Hybrid-time PINNs: Discontinuity-Aware Physics-Informed Neural Networks for Learning Hybrid Dynamical Systems

Shivanshu Tripathi, Maziar Raissi

Hybrid dynamical systems flow continuously but jump at discrete events. Physics-informed neural networks (PINNs) fit data while enforcing known dynamics, but a single network is smooth in time and cannot model these jumps. We show that the more closely a PINN follows a jump, the larger its physics loss must be. We propose hybrid-time PINNs (HT-PINNs), which assign one network to each flow interval of the hybrid time domain and train the networks jointly with the jump times and the unknown parameters. The number of jumps and the sequence of modes are found by enumeration. HT-PINNs recover the number of jumps and the restitution coefficient of a bouncing ball. In a MuJoCo simulation of robotic disassembly, where a robot pulls a press-fitted pin out of a housing through a spring, HT-PINNs find the number of jumps and the sequence of modes, and estimate the static and kinetic friction coefficients with small errors of 0.1% and 1.7%.