Large-scale Nonlinear Circuits Research Articles

OSSP-PTA: An Online Stochastic Stepping Policy for PTA on Reinforcement Learning

DC analysis is essential and still quite challenging in large-scale nonlinear circuit simulation. Pseudo transient analysis (PTA) is a widely-used and has great potential solver in the industry. However, the PTA convergence and simulation efficiency is still seriously affected by its stepping policy. This paper proposes an online stochastic stepping policy (OSSP) for PTA based on deep reinforcement learning (DRL). To achieve better policy evaluation and stronger stepping exploration ability, the dual soft Actor-Critic agents work with the proposed valuation splitting and online momental scaling, enabling our OSSP to intelligently encode PTA iteration status and online further adjust forward and backward time-step size for unseen test circuits without human intervention and domain knowledge, trained solely by RL from self-search. Our public sample buffer and priority sampling are also introduced to overcome the sparsity and imbalance of sample data. Numerical examples demonstrate that the proposed OSSP achieves a significant efficiency speedup (up to 47.0X less NR iterations) and convergence enhancement on unseen test circuits compared with the previous iter-based and SER-based stepping methods, in just one stepping iteration.

Adaptive Stepping PTA for DC Analysis Based on Reinforcement Learning

Solving the DC operating point efficiently for large-scale nonlinear circuit is crucial and quite challenging. Pseudo transient analysis (PTA) is a widely-used and promising DC solver in the industry, in which the stepping policy is of great importance for PTA convergence and simulation efficiency. In this brief, a reinforcement learning (RL)-enhanced stepping policy is proposed. It designs dual Actor-Critic agents with stochastic policy and online adaptive scaling to intelligently evaluate PTA convergence status, and adaptively adjust forward and backward time-step size. Numerical examples demonstrate that a significant efficiency speedup and convergence improvement over the previous stepping methods is achieved by the proposed RL-enhanced stepping policy.

EI-NK: A Robust Exponential Integrator Method With Singularity Removal and Newton–Raphson Iterations for Transient Nonlinear Circuit Simulation

In this article, we propose an exponential-integrator-Newton–Krylov (EI-NK) method for transient simulation of large-scale nonlinear circuits. This method aims to address two long-standing problems that affect the performance and robustness of EI in handling nonlinear circuits. First is the numerical instability caused by the singularity in the differential-algebraic equation system. We provide an in-depth analysis of the problem and propose a systematic, algebraic, and sparsity preserving regularization technique to eliminate the unstable modes in the system to be solved. Next, we develop a scheme to enable the iterative Newton–Raphson solution in the EI framework for enhanced nonlinearity handling capability. With the two techniques, we wish to elevate EI’s robustness and performance and make it a competitive alternative to the existing SPICE-type simulators in practical applications.

Method for Analyzing Bit Error Rates (BERs) of Nonlinear Circuits and Systems for High-Performance Signaling

Bit error rate (BER) is an important figure of merit to evaluate the performance of a communication system. Analyzing the BER of a linear-time-invariant system has been extensively studied. However, analyzing the BER of nonlinear circuits and systems is challenging because it cannot rely on linear time invariant (LTI) principles, while an exhaustive nonlinear simulation is computationally prohibitive. To find BER, an exhaustive approach requires nonlinear simulations of $2^m$ bit patterns for a channel of m-bit memory, where m can be larger than 100 in today's high-speed and high-performance design. In this work, we develop a fast and accurate method to analyze the BER of large-scale nonlinear circuits. Only O(k) nonlinear simulations are required, with k much less than 2^m and independent of $2^m$ . While performing O(k) nonlinear simulations only, we find a method to determine the probability density function of the nonlinear responses, from which accurate BER results can be obtained. An error assessment method is also developed to evaluate the true error of the nonlinear signaling analysis without the need for knowing the entire nonlinear responses of the channel. Simulations of large-scale real-world nonlinear circuits have demonstrated the accuracy, efficiency, and capacity of the proposed method. A BER as low as $10^{-56}$ is accurately predicted.

An analytic modeling strategy for memristor cell applicable to large-scale memristive networks

Memristive networks are large-scale non-linear circuits based on memristor cells, playing a crucial role in developing the emerging researches such as next-generation artificial intelligence, bioelectronics, and high-performance memory. The performance of memristive networks is greatly affected by the memristor model describing physical and electrical characteristics of a memristor cell. However, existing models are mainly non-analytic and, accordingly, may have convergence issues in their applications in memristive networks’ analyses. Therefore, aiming at improving convergence of memristive networks, we propose an analytic modeling strategy for memristor based on homotopy analysis method (HAM). In this strategy, the HAM is used to obtain an analytic memristor model through solving the state equations of memristors in original physical model. Specifically, the HAM is used to solve the analytic approximate solution of the core parameter of memristor—state variable, from the state equations, in the form of analytic homotopy series. Then the analytic approximate model of memristor is obtained by using the solved state variables. The characteristics of the proposed strategy are as follows. 1) Its solution has a closed-form expression, i.e. an explicit function, 2) its approximation error is optimized, thereby realizing the convergence optimization. Moreover, according to the characteristics of memristive networks, we introduce an analysis criterion for memristor model applicable to memristive networks. Through the long-time evolution experiments of a memristor cell and a benchmark memristive matrix network with different inputs, and the comparisons with the traditional non-analytic (numeric) method, we verify the analyticity and convergence superiority of the modeling strategy. Besides, based on this strategy and the comparison experiments, we reveal that one of the underlying reasons for non-convergence in the large-scale memristive network simulation possesses the non-analyticity of the used memristor model. The strategy can be further used for analyzing the performances of a memristor cell and memristive networks in long-time. It also has potential applications in emerging technologies.

