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

Load-independent characterization of trade-off fronts for operational amplifiers

Abstract—In emerging design methodologies for analog integrated circuits, the use of performance trade-off fronts, also known as Pareto fronts, is a keystone to overcome the limitations of the traditional top-down methodologies. However, most techniques reported so far to generate the front neglect the effect of the surrounding circuitry (such as the output load impedance) on the Pareto-front, thereby making it only valid for the context where the front was generated. This strongly limits its use in hierarchical analog synthesis because of the heavy dependence of key performances on the surrounding circuitry, but, more importantly, because this circuitry remains unknown until the synthesis process. We will address this problem by proposing a new technique to generate the trade-off fronts that is independent of the load that the circuit has to drive. This idea is exploited for a commonly used circuit, the operational amplifier, and experimental results show that this is a promising approach to solve the issue

Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition

Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient ANOVA-based stochastic circuit/MEMS simulator to extract efficiently the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is simulated efficiently by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.Comment: 14 pages (IEEE double column), 11 figure, accepted by IEEE Trans CAD of Integrated Circuits and System

Two- and Three-dimensional High Performance, Patterned Overlay Multi-chip Module Technology

A two- and three-dimensional multi-chip module technology was developed in response to the continuum in demand for increased performance in electronic systems, as well as the desire to reduce the size, weight, and power of space systems. Though developed to satisfy the needs of military programs, such as the Strategic Defense Initiative Organization, the technology, referred to as High Density Interconnect, can also be advantageously exploited for a wide variety of commercial applications, ranging from computer workstations to instrumentation and microwave telecommunications. The robustness of the technology, as well as its high performance, make this generality in application possible. More encouraging is the possibility of this technology for achieving low cost through high volume usage

Radiation safety based on the sky shine effect in reactor

In the reactor operation, neutrons and gamma rays are the most dominant radiation. As protection, lead and concrete shields are built around the reactor. However, the radiation can penetrate the water shielding inside the reactor pool. This incident leads to the occurrence of sky shine where a physical phenomenon of nuclear radiation sources was transmitted panoramic that extends to the environment. The effect of this phenomenon is caused by the fallout radiation into the surrounding area which causes the radiation dose to increase. High doses of exposure cause a person to have stochastic effects or deterministic effects. Therefore, this study was conducted to measure the radiation dose from sky shine effect that scattered around the reactor at different distances and different height above the reactor platform. In this paper, the analysis of the radiation dose of sky shine effect was measured using the experimental metho

Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\it a-priori}. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201

Index to NASA Tech Briefs, 1975

This index contains abstracts and four indexes--subject, personal author, originating Center, and Tech Brief number--for 1975 Tech Briefs