Geoscience Reference
In-Depth Information
A related opportunity for a quick gain in benefit from HPC is the use of the bootstrap to estimate
parameter variances. This is quite straightforward. You merely have to run the model of interest a
few hundred or a few thousand times. It is naturally parallel because each run can be assigned to a
different processor or else the code is left running on a workstation for a week or two. This raises
another point of general significance. Research with a multiregion population forecasting model,
which was used to make population forecasts for the European Union (EU), used this bootstrap
approach to identify the error limits to forecasts for 2021-2051. This can be used to identify model
data weaknesses. It also shows that currently there are no reliable long-term forecasts for the EU
as the confidence limits are extremely wide. The problem appears to be due to uncertainty in the
migration forecasting; see Turton and Openshaw (1998) for further details. Previously these error
bands were unknown. Cross-validation using a jackknife is another useful computationally intensive
tool. Here, the additional computation is a factor of
N
times, where
N
is the number of observations.
1.7.3 n
etwork
and
l
location
o
PtiMiSation
The basic spatial interaction model is often embedded in a non-linear optimisation framework that
can require the model to be run many thousands of times in the search for optimal locations, for
example, to determine the optimal network of shopping centres or car show rooms or good sites.
There are many different types of important public and private sector location optimisation prob-
lems of this sort. The quality of the final result is now critically dependent on the resolution of
the data, the performance of the embedded model and the quality of the optimisation algorithm.
The latter is, crudely put, usually related to how many million different candidate solutions can be
evaluated in a fixed time period, because the problem can only be tackled by heuristic methods. The
number of model evaluations per hour is dependent on processor speed, size of problem, granular-
ity of the parallelism and the skills of the programmer in teasing it out to ensure good performance
on particular hardware; see Turton and Openshaw (1998) for an example. The problem here is that
end users (surprisingly) may be far more interested in a good solution than in obtaining an opti-
mal solution, a view that is sometimes characterised by the dictum 'the best is the enemy of the
good'. However, this is a distraction. The only way of determining whether a good result has been
obtained is by knowing what the best attainable result is likely to be. Users will naturally assume
that all of the results that they obtain are optimal or nearly optimal, and it is a responsibility of the
researcher to ensure that they are. It is not something that can be fudged but neither is the best result
independent of the methodology used to find it, especially in complex non-linear applications where
optimality is determined by the computational technology.
1.7.4 a
utoMated
M
odelling
S
ySteMS
There is also a need to improve the quality of the models being used in geographical research and
not just speed up the time taken by legacy models or scale up the size of problem that can be tackled.
The new computational technologies offer new ways of building models that either replace existing
models based on mathematical and statistical approaches or else can be viewed as complementing
them. The
old
model shown in Equation 1.1 assumes a single global deterrence function. This was
quite reasonable when
N
was small and computer time was limited, and without access to HPC, not
much more could be done. Yet building good models of many human systems is hard because of the
complexity of the underlying processes, the lack of good relevant theory and the seemingly chaotic
non-linear behaviour of the systems of interest. It is important, therefore, to develop new ways of
designing and building good-performing models that can combine human intellect and modelling
skills with HPC.
One approach is to create an automated modelling system (AMS) that uses genetic algorithms
and genetic programming (GP) techniques to suggest potentiality useful models. The AMS of
Openshaw (1988) used a Cray vector supercomputer in an early attempt to define and then explore
