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

SCEE 2008 book of abstracts : the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE 2008), September 28 – October 3, 2008, Helsinki University of Technology, Espoo, Finland

This report contains abstracts of presentations given at the SCEE 2008 conference.reviewe

System- and Data-Driven Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Quantum simulation of Abelian gauge fields with ultracold gases

Gauge theories are ubiquitous in physics. Many intriguing phenomena in condensed matter physics owe to the action of the electromagnetic field, which is an Abelian gauge theory. The numerical treatment of many-body systems is inherently complex due to the exponentially growing size of the Hilbert space. While in one dimension an area law guarantees that numerical methods on classical computers can deal with strongly correlated systems, in higher dimensions the quantum simulation comes as the panacea for the many-body problem. The present thesis comprises the elaboration of experimentally feasible methods for the quantum simulation of dynamical Abelian gauge fields with ultra-cold gases of neutral atoms and the theoretical analysis of the related model Hamiltonians. As neutral atoms do not interact with external vector potentials like charged particles would do, the gauge fields have to be artificially engineered. The elements of a gauge theory that need to be replicated on a quantum simulator vary depending on the subject of investigation. The key ingredient at the root of many condensed matter phenomena, from the quantum Hall effect to superconductivity and chiral topological insulators, is the Berry phase. Whilst artificial static gauge fields have been widely explored, much remains to do regarding the realization of artificial dynamical gauge fields. In Chapter 3 we present a method based on the amplitude modulation of a one-dimensional optical lattice, which allows for an unprecedented degree of control over a wide range of parameters. The method also comprises the generation of a density-dependent complex phase, fundamental to the creation of anyonic pseudo-particles. The anyons are amenable of observation through interferometric measurement, realizable with the same experimental set-up. With regard to gauge theories, the Berry phase is just the visible tip of the iceberg. Below the waterline, there is more to consider in order to comprehensively reproduce a gauge theory, like the electric and magnetic fields in quantum electrodynamics. Moreover, a full account for the inherent symmetry is crucial to investigate phenomena proper of non-Abelian gauge theories in the context of high-energy physics, such as confinement. For this collection of topics, one can turn to lattice gauge theories. In Chapter 5, we consider a class of lattice gauge theories particularly suitable for quantum simulation, the Quantum Link Model. The study of the Abelian U(1) Quantum Link Model on a ladder geometry reveals a highly non-trivial phase diagram, featuring a symmetry-protected topological phase. In both Chapters, innovative solutions for the experimental realization of the model Hamiltonians are designed and proposed. To gain numerical access to the ground-state properties and the dynamics of the systems investigated we make use of state-of-the-art numerical methods based on Tensor Networks. The elements of the numerical analysis carried out throughout this thesis are presented in Chapter 6. In the last part we offer an outlook on research perspectives related to the topics discussed in the thesis