibility of capturing transient (non-periodic) events not registered in the training phase is further demonstrated by visualizing perfusion of a contrast agent in vivo. The suggested approach can be used to significantly boost the temporal resolution of optoacoustic imaging and facilitate development of more affordable and data efficient systems.