Danny M. Kaufman

Danny M. Kaufman, Dinesh K. Pai

We consider the geometric numerical integration of Hamiltonian systems subject to both equality and "hard" inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. We additionally, however, also consider invariant preservation over persistent, simultaneous and/or frequent boundary interactions. Appropriately formulating geometric methods to include such conditions has long-remained challenging due to the inherent nonsmoothness they impose. To resolve these issues we thus focus both on symplectic-momentum preserving behavior and the preservation of additional structures, unique to the inequality constrained setting. Leveraging discrete variational techniques, we construct a family of geometric numerical integration methods that not only obtain the usual desirable properties of momentum preservation, approximate energy conservation and equality constraint preservation, but also enforce multiple simultaneous inequality constraints, obtain smooth unilateral motion along constraint boundaries and allow for both nonsmooth and smooth boundary approach and exit trajectories. Numerical experiments are presented to illustrate the behavior of these methods on difficult test examples where both smooth and nonsmooth active constraint modes persist with high frequency.

Carlo Innamorati, Bryan Russell, Danny M. Kaufman et al.

We introduce a method to generate videos of dynamic virtual objects plausibly interacting via collisions with a still image's environment. Given a starting trajectory, physically simulated with the estimated geometry of a single, static input image, we learn to 'correct' this trajectory to a visually plausible one via a neural network. The neural network can then be seen as learning to 'correct' traditional simulation output, generated with incomplete and imprecise world information, to obtain context-specific, visually plausible re-simulated output, a process we call neural re-simulation. We train our system on a set of 50k synthetic scenes where a virtual moving object (ball) has been physically simulated. We demonstrate our approach on both our synthetic dataset and a collection of real-life images depicting everyday scenes, obtaining consistent improvement over baseline alternatives throughout.

Senthil Purushwalkam, Abhinav Gupta, Danny M. Kaufman et al.

We introduce an approach to model surface properties governing bounces in everyday scenes. Our model learns end-to-end, starting from sensor inputs, to predict post-bounce trajectories and infer two underlying physical properties that govern bouncing - restitution and effective collision normals. Our model, Bounce and Learn, comprises two modules -- a Physics Inference Module (PIM) and a Visual Inference Module (VIM). VIM learns to infer physical parameters for locations in a scene given a single still image, while PIM learns to model physical interactions for the prediction task given physical parameters and observed pre-collision 3D trajectories. To achieve our results, we introduce the Bounce Dataset comprising 5K RGB-D videos of bouncing trajectories of a foam ball to probe surfaces of varying shapes and materials in everyday scenes including homes and offices. Our proposed model learns from our collected dataset of real-world bounces and is bootstrapped with additional information from simple physics simulations. We show on our newly collected dataset that our model out-performs baselines, including trajectory fitting with Newtonian physics, in predicting post-bounce trajectories and inferring physical properties of a scene.