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
)
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