Browsing by Subject "Stochastic"

When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales and high-dimensionality can make simulations expensive. The computational cost is dictated by microscale properties and interactions of many variables, while interesting behavior often occurs on the macroscale with few important degrees of freedom. For many problems bridging the gap between the microscale and macroscale by direct simulation is computationally infeasible, and one would like to learn a fast macroscale simulator. In this paper we present an unsupervised learning algorithm that uses short parallelizable microscale simulations to learn provably accurate macroscale SDE models. The learning algorithm takes as input: the microscale simulator, a local distance function, and a homogenization scale. The learned macroscale model can then be used for fast computation and storage of long simulations. I will discuss various examples, both low- and high-dimensional, as well as results about the accuracy of the fast simulators we construct, and its dependency on the number of short paths requested from the microscale simulator.

In applications of ocean wave energy conversion, it is well known that feedback control can be used to achieve favorable performance. Current techniques include methods such as tuning a device to harvest energy at a narrow band of frequencies, which leads to suboptimal performance, or methods that are anticausal and require the future wave excitation to be known. This thesis demonstrates how to determine the maximum-attainable power generation and corresponding controller for a buoy type wave energy converter with multiple generators in a stochastic sea environment using a causal dynamic controller. This is accomplished by solving a nonstandard H2 optimal control problem. The performance of the causal controller is compared to the noncausal controller for various cases. This work provides a significant improvement over current control techniques because it involves a causal controller that can absorb a large amount of power over a broader bandwidth than other control techniques, including absorbing power across multiple modes of resonance. The importance of an adaptive control algorithm is also demonstrated.

Global climate is predicted to have significant impacts on the chemical, biological, and physical characteristics of wetlands and the watersheds in which they are contained. In particular, climate prediction models suggest a significant increase in extreme precipitation events - both more frequent and more intense flood and drought occurrences. A wetland model that incorporates surfacewater-groundwater interactions (WETSAND2.0) was used to investigate the potential impacts of these stochastically generated extreme events on wetland flow regimes in an urban watershed. The results predict increases in streamflow and flooding as well as drought conditions on a near yearly basis. However, the model also shows that the impact on the Sandy Creek-Duke University watershed will not be as extreme as many suggest. Although flooding will occur, it will be relatively minor and comparable to historic flows. And although droughts are also predicted, the balance of wet and dry in this wetland watershed can actually be a positive for the environment. Therefore watersheds, no matter the spatial scale, must be analyzed individually. Although some comparisons can be made between similar regions, the effects of extreme precipitation events vary greatly depending on watershed characteristics.