Friday 06 May 2016: Adaptive Sparse Grids and Applications: Coping with the Curse of Dimensionality
Dirk Pflueger - University of Stuttgart, Germany
High dimensionalities are a major roadblock for the numerical solution of problems in computational sciences. Straightforward discretizations are severely limited by the curse of dimensionality, the exponential dependency of the overall computational effort on the number of dimensions. It is therefore typically not feasible to treat more than four dimensions. But high-dimensional problems arise in many applications. Be it as a subtask in numerical simulations, for example to estimate or express parameter-dependent functionalities, or as a task in itself, such as approximations of scattered and often noisy data in data-driven applications or the direct solution of high-dimensional partial differential equations.
In this talk, sparse grids and recent applications are discussed. A short introduction to Sparse Grids shows how they provide a versatile way to overcome the curse of dimensionality to a large extent. Their application ranges from the nonlinear analysis of crash-test simulations and the quantification of uncertainties in subsurface simulations to regression problems in data mining. Finally, efficient algorithms, data structures and implementations are required to master data-driven applications with vast data sets.