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Given a hand mesh and an object mesh, a deep model trained on ground truth contact data infers desirable contact across the surfaces of the meshes. Then, ContactOpt efficiently optimizes the pose of the hand to achieve desirable contact using a differentiable contact model. Notably, our contact model encourages mesh interpenetration to approximate deformable soft tissue in the hand. In our evaluations, our methods result in grasps that better match ground truth contact, have lower kinematic error, and are significantly preferred by human participants. 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