Living systems, from cell colonies to bird flocks and insect swarms, display second order emergent dynamics. Disentangling the contributions of inertial terms, dissipation and noise to the dynamical behavior is crucial to describe their behaviour, cohesion and motion. Reliable methods are needed to extract that information from experimental data  . We develop a systematic inference approach to retrieve second order effective models from discrete finite length trajectories. We first show, using the analytically tractable stochastic harmonic oscillator, that a naive inference approach based on a measurement of velocities through finite differences does not retrieve the effective parameters of the underlying dynamics , regardless of the time resolution and the length of the sampled trajectories. We derive a higher order discretization framework that provides  excellent results even with moderately long trajectories. We apply our method to second order models of collective motion and show that our results also hold in the presence of interactions.
Many living and complex systems exhibit second order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in the quantitative reconstruction of the model from experimental data , even in the simple case of equilibrium Langevin dynamics of Hamiltonian systems . We develop a novel Bayesian inference approach to learn the parameters of such stochastic effective models from discrete finite length trajectories. We first discuss the failure of naive inference approaches based on the estimation of derivatives through finite differences , regardless of the time resolution and the length of the sampled trajectories. We then derive, adopting higher order discretization schemes, maximum likelihood estimators for the model parameters that provide excellent results even with moderately long trajectories. We apply our method to second order models of collective motion and show that our results also hold in the presence of interactions.
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Living systems, from cell colonies to bird flocks and insect swarms, display
Many living and complex systems exhibit
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Disentangling the contributions of inertial terms, dissipation and noise to the dynamical behavior is crucial to describe their behaviour, cohesion and motion. Reliable methods are needed to extract that information
Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in the quantitative reconstruction of the model
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, even in the simple case of equilibrium Langevin dynamics of Hamiltonian systems
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systematic
novel Bayesian
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retrieve second order
learn the parameters of such stochastic
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show, using the analytically tractable stochastic harmonic oscillator, that a naive inference approach based on a measurement of velocities
discuss the failure of naive inference approaches based on the estimation of derivatives
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does not retrieve the effective parameters of the underlying dynamics
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derive a
then derive, adopting
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framework that provides
schemes, maximum likelihood estimators for the model parameters
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that provide