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A Core Course on Modeling
Week 1- No Model Without a Purpose
     Contents     
• Models that Everybody Knows
• Various Kinds of Modeling Purposes
• Modeling Approaches
• The Modeling Process
• Example
Summary
References to lecture notes + book
References to quiz-questions and homework assignments (lecture notes)
1
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Models that Everybody Knows     
• Question
• Question
• Data, Measurements
• Data, Measurements
• Calculations, Approximations
• Calculations, Approximations
• Conclusion
• Conclusion
• Consequences
• Consequences
2
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Various Kinds of Modeling Purposes     
• Explanation
• Prediction (2)
• Compression
• Abstraction
• Unification
• Analysis
‘why…’, ‘how comes …’
‘when …’
‘what …’, ‘what if …’
‘Whythis
dodata
webe
sometimes
a
‘can
summarizedsee
in fewer
‘When
will fossile
fuel end?’
‘how
to formula?’
capture
the essence
of…?’
data
or
rainbow?’
‘What
the effect
of COof…?’
‘how
to is
capture
the essence
2
‘can
forest betraffic
seen as
through
How the
to describe
a fluidthe
to trees?’
´Can
GNP
data
whether
there
is an
emission?’
‘is
it true
that
…?’show
(+give
argument)
How
to
describe
traffic
and
fluids
in the
understand
congestions,
disregarding
‘how
can
adepression
known
audience
be informed?’
Can
we
understand
why
my
Internet
economic
or
not?´
same
way
to
understand
shock
waves?
‘how
canthat
an
unknown
audience
bealgorithm
Is
it true
this railway
signaling
individual
automobiles?
connection
is
sometimes
so
slow?
How
to explain
nuclear
fusion
to an?
informed?’
prevents
conflicting
signal
settings
ESSENT representative?
How to describe this new pathological
condition (BMT)?
• Verification
• Communication
• Documentation
3
purposes from research
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Various Kinds of Modeling Purposes     
• Exploration
• Decision
• Optimization
• Specification
• Realization
4
‘what are the options ?’
‘which of these is the best option’
‘what
is ways
the best
for these
In what
canvalue
we connect
A to B?
‘what
external
properties
should
some
Which
of these is the best material to
parameter(s)?’
‘what
internal
properties should some
artefact
have
?’
choose
fortime,
component
X?
‘what (real
online) interventions
artefact
have?’
What
should
dimensions
of ‘X be?
‘how
trainee
learn system,
to do X?
should
thisasystem
do?’
Whatdoes
should
a the
(machine,
What should a blueprint (recipe, algorithm), to
component,
process,
… ) do?
How
a driving
simulator
improve
Whatcan
should
a smart
–
realize
this artefact,
lookthermostat
like?
driver’s
alertness?
automatic
pilot – pacemaker … do?
• Steering and Control
• Training
purposes from design
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Various Kinds of Modeling Purposes     
Q: Why is purpose important for the
modeler?
A: The answer to
any question in
modeling will be: ‘check your purpose’
almost
5
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: material / immaterial     
6
19th century brain model, Boerhaave Museum
• can be construct e.g., scale model
(wind tunnel, towing tank)
20th century brain model (Wang & Chiew, UofCalgary, 2010)
• material representation is
irrelevant (ink+paper, computer
screen, …)
• can be natural object (e.g. guinee
pig for medical purposes)
a material object requires an immaterial story to become a model
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: static / dynamic     
7
• loads (or other quantities) are
invariant in time
• loads (or other quantities) vary in time
• no causality
• causality: cause precedes
effect
• d/dt doesn’t matter
• d/dt may matter
a dynamical model typically assumes a statical model first
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: continuous / discrete     
8
• Measuring rather than
counting
• Counting rather than
measuring
• Quantities have full range
of values (no holes, no
jumps: real numbers)
• Quantities have countably
many values: integers
• Limits, functions &
calculus (d/dt, d/dx, dx, …)
• Examples: smooth
mechanical & chemical
processes, fields, waves,
circuits, averages, …
sampling turns
• Newton’s cradle: a simple
machanical device showing
the interplay between
continuous and discrete
continuous
into a
motionbehaviour
behavior
• Enumeration, graphs &
algorithms (t:=t+1, , …)
• Examples: jumpy or
singular mechanical &
chemical processes,
particles, business
processes, …
series of discrete ones
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: numerical / symbolic     
9
• manipulate numbers:
3*5+6*3=3*(5+6)=33
• manipulate symbols:
ab+ca=a(b+c) = ?
• one expression accounts
for 1 single instance
• one formula represents 
numeric expressions but no
outcome
• computers can do
numbers better than
symbols
• people can do symbols better
than numbers
• approximations, inc.
round-off errors (may
explode)
• exact, but symbolic
manipulation is not always
possible (Mathematica)
• continuum problems need
sampling
• Various number systems (natural,
rational, real or complex), are all
invented by mathematicians. Yet,
they somehow appear useful to
make claims about the real world.
