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.

Abstract

The development of numerical weather prediction was one of the great scientific and computational achievements of the last century. Computer models that approximate solutions of the partial differential equations that govern fluid flow and a comprehensive global observing network are two components of this prediction enterprise. An essential third component is data assimilation, the computational method that combines observations with predictions from previous times to produce initial conditions for subsequent predictions. The best present-day numerical weather prediction systems have evolved over decades and feature model-specific assimilation systems built with nearly a person century of effort.

This talk describes the design of a community software facility for ensemble Kalman filter data assimilation, the Data Assimilation Research Testbed (DART). DART can produce high-quality weather predictions but can also be used to build a comprehensive forecast system for any prediction model and observations. DART forecast systems must be inexpensive to implement and must run efficiently on computing platforms ranging from laptops to the largest available supercomputing. A description of the basic ensemble Kalman filter algorithm is followed by a discussion of algorithmic enhancements, in particular localization of observation impacts and inflation of prior ensembles that are essential for efficient implementations for large prediction models. Several example applications in geosciences will be used to examine additional capabilities of modern ensemble prediction systems.

Bio of the speaker:

Jeffrey Anderson’s research career has spanned two decades and has been focused by the common theme to improve predictions of the earth’s atmosphere. He has made research contributions in theoretical geophysical fluid dynamics, seasonal prediction, predictability, ensemble prediction and ensemble data assimilation. His accomplishments in software engineering, applied mathematics and statistics have been directly in support of his goal to improve prediction.