Model reduction and simulation of nonlinear circuits via tensor decomposition

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Model Reduction and Simulation of Nonlinear Circuits via Tensor Decomposition

Abstract-Model order reduction of nonlinear circuits (especially highly nonlinear circuits), has always been a theoretically and numerically challenging task. In this paper we utilize tensors (namely, a higher order generalization of matrices) to develop a tensor-based nonlinear model order reduction (TNMOR) algorithm for the efficient simulation of nonlinear circuits. Unlike existing nonlinear model order reduction methods, in TNMOR high-order nonlinearities are captured using tensors, followed by decomposition and reduction to a compact tensor-based reducedorder model. Therefore, TNMOR completely avoids the dense reduced-order system matrices, which in turn allows faster simulation and a smaller memory requirement if relatively lowrank approximations of these tensors exist. Numerical experiments on transient and periodic steady-state analyses confirm the superior accuracy and efficiency of TNMOR, particularly in highly nonlinear scenarios

STORM: a nonlinear model order reduction method via symmetric tensor decomposition

Nonlinear model order reduction has always been a challenging but important task in various science and engineering fields. In this paper, a novel symmetric tensor-based orderreduction method (STORM) is presented for simulating largescale nonlinear systems. The multidimensional data structure of symmetric tensors, as the higher order generalization of symmetric matrices, is utilized for the effective capture of highorder nonlinearities and efficient generation of compact models. Compared to the recent tensor-based nonlinear model order reduction (TNMOR) algorithm [1], STORM shows advantages in two aspects. First, STORM avoids the assumption of the existence of a low-rank tensor approximation. Second, with the use of the symmetric tensor decomposition, STORM allows significantly faster computation and less storage complexity than TNMOR. Numerical experiments demonstrate the superior computational efficiency and accuracy of STORM against existing nonlinear model order reduction methods.postprin

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

Review of polynomial chaos-based methods for uncertainty quantification in modern integrated circuits

Advances in manufacturing process technology are key ensembles for the production of integrated circuits in the sub-micrometer region. It is of paramount importance to assess the effects of tolerances in the manufacturing process on the performance of modern integrated circuits. The polynomial chaos expansion has emerged as a suitable alternative to standardMonte Carlo-based methods that are accurate, but computationally cumbersome. This paper provides an overview of the most recent developments and challenges in the application of polynomial chaos-based techniques for uncertainty quantification in integrated circuits, with particular focus on high-dimensional problems

ADAPTIVE NONLINEAR MODEL REDUCTION FOR FAST POWER SYSTEM SIMULATION

The dissertation proposes a new adaptive approach to power system model reduction for fast and accurate time-domain simulation. This new approach is a compromise between linear model reduction for faster simulation and nonlinear model reduction for better accuracy. During the simulation period, the approach adaptively switches among detailed and linearly or nonlinearly reduced models based on variations of the system state: it employs unreduced models for the fault-on period, uses weighted column norms of the admittance matrix to decide which functions are to be linearized in power system differential-algebraic equations for large changes of the state, and adopts a linearly reduced model for small changes of the state.Two versions of the adaptive model reduction approach are introduced. The first version uses traditional power system partitioning where the model reduction is applied to a defined large external area in a power system and the other area that is defined as the study area keeps full detailed models. The second version applies the adaptive model reduction to the whole system.Speed improvement techniques using parallelization are investigated. The first technique uses parallelism in space; it further divides the study area into subareas that can be simulated in parallel. The second technique uses parallelism in time; it integrates the adaptive model reduction into the coarse solver of the Parareal method.In addition, the dissertation proposes integration of tensor decomposition into the adaptive model reduction approach to further improve the speed and accuracy of simulation.All proposed approaches are validated by comprehensive case studies on the 140-bus 48-machine Northeast Power Coordinating Council system, 2383-bus 327-machine Polish system, and 5617-machine 70285-bus Eastern Interconnection system using different dynamic models

A Holistic Approach to Functional Safety for Networked Cyber-Physical Systems

Functional safety is a significant concern in today's networked cyber-physical systems such as connected machines, autonomous vehicles, and intelligent environments. Simulation is a well-known methodology for the assessment of functional safety. Simulation models of networked cyber-physical systems are very heterogeneous relying on digital hardware, analog hardware, and network domains. Current functional safety assessment is mainly focused on digital hardware failures while minor attention is devoted to analog hardware and not at all to the interconnecting network. In this work we believe that in networked cyber-physical systems, the dependability must be verified not only for the nodes in isolation but also by taking into account their interaction through the communication channel. For this reason, this work proposes a holistic methodology for simulation-based safety assessment in which safety mechanisms are tested in a simulation environment reproducing the high-level behavior of digital hardware, analog hardware, and network communication. The methodology relies on three main automatic processes: 1) abstraction of analog models to transform them into system-level descriptions, 2) synthesis of network infrastructures to combine multiple cyber-physical systems, and 3) multi-domain fault injection in digital, analog, and network. Ultimately, the flow produces a homogeneous optimized description written in C++ for fast and reliable simulation which can have many applications. The focus of this thesis is performing extensive fault simulation and evaluating different functional safety metrics, \eg, fault and diagnostic coverage of all the safety mechanisms