Congratulations to Deepak Subramani, PhD Student, for winning the Esteemed Presenter award in the Best Theoretical or Computational Category at the Mechanical Engineering Research Exhibition (MERE) 2015 (Link). The exhibition had more than 80 presenters and 450 attendees.

Congratulations to Tapovan Lolla on his successful PhD defense and graduation! Tapovan received a PhD from Mechanical Engineering for his comprehensive research on “Path Planning and Adaptive Sampling in the Coastal Ocean”.

PhD student, Deepak Subramani, will present a poster on “Optimal Path Planning in Dynamic Environments” at the Mechanical Engineering Research Exhibition 2015 (MERE ’15) to be held on Sept 18, 2015 at Walker Memorial.

Path-planning has many applications, ranging from self-driving cars to flying drones, and to our daily commute to work. Path-planning for autonomous underwater vehicles presents an interesting problem: the ocean flow is dynamic and unsteady. Additionally, we may not have perfect knowledge of the ocean flow. Our goal is to develop a rigorous and computationally efficient methodology to perform path-planning in uncertain flow fields. We obtain new stochastic Dynamically Orthogonal (DO) Level Set equations to account for uncertainty in the flow field. We first review existing path-planning work: time-optimal path planning using the level set method, and energy-optimal path planning using stochastic DO level set equations. We build on these methods by treating the velocity field as a stochastic variable and deriving new stochastic DO level set equations. We use the new DO equations to simulate a simple canonical flow, the stochastic highway. We verify that our results are correct by comparing to corresponding Monte Carlo results. We explore novel methods of visualizing the results of the equations. Finally we apply our methodology to an idealized ocean simulation using Double-Gyre flows.

Abstract

I will discuss a nonparametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. In the limit of large data, this approach converges to a Galerkin projection of the semigroup solution of the backward Kolmogorov equation of the underlying dynamics on a basis adapted to the invariant measure. This approach allows one to evolve the probability distribution of non-trivial dynamical systems with equation-free modeling. I will also discuss nonparametric filtering methods, leveraging the diffusion forecast in Bayesian framework to initialize the forecasting distribution given noisy observations.

Bio

John Harlim is an associate professor of mathematics and meteorology at the Pennsylvania State University. He received Ph.D. in Applied Mathematics and Scientific Computation from University of Maryland in 2006. His research interests is applied mathematics related to data-driven estimation and prediction problems; this includes filtering multiscale dynamical systems, stochastic parameterization, uncertainty quantification, diffusion maps, non-parametric modeling.

Co-hosted with Prof. Themis Sapsis.