Data-driven Bayesian olfactory search in turbulent flows*

A number of animals depend on an ability to locate the source of chemical cues which are advected by a macroscopic flow, including certain flying insects and aquatic animals. This search problem is complicated by turbulence, which randomizes cue encounters and renders gradient estimation slow and inefficient. Previous work has shown the problem can be modeled as a partially observable Markov decision process (POMDP), which was then solved assuming a simple model for the statistics of encounters [1,2,3], but the question of searching in a more realistic flow—where correlations may be important, violating the Markov assumption—was left open. In this work, we perform high-fidelity direct numerical simulations of a flow with mean wind, while tracking Lagrangian tracers which are emitted from a point source. The tracers are taken as a proxy for a chemical cue, and the simulation data are used to extract the statistics of encounters (we discuss how best to do this). We solve an extended POMDP which includes short-range (exponential in time) correlations between consecutive encounters, and compare the search performance of the resulting strategies to those computed while ignoring correlations. We demonstrate, using both empirical results and physical arguments, that the presence of correlations fundamentally impedes the search, fattening the tail of the arrival time distribution. We also show how this effect depends on the movement speed of the agent and the threshold concentration for detection.

 

[1] A. Loisy and C. Eloy. Proceedings of the Royal Society A 478, 20220118 (2022). 

[2] A. Loisy and R. A. Heinonen. The European Physical Journal E 46, 17 (2023). 

[3] R. A. Heinonen, L. Biferale, A. Celani, and M. Vergassola. Physical Review E 107, 055105 (2023).