||General Reduced-Order Models: Dimensionality reduction is a powerful technique that makes very high-dimensional simulations tractable. As an instance of data-driven simulation, creating a reduced-order model requires examples that have to be generated using traditional simulation techniques. Furthermore, the reduction process is computationally expensive, imposing severe limits on the size of reduced models. Each reduced model can only be used with the exact boundary conditions that were specified while the model was created.
In this project, we aim to relax these restrictions. By computing reduced models in a modular fashion, more complex simulations can be set up without repeating the expensive model reduction step. Combining several of these tiles requires a coupling mechanism that has to be fast and flexible, while guaranteeing important physical invariants and providing useful error bounds.
Measuring Fluid Flow: Fluid flows are complex and hard to measure. One of the most commonly used techniques injects probes into the fluid whose position is then tracked over time. The recorded trajectories can then be used to reconstruct the (time-dependent) flow field.
In this project, traditional flow reconstruction methods are augmented using knowledge about the physical processes. Since we can compute the time-dependent behavior of a fluid given an initial condition, measurements at one timestep can be validated by subsequent measurements. This mechanism makes it possible to use far fewer sample points to reconstruct time-varying flow fields.
To validate this method, we design and build an experimental setup that can be used to measure small-scale fluid flows using optical tracking of small objects, similar to traditional particle image velocimetry approaches.
Handling Mobility in Sensor Networks: Most algorithms for routing and data managements are designed for static or slowly changing networks. While they adapt well to gradual changes in network topology and mechanisms exists that help recover from temporary failures, mobility of some nodes poses significant challenges. This is especially true for sensor networks, whose nodes are typically small, low-power devices,placing severe constraints on admissible computation and power consumption.
This project aims to gracefully handle node mobility in networks, in particular sensor networks. Exploiting typical user behaviour can help implement proactive handoff procedures to prevent link failures. Intermediate goals include a robust and efficient streaming mechanism, as well as reliable predictive routing.