Information Technology Reference
In-Depth Information
analysis, design space exploration, and visualization become difficult, even if a single
simulation takes only a short period of time. The analyses are getting impractical as
when some of the circuit simulations are computationally expensive and time-
consuming. Moreover, when variations are considered in a circuit design, the situation
becomes even more complex. One way to reduce the design complexities and costs
is to build performance models which can be used as replacements for the real circuit
performance responses.
In this work, performance models are built by directly approximating circuit per-
formance parameters (e.g. S-parameter, gain, power consumption, noise figure, etc.)
with design variables (e.g. transistor size, bias voltage, current, etc.) and parametric
variations (e.g. V th , t ox , L eff ). The idea is illustrated in Fig. 1. This method is data-
driven and black-box by nature, and thus it can be applied to a wide range of circuit
design problems.
2.2
Model Construction
Techniques. Global surrogate modeling [1] is used to create performance models
with good accuracy over the complete design space. This is different from building
local surrogate model for the purpose of optimization [2].
Surrogate modeling accuracy and efficiency are determined by several key factors
including the sampling plan, model template, and validation. These factors are the
three steps in surrogate modeling. Multiple techniques are available and they need
to be carefully selected according to the nature of the problem and computational
complexity.
In the first step, the key question in designing the sampling plan is how to
efficiently choose samples for fitting models, considering that the number of samples
is limited by the computational expense. Traditionally, methods such as Latin Hyper-
cube sampling or orthogonal arrays, is used for one-shot sampling [3]. Recently,
adaptive sampling techniques were developed in order to achieve better efficiency in
sampling [4, 5]. Adaptive sampling is an iterative sampling process which analyzes
the data from previous iterations in order to select new samples in the areas that are
more difficult to fit.
In the model template selection step, the surrogate model type needs to be
determined. Popular surrogate model types include Rational Functions, Kriging mod-
els, Radial Basis Function (RBF) models, Artificial Neural Networks (ANNs), and
Support Vector Machines (SVMs). After the model type has been selected, model
complexity also needs to be decided. Model complexity is controlled by a set of
hyper-parameters which would be optimized during a modeling process.
The step of model validation establishes the predictive capabilities of the models
and estimates their accuracy. One popular method is five-fold cross-validation [6] in
which the training data are divided into five subsets. A surrogate model is con-
structed five times, each time four subsets are used for model construction and one
subset is used for error measurement. Model error can be measured as a relative error,
for example Root Relative Square Error (RRSE), Bayesian Estimation Error Quotient
(BEEQ), etc., or an absolute error, e.g. Maximum Absolute Error (MAE), Root Mean
Square Error (RMSE), etc.
Search WWH ::




Custom Search