Non-rigid registration is a key component in soft-tissue navigation. We focus\non laparoscopic liver surgery, where we register the organ model obtained from\na preoperative CT scan to the intraoperative partial organ surface,\nreconstructed from the laparoscopic video. This is a challenging task due to\nsparse and noisy intraoperative data, real-time requirements and many unknowns\n- such as tissue properties and boundary conditions. Furthermore, establishing\ncorrespondences between pre- and intraoperative data can be extremely difficult\nsince the liver usually lacks distinct surface features and the used imaging\nmodalities suffer from very different types of noise. In this work, we train a\nconvolutional neural network to perform both the search for surface\ncorrespondences as well as the non-rigid registration in one step. The network\nis trained on physically accurate biomechanical simulations of randomly\ngenerated, deforming organ-like structures. This enables the network to\nimmediately generalize to a new patient organ without the need to re-train. We\nadd various amounts of noise to the intraoperative surfaces during training,\nmaking the network robust to noisy intraoperative data. During inference, the\nnetwork outputs the displacement field which matches the preoperative volume to\nthe partial intraoperative surface. In multiple experiments, we show that the\nnetwork translates well to real data while maintaining a high inference speed.\nOur code is made available online.\n