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

Multistep Parametric Processes in Nonlinear Optics

We present a comprehensive overview of different types of parametric interactions in nonlinear optics which are associated with simultaneous phase-matching of several optical processes in quadratic nonlinear media, the so-called multistep parametric interactions. We discuss a number of possibilities of double and multiple phase-matching in engineered structures with the sign-varying second-order nonlinear susceptibility, including (i) uniform and non-uniform quasi-phase-matched (QPM) periodic optical superlattices, (ii) phase-reversed and periodically chirped QPM structures, and (iii) uniform QPM structures in non-collinear geometry, including recently fabricated two-dimensional nonlinear quadratic photonic crystals. We also summarize the most important experimental results on the multi-frequency generation due to multistep parametric processes, and overview the physics and basic properties of multi-color optical parametric solitons generated by these parametric interactions.Comment: To be published in Progress in Optic

Self-healing composites: A review

Self-healing composites are composite materials capable of automatic recovery when damaged. They are inspired by biological systems such as the human skin which are naturally able to heal themselves. This paper reviews work on self-healing composites with a focus on capsule-based and vascular healing systems. Complementing previous survey articles, the paper provides an updated overview of the various self-healing concepts proposed over the past 15 years, and a comparative analysis of healing mechanisms and fabrication techniques for building capsules and vascular networks. Based on the analysis, factors that influence healing performance are presented to reveal key barriers and potential research directions

Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multi-resolution functional ANOVA model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed multi-resolution functional ANOVA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, both in terms of sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy