Database Reference
In-Depth Information
Evaluator (E)
x
i
...
...
Simulator (S)
f
f(x
j
)
f(x
i+1
)
...
...
(a)
Evaluator (E)
x
i
...
...
Simulator (S)
f
f
^
^
f(x
i+1
)
...
f(x
j
)
...
(b)
Figure 11.11
Simulation workflow.
During each timestep some particles in the chamber react, causing their com-
positions to change. This reaction is described by a complex high-dimensional
function called the
reaction function
, which, given the current composition
vector of a particle and other simulation properties, produces a new composi-
tion vector for the particle. Combustion simulations usually require up to 10
8
to 10
10
reaction function evaluations.
Figure 11.11(a) summarizes the computational workflow. The Simulator
(
S
) generates a sequence of compositions
at which the reaction func-
tion should be evaluated. The Evaluator (
E
) performs these reaction function
evaluations, which are then used by
S
to generate future compositions. Many
scientific simulations have a similar workflow.
{
...
x
i
}
Problem Formulation
Scientists often face serious computational challenges in running large-scale
scientific simulations. The more realistic the model, the more complex the
corresponding mathematical equations and the design of
E
(Figure 11.11).
For example, in combustion simulations
E
is a differential equation solver
that takes in the order of tens of milliseconds for a single reaction function
(denoted as
f
in the figure) evaluation. As a result, even small simulations
can run for days; larger, more complex simulations, would run for months or
even years.
To make large-scale simulations computationally feasible, scientists trade
off accuracy for speed. This is done by modifying the simulation workflow,
as shown in Figure 11.11(b). The main idea is to build a computationally
inexpensive approximate model (
f
) of the original complex model (
f
). The
approximate model
f
is also built and maintained during the course of the
simulation, and the Evaluator for each input point
x
can either evaluate
f
(
x
)