Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Algorithmic and infrastructural software development for cryo electron tomography

Many Cryo Electron Microscopy (cryoEM) software packages have accumulated significant technical debts over the years, resulting in overcomplicated codebases that are costly to maintain and that slow down development. In this thesis, we advocate for the development of open-source cryoEM core libraries as a solution to this debt and with the ultimate goal of improving the developer and user experience. First, a brief summary of cryoEM is presented, with an emphasis on projection algorithms and tomography. Second, the requirements of modern and future cryoEM image processing are discussed. Third, a new experimental cryoEM core library written in modern C++ is introduced. This library prioritises performance and code reusability, and is designed around a few core functions which offers an efficient model to manipulate multidimensional arrays at an index-wise and element-wise level. C++ template metaprogramming allowed us to develop modular and transparent compute backends, that provide great CPU and GPU performance, unified in an easy to use interface. Fourth, new projection algorithms will be described, notably a grid-driven approach to accurately insert and sample central slices in 3-dimensional (3d) Fourier space. A Fourier-based fused backward-forward projection, further improving the computational efficiency and accuracy of reprojections, will also be presented. Fifth, and as part of our efforts to test and showcase the library, we have started to implement a tilt series alignment package that gathers existing and new techniques into an automated pipeline. The current program first estimates the per-tilt translations and specimen stage rotation using a coarse alignment based on cosine stretching. It then fits the Thon rings of each tilt image as part of a global optimization to estimate the specimen inclination. Finally, we are using our Fourier-based fused reprojection to efficiently refine the per-tilt translations, and are starting to explore ways that would allow us to refine the per-tilt stage rotations

Field Programmable Gate Arrays (FPGAs) II

This Edited Volume Field Programmable Gate Arrays (FPGAs) II is a collection of reviewed and relevant research chapters, offering a comprehensive overview of recent developments in the field of Computer and Information Science. The book comprises single chapters authored by various researchers and edited by an expert active in the Computer and Information Science research area. All chapters are complete in itself but united under a common research study topic. This publication aims at providing a thorough overview of the latest research efforts by international authors on Computer and Information Science, and open new possible research paths for further novel developments

PyClaw: Accessible, Extensible, Scalable Tools for Wave Propagation Problems

Development of scientific software involves tradeoffs between ease of use, generality, and performance. We describe the design of a general hyperbolic PDE solver that can be operated with the convenience of MATLAB yet achieves efficiency near that of hand-coded Fortran and scales to the largest supercomputers. This is achieved by using Python for most of the code while employing automatically-wrapped Fortran kernels for computationally intensive routines, and using Python bindings to interface with a parallel computing library and other numerical packages. The software described here is PyClaw, a Python-based structured grid solver for general systems of hyperbolic PDEs \cite{pyclaw}. PyClaw provides a powerful and intuitive interface to the algorithms of the existing Fortran codes Clawpack and SharpClaw, simplifying code development and use while providing massive parallelism and scalable solvers via the PETSc library. The package is further augmented by use of PyWENO for generation of efficient high-order weighted essentially non-oscillatory reconstruction code. The simplicity, capability, and performance of this approach are demonstrated through application to example problems in shallow water flow, compressible flow and elasticity