Abstract: System and method for synthesizing a controller for a dynamical system includes a feeder neural network trained to estimate an ordinary differential equation (ODE) from time series training data (X) of a trajectory having embedded angular data and configured to learn dynamics of a physical system by encoding a generalization of a Hamiltonian representation of the dynamics using a constant external control term (u). A neural ODE solver receives the estimate of the ODE from the feeder neural network and synthesizes a controller to control the system to track a reference configuration.

Abstract: System and method for performing natural language processing are disclosed. An encoder includes a multi-head attention block for nonlinear transformation of inputs and a feed-forward network for learning parameters that result in best function approximation. Output of the multi-head attention block and the feed-forward network are coupled in parallel to produce a summed output. An ODE solver performs continuous depth integration of the summed output for reduced number of parameters.

Abstract: System and method for modeling motion and collision of rigid bodies in a dynamic system includes a collision detector that detects active contacts of the rigid bodies. A differentiable contact impulse solver applies constraints on contact forces related to a compression phase, applies coefficient of restitution on contact forces related to a restitution phase, solves for contact forces and velocity impulses associated with the active contacts in the compression phase and the restitution phase, and estimates trajectories of the rigid bodies while optimizing for maximum rate of energy dissipation.

Abstract: System and method for synthesizing a controller for a dynamical system includes a feeder neural network trained to estimate an ordinary differential equation (ODE) from time series training data (X) of a trajectory having embedded angular data and configured to learn dynamics of a physical system by encoding a generalization of a Hamiltonian representation of the dynamics using a constant external control term (u). A neural ODE solver receives the estimate of the ODE from the feeder neural network and synthesizes a controller to control the system to track a reference configuration.