Hongda Qiu

Mauro Maggioni, Jason Miller, Hongda Qiu et al.

Interacting agent and particle systems are extensively used to model complex phenomena in science and engineering. We consider the problem of learning interaction kernels in these dynamical systems constrained to evolve on Riemannian manifolds from given trajectory data. The models we consider are based on interaction kernels depending on pairwise Riemannian distances between agents, with agents interacting locally along the direction of the shortest geodesic connecting them. We show that our estimators converge at a rate that is independent of the dimension of the state space, and derive bounds on the trajectory estimation error, on the manifold, between the observed and estimated dynamics. We demonstrate the performance of our estimator on two classical first order interacting systems: Opinion Dynamics and a Predator-Swarm system, with each system constrained on two prototypical manifolds, the $2$-dimensional sphere and the Poincaré disk model of hyperbolic space.

Hongda Qiu

We develop a new framework for multi-agent collision avoidance problem. The framework combined traditional pathfinding algorithm and reinforcement learning. In our approach, the agents learn whether to be navigated or to take simple actions to avoid their partners via a deep neural network trained by reinforcement learning at each time step. This framework makes it possible for agents to arrive terminal points in abstract new scenarios. In our experiments, we use Unity3D and Tensorflow to build the model and environment for our scenarios. We analyze the results and modify the parameters to approach a well-behaved strategy for our agents. Our strategy could be attached in different environments under different cases, especially when the scale is large.