Yi Cao

State-space dynamic neural network technique for high-speed IC applications: modeling and stability analysis

We present a state-space dynamic neural network (SSDNN) method for modeling the transient behaviors of high-speed nonlinear circuits. The SSDNN technique extends the existing dynamic neural network (DNN) approaches into a more generalized and robust formulation. For the first time, stability analysis methods are presented for neural modeling of nonlinear microwave circuits. We derive the stability criteria for both the local stability and global stability of SSDNN models. Stability test matrices are formulated from SSDNN internal weight parameters. The proposed criteria can be conveniently applied to the stability verification of a trained SSDNN model using the eigenvalues of the test matrices. In addition, a new constrained training algorithm is introduced by formulating the proposed stability criteria as training constraints such that the resulting SSDNN models satisfy both the accuracy and stability requirements. The validity of the proposed technique is demonstrated through the transient modeling of high-speed interconnect driver and receiver circuits and the stability verifications of the obtained SSDNN models

A New Training Approach for Robust Recurrent Neural-Network Modeling of Nonlinear Circuits

A new approach for developing recurrent neural-network models of nonlinear circuits is presented, overcoming the conventional limitations where training information depends on the shapes of circuit waveforms and/or circuit terminations. Using only a finite set of waveforms for model training, our technique enables the trained model to respond accurately to test waveforms of unknown shapes. To relate information of training waveforms with that of test waveforms, we exploit an internal space of a recurrent neural network, called the internal input-neuron space. We formulate a new circuit block combining a generic load and a generic excitation to terminate the circuit. By sweeping the coefficients of the proposed circuit block, we obtain a rich combination of training waveforms to cover the region of interest in the internal input-neuron space effectively. We also present a new method to reduce the amount of training data while maintaining the necessary modeling information. The proposed method is demonstrated through examples of recurrent neural-network modeling of high-speed drivers and an RF amplifier. It is confirmed that, for different terminations and test waveforms, the model trained with the proposed technique has better accuracy and robustness than that using the existing training methods.

Parallel Automatic Model Generation Technique for Microwave Modeling

In this paper, a parallel automatic model generation (PAMG) technique is proposed to speedup the development of artificial neural network (ANN) models for microwave modeling. The automatic model generation (AMG) converts human based manual modeling into an automated computational process. AMG typically involves intensive computations in adaptive data sampling by repetitively driving detailed EM/physics/circuit simulators, and automatic ANN structure adaptation through iterative training stages. To improve AMG efficiency, a parallel mechanism is developed, in which the computationally intensive processes are split into smaller sections. These sections are concurrently executed on parallel processors in a multi-processor environment. The proposed parallel algorithm is formulated to maximize the number of parallel processes while minimizing the sequential overhead in the AMG to achieve the highest possible modeling efficiency. Examples of driving a physics-based device simulator for MESFET modeling and driving a circuit simulator for power amplifier behavior modeling demonstrate that the proposed PAMG dramatically shortens the model development time with parallel efficiency above 90%, thus is very useful for large-scale microwave modeling.

Transient Behavioral Modeling of Nonlinear I/O Drivers Combining Neural Networks and Equivalent Circuits

In this letter, a new method for nonlinear behavioral modeling of high-speed I/O drivers is presented, combining neural networks with driver specific circuit knowledge. In the proposed technique, the circuit knowledge of the driver is exploited to preserve the physical property of the driver. In addition, several neural network sub-models are incorporated into the overall model structure to effectively compensate the missing information in the existing buffer models, when dealing with analog input signals of various shapes. The validity and efficiency of the proposed technique are demonstrated through the modeling of a commercial I/O driver and the use of the resulting model for signal integrity simulations.

Time-Domain Neural Network Approaches to EM Modeling of Microwave Components

Time-domain modeling of EM behaviors with geometrical parameters as variables is addressed in this paper. Two approaches, a combined-state-space equation/neural network technique (SSE-NN), and a recurrent neural network (RNN) technique are described. In the SSE-NN approach, the model is a hierarchical structure with two levels. In the lower level, a neural network maps the geometrical/physical parameters of the passive component into coefficient matrices of state equations. In the higher level, the coefficient matrices are transformed into the state space equation to compute the EM response in time domain circuit design. The RNN approach provides a direct time-domain model trained from data generated by time-domain EM simulation. A time-domain neural network structure called RNN is exploited to model the transient EM responses for varying material and geometrical parameters. An automated RNN modeling technique is introduced to efficiently determine the training waveform distribution and internal RNN structure during the offline training process. Through two examples it’s demonstrated that the trained time domain neural network model provides fast EM solutions with variable values of the geometrical parameter in the model.

