Bayesian inference of active Brownian motion

For the study of motile cells (L2) and other (synthetic or biological) self-propelled particles it is often key to extract quantitative features from trajectories of these particles, both to quantify experimental trajectories and to parametrise theoretical models [1]. Bayesian inference provides a method that not only provides optimal parameter values, but their full probability distribution (conditioned on the given trajectory data). This allows a straightforward quantitative assessment of the knowledge about these parameters. Here, we address the case where the data provide only positions of the particles and not their orientation states. Two complications in applying these Bayesian methods to such problems are the coupling of the orientation and position degree of freedom over finite time intervals and the memory induced by previous directional states in the motion. In this project, we will develop methods to overcome these challenges and combine simulations (T9) and Bayesian inference (T11) to infer unobserved properties from the motion of active particles.

We will address the two challenges in two ways: (i) Discretised-time approximation: If observations are made with a resolution that corresponds to the discrete microscopic timescale of the dynamics, the position and orientation degrees of freedom decouple in the calculation of the likelihood and allow for exact results [2]. As an approximation, we will extend this to arbitrary time steps of the observations and test the inference for different time resolutions to estimate the required time resolution. (ii) Brownian bridges approach: We will develop an active variant of Brownian bridges, i.e., Brownian motion with correlated noise that generates stochastic trajectories with given start and end positions and use this for improved sampling of trajectories consistent with the data for efficient Monte Carlo calculation of the likelihood. We will apply these methods to learn interactions with obstacles from trajectories of self-propelled particles in obstacle arrays and to infer the magnetic moment of magnetic swimmers (e.g., magnetotactic bacteria) from trajectories. In both cases, the learned features of the motion will also provide a basis for the control of the motion (T6), e.g. for externally steering a magnetotactic cell through an obstacle course or learning the (optimal) internal control employed by the cell itself.

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[1] Codutti, A, et al. (2024) eLife 13:RP98001 [2] Lambert, S, et al (2024) arXiv:2409.03533