In search of a theory for inference of heterogeneous collectives
Collectives in the real world are heterogeneous: made up of agents that aren't identical. In animal groups, heterogeneity can arise due to the differences in age, sex or behavioural tendencies of the individuals. In material-collectives like droplets in a microchannel, differences in sizes could modify the level of confinement which alters the dynamics significantly. In synthetic active particles, differences in catalyst coating could alter the mobilities considerably. In all these systems, it is usually of interest to identify the individual differences among agents, based on the movement information of the agents and their effect on the dynamics. The question however is, how well can one make such inferences from data, and how does the collective dynamics affect the inferences?
Learning governing equations for droplet motion from data
When modeling material systems, the first-principles knowledge of mass, momentum and energy conservation, can be used to tightly constrain the search for the 'correct' model in the space of possible models.
However, it is seldom possible to derive closed-form expressions for the different forces on the droplets for the conditions of the microchannels in a device. Hence, any model derived purely from these first principles would leave us with an incomplete set of models that have little or no capacity to satisfactorily reproduce the observed phenomena. The challenge here is to infer the governing equations from data while incorporating the known physics to develop data-physics hybrid models for droplet motion.
Configurational space mixing
Mean field models are often employed to study the collective behavior exhibited by organismal systems which assumes 'fully connectedness' -- an agent can perceive all agents in the system. However, we know that organisms have finite field of vision and only interact with nearby neighbors. If that is the case, when is any mean-field analysis valid? We observe that the agents exhibit, what we call, configurational space mixing, due to the probabilistic nature of the interactions. We study how this mechanism may allow the agents to access information available in the entire system from just its neighbors---resulting in 'meanfield-ness'.
Noise induced phenomena
Collaboration: Vishwesha Guttal,
Interactions between social organisms are probabilistic in nature, which gives rise to a noisy group-level dynamics. We discovered that the finite-size noise observed (And recorded) encodes interesting information about the nature of the interactions. We analyze the noise in several different organisms and experimental conditions and compute the jump moments corresponding to the fluctuations, using which we decipher the underlying collective dynamics of the organisms.
Cohesion in mobile animal groups
Collaboration: Vishwesha Guttal
Many organisms are often found to interact with one nearby organism at a time, in what is called a simple pairwise manner. It is not obvious how these social groups stay cohesive and polarized with only a pairwise interaction. In this study, we develop a spatial-model for the mobile groups where individuals interact stochastically: spontaneously change direction and speed, copy the velocity of a neighbor and move towards a nearby neighbor. We look at how the stochastic decision making in these organisms lead to the emergence of cohesion and polarization in these moving animal groups.
Learning a traffic rule from granular materials
Is it possible to take advantage of the similarities between traffic and granular flows, to solve a complex problem in one field using the existing knowledge in another?
We explore this question in the context of the traffic problem of moving through a crowd, where an elite agent with priority for motion tries to maneuver through a dense crowd of agents that are otherwise inert: similar to the movement of an ambulance through a dense assembly of vehicles. We propose a traffic rule for the inert agents, inspired from the nature of granular flows, that will help maximize the motion of an elite agent through the crowd.