Neural-based Transient Behavioral Modeling of IC Buffers for High-speed Interconnect Design

Artiflcial neural networks (ANN) have gained attention as fast and ∞exible vehicles to microwave modeling and design. This paper reviews a recent advance of neural network modeling, i.e., state-space dynamic neural network (SSDNN) for transient behavioral modeling of high-speed nonlinear circuits. The SSDNN model can be directly trained from the input and output waveforms without relying on the circuit internal details. A training algorithm exploiting adjoint sensitivities is summarized for training the model in an e-cient manner. An example of the SSDNN technique for IC bufier modeling and its use with transmission line elements in high-speed interconnect design are included. DOI: 10.2529/PIERS060907175229 With the continuous increase of signal speed and frequency, signal integrity (SI) in VLSI pack- ages becomes more and more prominent. Fast and accurate representations of the nonlinear analog behaviors of driver/receiver bufiers are the key to the success of SI-based design of high-speed inter- connects with nonlinear terminations (1,2). As such, developing e-cient bufier models for transient applications has become an important topic (3{5). To ensure model reliability in circuit simula- tions, the model stability remains one of the most critical aspects of nonlinear transient modeling. In the neural network community, global asymptotical stability and global exponential stability have been studied for some special classes of dynamic networks, e.g., Hopfleld neural networks (6), recurrent neural networks (7), and discrete-time state-space neural networks (8). Recently stability for ANN-based analog microwave modeling has also been addressed (9). This paper summarizes a state-space dynamic neural network (SSDNN) technique for modeling nonlinear transient behaviors of IC drivers and receivers (5). We describe the detailed structure of SSDNN and how to train the model based on the transient waveforms from the original circuits. An example is provided to demonstrate the application of the SSDNN model in coupled transmission line environments. Let u 2 < M be transient input signals of a nonlinear circuit, e.g., input voltages and currents, and y 2 < K be transient output signals of a nonlinear circuit, e.g., output voltages and currents where M and K are the numbers of circuit inputs and outputs respectively. Based on combining state-space concept and continuous recurrent neural network method (10), the SSDNN nonlinear model is formulated as (5) ( _ x(t) = ix(t) + ?g ANN (u(t);x(t);w)

Efficient Harmonic Balance Simulation of Nonlinear Microwave Circuits with Dynamic Neural Models

This paper presents a novel approach aimed at enhancing the speed and accuracy of harmonic balance (HB) simulation of nonlinear circuits represented by dynamic neural network (DNN) models. A set of constraint functions are proposed using the boundary information extracted from the time-domain training data for developing DNN models. Using these constraints, an expanded HB formulation of DNN is presented ensuring the DNN HB solutions to be within its training region. To further enhance the simulation efficiency, we propose a systematic method for setting the initial values of the DNN HB variables taking advantage of the knowledge of frequency-domain training data. The proposed methods are demonstrated through the HB simulations of a power amplifier circuit and DBS subsystem. It is shown that for simulation of DNN-based circuits, the proposed HB method gives more accurate solutions in shorter time than that using conventional HB method

Neural Based EM Modeling

This paper reviews state-of-the art neural network (NN) modeling techniques for electromagnetic (EM) modeling. We describe the advantages of neural network models in terms of speed and accuracy. Conventional simulator based EM models are time consuming. An iterative evaluation of these models is used for the design parameters, which are CPU intensive. Neural network model can provide fast and accurate models for electromagnetic devices. Time domain EM modeling is also presented here using recurrent neural network (RNN) technique. The trained RNN model can be used in the circuit simulators for circuit analysis. Examples of neural network based EM models are also presented which proves that neural network base models are both fast and accurate and thus efficient for EM based design.

State-Space Dynamic Neural Network Technique for High-Speed IC Buffer Modeling

Artificial neural networks (ANN) have been recently recognized as useful tools for RF/microwave modeling and design. In this paper, a recent state-space dynamic neural network (SSDNN) approach for transient behavior modeling of high-speed nonlinear circuit is summarized. This technique extends the existing dynamic neural network (DNN) approach into a more generalized and robust state-space formulation. A training algorithm exploiting the adjoint sensitivity computation is utilized to enable SSDNN to efficiently learn from the transient input and output waveform data without relying on the circuit internal details. Through an exact circuit representation, the trained SSDNN model can be conveniently implemented and used in SPICE-like circuit simulators. We also review a set of stability criteria for checking local and global stabilities of the SSDNN model. An example of SSDNN modeling of physics-based high-speed driver circuit is presented. Its demonstrated that the SSDNN model can offer fast and accurate transient responses for high-speed interconnect design.

Recent advances in neural based time domain EM modeling and simulation

In this paper, the recent neural network (NN) approaches to time domain electromagnetic (EM)-based modeling are summarized. Fast and accurate passive EM models can be created using three recent methods, i.e., (equivalent circuit and neural network) EC-NN, (state space equation and neural network) SSE-NN and (equivalent circuit, state space equation and neural network) EC-SSE-NN. Those methods are based on combined equivalent circuit and/or state space theory. Each of the combined modeling techniques has its own usage depending on the availability of the equivalent circuit and user-desired accuracy. In order to develop a nonlinear transient model to be used together with passive components in time domain EM-based simulation, the adjoint dynamic neural network (ADNN)-based modeling technique can be utilized. Through accurate and fast time domain EM-based neural models of passive/active components, we enable consideration of EM effects in high-frequency and high-speed computer-aided design (CAD), including components geometrical/physical parameters as optimization variables. Examples of EM modeling of embedded passives and their use in time domain EM-based simulation and design are presented.