We present a 3D model of human lips and develop a framework for training it from real data. The model starts off with generic physics specified with the finite element method and ``learns'' the correct physics through observations. The model's physics allow physically-based regularization between sparse observation points and the resulting set of deformations are used to derive the correct physical modes of the model. Preliminary results showing the model's ability to reconstruct lip shapes from sparse data are shown. The resulting model can be used for both analysis and synthesis.