SCCS Colloquium - May 20, 2020
|Date:||May 20, 2020|
|Room:||Online (password: SCCS)|
|Time:||15:00 - 16:00|
Tianyi Ge: Python software suite of geometry-oblivious Fast Multipole Methods: its application in statistical plotting and high dimensional data classification
Guided Research project submission talk. Tianyi is advised by Severin Reiz.
This guided research focuses on optimizing pre-existing python codes of GOFMM and incorporating new functionality into the embedded balanced tree data structure by GOFMM. The original codes rely heavily on nested loops, conditional checks and index tracking, making it difficult to apply GOFMM to new applications. The revised version implements a set-oriented interface on setting up the GOFMM data structure. Particularly, we formalize all sampling methods in set. As a result, the codes are much shorter, understandable and efficient as it involves basic mathematical operations on a fundamental data structure. Furthermore, we utilize scipy.linalg.interpolative package to simplify analysis in skeleton, such as interpolative decomposition and QR factorization. The resultant codes run much faster and are user-friendly in implementing related applications.
With our new GOFMM interface, we devised two examples that demonstrate high usability of GOFMM in statistical plotting and image recognition. Our first example takes in 2D position data and classifies points based on their density. By exploiting relative fast search and data structure in GOFMM, this user case accelerates underlying matrix-vector multiplication. In comparison to its raw data plot, our plot uses Gaussian kernel density estimation (Gaussian KDE) and displays a high level of accuracy. Our second example pipes over one thousand 8x8 images into GOFMM, utilizing its tree-like data structure for fast search and low storage. Then, we implement Gaussian KDE to learn over training dataset so that the updating model can accurately classify testing data. The result shows high accuracy of our model classification. With 30 training images, the accuracy of classifying 44 images is 43/44.
Keywords: GOFMM, Gaussian KDE, Image Classification
Dominik Mehringer: Solving the Shallow Water Equations on Heterogeneous Architectures with Kokkos
Fluid simulation is a computationally intensive task and therefore requires a lot of resources. A deduction of the Navier-Stokes-Equations leads to a more simplified version called the shallow water equations. An example application named 'SWE' already implements simulations using these equations, with the use of several Riemann solvers, and additional support of different frameworks like MPI. In this bachelor's thesis, the speed-up of computation using the framework 'Kokkos' is investigated. The framework will generate performance portable code for heterogeneous architectures, which will optimize computation time independently of the underlying hardware. It is achieved by providing an abstraction of the computational devices and using hardware-specific characteristics like data layout or memory performance.
Keywords: Kokkos, Shallow Water Equations, CUDA, OpenMP