• continuum problems: do
without sampling
eventually, numerical outcomes are typically needed anyway
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: geometric / non geometric     
10
intuitions
relating
to perception of space (Euclid):
geometry
may mean:
•continuous geometry (mechanical engineering,
• location
physics)
two locations can be close or
• distance
•sampled geometry distant
(civil engineering, BMT,
shortest path between two points
mechanical engineering)
• straight
•discrete geometrya(electronics,
straight pathurban studies,
games,
…)
• line
(segment)
lines that intersect in 
• parallel
• direction
• angle
what parallel lines have in common
to measure difference between
• ‘Geometry’ is the language to
talk about situations where
directions spatial configurations are
relevant.
• … if these notions matter  geometric modeling
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: deterministic / stochastic     
11
• Many mechanisms contain
uncertainty
• Uncertainty may stay, even with more
accurate measuring
• Repetition: ensemble
•(e.g., 1000 dice throws)
• Observations on ensemble:
aggregated quantities
•(e.g., averaging)
• … if these notions matter 
stochastic modeling
• Drawing by Leonardo Da Vinci. Although the
patterns of water are determined by stochastic
processes, there are emergent regular patterns
such as swirls and eddies. Advanced models
serve to describe their behavior in statistical
terms.
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: calculating / reasoning     
12
• number-valued
quantities (numbers):
1,2,3,4,…
• truth-valued quantities
(propositions): TRUE, FALSE
• operations: AND, OR, IMPLIES, …
• operations: +,-,*,/
• outcome: numbers
• calculating with
expressions
•
• Some see logic as a model for
natural language. Natural
reasoning seems to follow
applications: physics, certain rules; logic tries to
formulate and analyse these
chemistry, electrical
rules, and even to propose
alternative ones.
engineering
• outcome: the truth or non-truth
of a proposition
• deriving consequences (e.g.,
database queries, expert
systems)
• applications: ICT, business
engineering
logic: connecting and founding both calculating and reasoning
A Core Course on Modeling
Week 1- No Model Without a Purpose
     Modeling Approaches: black box/ glass box     
13
• only known what comes out –
perhaps manipulate inputs
• idea of the inner causality
connecting inputs to outputs
• model follows from finding
patterns in data
• model follows by proposing
math. representations for
causal mechanisms
• techniques: data fitting,
extrapolation, data mining
• techniques: postulating
functional relations,
• typically empirical research• Illusionis David Blaine: locked equations, algorithms
(ID, IE & IS, urban studies, up for 44 days in a glass box
without food: ‘this is my most
BMT)
• typically simulation (physics,
difficult stunt ever’
mechanical engineering,
BMT)
black glass: postulate model based on data; fit parameters to data
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
14
define
context  initial problem
conceptualize
initial problem  conceptual model
formalize
conceptual model  formal model
execute
conclude
formal model  result
result  resolve initial problem?
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
define
conceptualize
formalize
execute
conclude
sometimes, all
modeling phases
may be skipped
15
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
A geographic map and/or a compass are examples
define
of conceptual models that may help to solve
problems without further need for formal
manipulations.
conceptualize
formalize
execute
conclude
sometimes, the
formal phases
may be skipped
16
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
define
formulate
purpose
conceptualize
• What problem are we
solving?
• What context?
formalize
• What purpose?
execute
• What will be done with
the results?
conclude
17
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
define
• What entities do we
consider?
formulate
purpose
conceptualize
formalize
execute
conclude
18
identify
choose
entities
relations
• What properties do we
have per entity?
• What qualitative relations
do these entities have?
• What do we already
know about the values of
properties?
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
purpose
conceptualize
formalize
identify
choose
entities
relations
obtain
formalize
values
relations
19
• Which properties have
known values (and which
not)?
• How do we obtain
(measure?) the required
values?
execute
• Which properties do we
need to know?
conclude
• How do translate relations
to formal relations?
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
• What can we / must we
do with the model?
formulate
define
purpose
conceptualize
formalize
execute
conclude
20
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
• How can we do that?
• What result do we get
out?
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
• In which context should
we present the result?
formulate
define
purpose
conceptualize
formalize
execute
conclude
21
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
• What presentation is
appropriate?
• What does the result
mean?
• What further conclusions
can we draw from it?
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
22
formulate
define
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
reflecting
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
23
Right problem?
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
(problem validation)
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
24
Right problem?
purpose
conceptualize
identify
choose
entities
relations
(problem
validation)
Right concepts?
(concepts validation)
formalize
execute
conclude
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
25
Right problem?
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
(problem
validation)
Right concepts?
(Right
concepts
validation)
model?
(model verification)
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
26
Right problem?
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
(problem
validation)
Right concepts?
(Right
concepts
validation)
model?
