Before revision:  Currently, a general method to reliably infer inertial dynamics from realistic experimental trajectories -- sampled at discrete times and subject to measurement noise -- is lacking. Here, we derive a principled framework to infer the deterministic and stochastic fields from realistic trajectories of inertial systems with multiplicative noise. Our framework yields an operational method, termed Stochastic Inertial Force Inference , which performs well on experimental trajectories of single migrating cells and in complex high-dimensional systems  including flocks with Viscek-like alignment interactions.  .
After revision:  Currently, a general method to reliably infer inertial dynamics from realistic experimental trajectories -- sampled at discrete times and subject to measurement errors. This framework yields an operational method, termed Stochastic Inertial Force Inference , which performs well on experimental trajectories of single migrating cells and in complex high-dimensional systems including flocks with Viscek-like alignment interactions. .