Database Reference
In-Depth Information
to update
f
. Thus,
we need to design an Evaluator that ensures that all model evaluations are
within an error tolerance (i.e.,
f
approximates
f
within an error threshold)
and the total simulation cost is minimized. The total simulation cost includes
the cost of evaluating the model and also the cost of building
f
.
or use the expensive model to compute
f
(
x
)
and use
f
(
x
)
11.4.1 Survey of Existing Projects
Approximating complex models with simpler and faster ones has been studied
in many domains. In the combustion research community, early approaches
were oine in the following sense. Function evaluations were collected from
simulations and used to learn multivariate polynomials approximating the
reaction function.
25
These polynomials were then used later in different simu-
lations, replacing the original reaction function. Recently, more powerful mod-
els like neural networks and self-organizing maps have also been used.
26
The
oine approaches had only limited success because a single model cannot
generalize to a large class of simulations.
In 1997 Pope developed the
In Situ Adaptive Tabulation
(ISAT)
Algorithm.
27
ISAT takes an online approach to speeding up combustion sim-
ulations. The algorithm caches reaction function evaluations from certain fre-
quently seen regions in the composition space. It then uses the cached values to
approximate the reaction function at compositions encountered later on dur-
ing the simulation. The technique was a major breakthrough in combustion
simulation because it enabled scientists to run different simulations without
having to first build a model for the reaction function. ISAT was the first
algorithm that approached the function approximation problem in combus-
tion simulations according to a stream model, and the algorithm, even today,
remains the state of the art in the field.
Several modifications and improvements to ISAT have been proposed.
DOLFA
28
and PRISM
29
rely on alternative methods of caching reaction func-
tion evaluations. More recently, Panda et al.
30
studied the storage and retrieval
problem arising out of caching and reusing reaction function evaluations in
ISAT. Their work demonstrates how the streaming nature of simulations cre-
ates interesting tradeoffs that can be exploited for significant speed-ups in
simulations. This article discusses their major findings and observations.
11.4.2 Technology Description
Even though the ISAT Algorithm was originally proposed in the context of
combustion simulations, it can easily be generalized for building approximate
models for other high-dimensional functions. This section begins with a discus-
sion on
local models
, which represent the general class of models built by ISAT
(Section 11.4.2.1). This is followed by a description of the ISAT Algorithm
that uses selective evaluations of the expensive function
f
to build a local
