Response Surface Modeling for Design Space Exploration of Embedded Systems - Multi-objective Design Space Exploration of Multiprocessor SoC Architectures - page 77

descriptions of the RSM algorithms while Sect. 4.5 presents the general validation
flow. Section 4.6 summarizes the main content of this chapter.

4.2 Background on Response Surface Models

RSM techniques are typically introduced to decrease the time due to the evaluation of
a system-level metric f ( x ) for each architecture configuration x 1 . In fact, for appli-
cations of commercial interest, evaluating f ( x ) can involve one or more simulations
which can take several hours, depending on the platform complexity and the system
resources dedicated to the simulation.
The principle of RSM is to exploit a set of simulations generated by a Design of
Experiment strategy to build a surrogate model to predict the system-level metrics.
The response model has the same input and output features of the original simulation-
based model but offers dramatic speed-up in terms of evaluation since it consists of
an analytical, closed-form function.
A typical RSM-based flow involves a training phase , in which simulation data
(or training set ) is used to tune the RSM, and a prediction phase in which the RSM
is used to forecast unknown system response (see Fig. 4.2 ).
Given a system-level metric f ( x ) associated with an architectural configuration
x , a response surface model ρ ( x ) is defined such that:

f ( x ) = ρ ( x ) + ε (4.1)

where ε is an ideally negligible estimation error. The prediction ρ ( x ) is a function of
the target architecture x .
In simple cases, ρ ( x ) may consists of a closure 2 of a more general function ( x , w )
where the vector of parameters w has been fixed to w 0 :

=

ρ ( x ) ( x , w 0 ) (4.2)

Training phase

Design of Experiments Simulations

Prediction phase

Fig. 4.2 Typical usage of a
Response Surface Model

1 Each architecture configuration is seen as a vector of configuration parameters. We use bold font
to specify vector values.
2 A closure is a first-class function with free variables that are bound in the lexical environment.
Such a function is said to be “closed over” its free variables. (Source: Wikipedia).