Collective steering: Tracer-informed dynamics

TL;DR

This paper develops methods for controlling and inferring flow dynamics using data from ensemble statistics and tracer particles, focusing on linear flows and Gaussian distributions.

Contribution

It introduces a framework for designing control protocols and recovering internal dynamics based on tracer-informed data in linear Gaussian flow models.

Findings

Control protocols can be optimized to meet flow constraints.

Internal dynamics can be inferred from tracer data.

The approach applies to linear flow systems with Gaussian assumptions.

Abstract

We consider control and inference problems where control protocols and internal dynamics are informed by two types of constraints. Our data consist of i) statistics on the ensemble and ii) trajectories or final disposition of selected tracer particles embedded in the flow. Our aim is i') to specify a control protocol to realize a flow that meets such constraints or ii') to recover the internal dynamics that are consistent with such a data set. We analyze these problems in the setting of linear flows and Gaussian distributions. The control cost is taken to be a suitable action integral constrained by either the trajectories of tracer particles or their terminal placements.