We propose to address the complexity of digitizing human biomechanics and the interaction of humans and surrounding objects by combining two fundamental methodologies of computational modeling: physics-based simulation and machine learning. The cornerstone of the approach lies in building subspace models of human biomechanics, object deformation, and human-object interaction that tightly connect physics-inspired and machine-learning representations. In our research group, we have already gathered evidence of successful combinations of physics-based and machine-learning representations to build subspace simulation models. This talk will summarize those methods, share insights, and discuss possible new directions.