Many complex systems, ranging from migrating cells to interacting swarms, exhibit effective inertial dynamics described by second order stochastic differential equations . Inferring such an equation of motion from experiments can provide profound insight into the physical laws governing the system. 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.  .
Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation . Inferring such an equation of motion from experimental data can provide profound insight into the physical laws governing the system. Here, we derive a principled framework to infer the dynamics of underdamped stochastic systems from realistic experimental trajectories , sampled at discrete times and subject to measurement errors. This framework yields an operational method, Underdamped Langevin Inference (ULI) , which performs well on experimental trajectories of single migrating cells and in complex high-dimensional systems , including flocks with Viscek-like alignment interactions. Our method is robust to experimental measurement errors, and includes a self-consistent estimate of the inference error .
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interacting swarms, exhibit effective inertial
animal groups, exhibit stochastic
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second order stochastic differential equations
the underdamped Langevin equation
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experiments
experimental data
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Currently, a general method to reliably infer inertial dynamics
Here, we derive a principled framework to infer the dynamics of underdamped stochastic systems
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--
,
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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
errors. This framework
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termed Stochastic Inertial Force Inference
Underdamped Langevin Inference (ULI)
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,
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Our method is robust to experimental measurement errors, and includes a self-consistent estimate of the inference error