Subspace Trajectory Piecewise-Linear Model Order Reduction for Nonlinear Circuits

AbstractDespite the efficiency of trajectory piecewise-linear (TPWL) model order reduction (MOR) for nonlinear circuits, it needs large amount of expansion points for large-scale nonlinear circuits. This will inevitably increase the model size as well as the simulation time of the resulting reduced macromodels. In this paper, subspace TPWL-MOR approach is developed for the model order reduction of nonlinear circuits. By breaking the high-dimensional state space into several subspaces with much lower dimensions, the subspace TPWL-MOR has very promising advantages of reducing the number of expansion points as well as increasing the effective region of the reduced-order model in the state space. As a result, the model size and the accuracy of the TWPL model can be greatly improved. The numerical results have shown dramatic reduction in the model size as well as the improvement in accuracy by using the subspace TPWL-MOR compared with the conventional TPWL-MOR approach.

DC Large-Scale Simulation of Nonlinear Circuits on Parallel Processors

Abstract Newton-Raphson DC analysis of large-scale nonlinear circuits may be an extremely time consuming process even if sparse matrix techniques and bypassing of nonlinear models calculation are used. A slight decrease in the time required for this task may be enabled on multi-core, multithread computers if the calculation of the mathematical models for the nonlinear elements as well as the stamp management of the sparse matrix entries is managed through concurrent processes. In this paper it is shown how the numerical complexity of this problem (and thus its solution time) can be further reduced via the circuit decomposition and parallel solution of blocks taking as a departure point the Bordered-Block Diagonal (BBD) matrix structure. This BBD-parallel approach may give a considerable profit though it is strongly dependent on the system topology. This paper presents a theoretical foundation of the algorithm, its implementation, and numerical complexity analysis in virtue of practical measurements of matrix operations.

CNNEDGEPOT: CNN based edge detection of 2D near surface potential field data

All anomalies are important in the interpretation of gravity and magnetic data because they indicate some important structural features. One of the advantages of using gravity or magnetic data for searching contacts is to be detected buried structures whose signs could not be seen on the surface. In this paper, a general view of the cellular neural network (CNN) method with a large scale nonlinear circuit is presented focusing on its image processing applications. The proposed CNN model is used consecutively in order to extract body and body edges. The algorithm is a stochastic image processing method based on close neighborhood relationship of the cells and optimization of A, B and I matrices entitled as cloning template operators. Setting up a CNN (continues time cellular neural network (CTCNN) or discrete time cellular neural network (DTCNN)) for a particular task needs a proper selection of cloning templates which determine the dynamics of the method. The proposed algorithm is used for image enhancement and edge detection.The proposed method is applied on synthetic and field data generated for edge detection of near-surface geological bodies that mask each other in various depths and dimensions. The program named as CNNEDGEPOT is a set of functions written in MATLAB software. The GUI helps the user to easily change all the required CNN model parameters. A visual evaluation of the outputs due to DTCNN and CTCNN are carried out and the results are compared with each other. These examples demonstrate that in detecting the geological features the CNN model can be used for visual interpretation of near surface gravity or magnetic anomaly maps.

Nonlinear function generators and chaotic signal generators using a pulse-width modulation method

A new approach for making arbitrary nonlinear transfer function generator circuits is proposed. Arbitrary non-monotone functions can be made by combining plural pulse-width modulation (PWM) circuits. Chaotic signal generators can be made by using these circuits. This approach is useful for implementing large-scale nonlinear circuit systems.

A multilevel Newton algorithm with macromodeling and latency for the analysis of large-scale nonlinear circuits in the time domain

Analysis techniques which take advantage of the structural properties of large-scale electrical networks are discussed. Exact macromodels of a subnetwork are defined and a sufficient condition on the subnetwork equations for the existence of a macromodel is given. A multilevel Newton algorithm based on macromodels is presented. The algorithm is shown to have local quadratic convergence provided that suitable conditions on the continuity and nonsingularity of the Jacobian of the network equations are satisfied. The concept of latency for the analysis of large-scale networks in the time domain is discussed. The relationship between latency and numerical integration methods is investigated.