(Right
modeloutcome?
verification)
(outcome verification)
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
27
Right problem?
purpose
conceptualize
formalize
execute
conclude
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
(problem
validation)
Right concepts?
(Right
concepts
validation)
model?
(Right
modeloutcome?
verification)
(outcome verification)
Right answer?
(answer verification)
A Core Course on Modeling
Week 1- No Model Without a Purpose
    The modeling process    
formulate
define
define
identify
choose
entities
relations
conceptualize
obtain
conceptualize
values
formalize
execute
formulate
purpose
operate
model
present
formalize
result
conclude
execute
conclude
purpose
formalize
identify
choose
relations
entities
obtain
relations
result
interpret
obtain
result
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
28
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
• explore: ‘How
should we
illuminate a
motorway?’
• decide: ‘Shall we
use LED or gas
discharge?
• optimize: ‘what is
the best height –
distance ratio?’
• verify: ‘is adaptive
possible?’
29
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
• What sort of entities do
we need (cars, road,
lanterns …)?
• What properties of these
entities do we need
(speed, amount, height,
…)
30
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
• What relations between
properties come into play
(e.g., light reflects on the
road)?
31
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
• Do we need
measurements (e.g.,
traffic statistics)?
• How accurate do we
need these values?
• Can we lump /
average them ?
32
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
• What formal relations
do we need?
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
• What does depend on
what?
• Can we give
mathematical
expressions?
• If not, what else ?
• What are we going to
do with the math.
expressions?
33
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
• Is a simulation
necessary / helpful / fun
/ superfluous /
misleading?
• Is performance an
issue?
• How to deal with the
precision / effort
balance?
This example deals with
a calculation-type
model. For reasoningtype models, somewhat
different questions may
apply
34
Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
How certain is
our answer?
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
• How stable is
our answer?
35
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
• Who will be using the
(numeric) outcome?
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
• How will the outcome
be used?
• What is a meaningful
format?
• Is there need for
interaction?
• How to show any
uncertainties?
36
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
• Who should do the
interpretation?
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
• What are the
consequences of the
outcome?
37
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
Right problem?
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
(problem validation)
38
• Are we asking the right
question?
•does our effort
balance with the
benefits?
•are we wellequipped to tackle
this problem?
•has the problem
been tackled
before?
•are there related
problems?
•are there alternative
formulations?
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
Right concepts?
39
• Do we take the right
things into account?
(concepts validation)
•We didn’t talk about
maintenance, is that
OK?
•We did not consider
the relation between
cars, is that OK?
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
• What simple cases can
you think of?
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
40
•no traffic at all
Right model?
(model verification)
•no adaptivity at all
•what traffic density
gives 0% energy
reduction?
• Is there ground truth
data?
• Are there independent
models?
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
• Are results in
correspondence with
assumptions in the
model?
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
conceptualize
formalize
execute
conclude
result
41
Right outcome?
(outcome verification)
Example:
in some design
result
disciplines, there is a ‘6’attitude: irrespective of the
problem context,
probabilities should be
better than 99,99966%
• Are accuracy and
stability sufficient?
• Do we need to REFINE
the model?
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
formulate
define
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
Right answer?
(answer verification)
42
• To what extent does
the presented and
interpreted answer,
after the formal
outcome has been
mappend back to the
problem, really solve
the problem?
A Core Course on Modeling
Week 1- No Model Without a Purpose
    Example    
• What went really well?
formulate
define
43
purpose
identify
choose
entities
relations
obtain
formalize
values
relations
operate
obtain
model
result
present
interpret
result
result
conceptualize
formalize
execute
conclude
• How do we
consolidate?
• What went not so well?
• How can we improve?
after the party…
• What lessons did we
learn?
• take influence of remote lamp
posts into account
• 1-D approximation to the 2-D
model (ignore road width)
A Core Course on Modeling
Week 1- No Model Without a Purpose
   Summary    
44
• A model  clearly defined purpose;
• purposes are: explanation, prediction (two cases!), compression, abstraction, unification, communication,
documentation, analysis, verification, exploration, decision, optimization,specification, realization, training,
steering and control.
• Modeling dimensions:
•material – immaterial: does the model have a physical component?
•static - dynamic: does time play a role?
•continuous - sampled - discrete: 'counting' or 'measuring'?
•numeric - symbolic: manipulating numbers or expressions?
•geometric - non-geometric: do features from 2D or 3D space play a role?
•deterministic - stochastic: does
probability
play a role?
after
the party…
•calculating - reasoning: rely on numbers or on propositions?
•black box - glass box: start from data or from causal mechanisms?
• Modeling is a process involving 5 stages:
•define: establish the purpose
•conceptualize: in terms of concepts, properties and relations
•formalize: in terms of mathematical expressions
•execute: running the model to obtain an outcome
•conclude: adequate presentation and interpretion