Faculty:
Postdocs:
Bingze LuGraduate Students:
Rui Fang
Lewis Liu
Lukas Taus
Andrew Moore
(Some previous photos of group members and activities can be found here.)
A collection of selected papers can be found here.
We propose a new framework for the sampling, compression, and analysis of distributions of point sets embedded in Euclidean spaces. Our approach involves constructing a tensor called the RaySense sketch, which captures nearest neighbors from the underlying geometry of points along a set of rays.
We introduce a new objective function for the greedy algorithm to design efficient and robust sensor networks and derive theoretical bounds on the network's optimality. We further introduce a Deep Learning model to accelerate the algorithm for near real-time computations. Correspondingly, we show that understanding the geometric properties of the training data set provides important insights into the performance and training.
We study linear regression applied to data structured on a manifold. Our objective is to reveal the impact of the data manifold's extrinsic geometry on the regression.
We propose a deep learning approach for wave propagation in media with multiscale wave speed, using a second-order linear wave equation model.
We study how the low dimensional manifold hypothesis of data will interact with deep learning models.
We are developing a data-driven parallel-in-time iterative method to solve the homogeneous second-order wave equation.
We study a two-player game with a quantitative surveillance requirement on an adversarial target moving in a discrete state space and a secondary objective to maximize short-term visibility of the environment.
We develop a new state-of-the-art deep learning strategy for prescribing vantage points for optimal sensor placement. This approach uses a robust volumetric visibility computation to efficiently model arbitrary geometries.
We consider a problem of identification of point sources in time dependent advection-diffusion systems with a non-linear reaction term.
We consider the inverse problem of finding sparse initial data from the sparsely sampled solutions of the heat equation. The initial data are assumed to be a sum of an unknown but finite number of Dirac delta functions at unknown locations.