A Core Course on Modeling

1
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)

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? ? Models that Everybody Knows ? ? ? ? ?
2

• Question
• Data, Measurements
• Calculations, Approximations
• Conclusion
• Consequences

• Question
• Data, Measurements
• Calculations, Approximations
• Conclusion
• Consequences

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? ? Various Kinds of Modeling Purposes ? ?
? ? ?
3

• Explanation
• Prediction (2)
• Compression
• Abstraction
• Unification
• Analysis
• Verification
• Communication
• Documentation

why, how comes Why do we sometimes see a
rainbow?
when When will fossile fuel end?
what , what if What is the effect of CO2
emission?
can this data be summarized in fewer data or
formula? Can GNP data show whether there is an
economic depression or not?
how to capture the essence of? How to describe
traffic as a fluid to understand congestions,
disregarding individual automobiles?
how to capture the essence of? How to describe
traffic and fluids in the same way to understand
shock waves?
can the forest be seen through the trees? Can
we understand why my Internet connection is
sometimes so slow?
is it true that ? (give argument) Is it true
that this railway signaling algorithm prevents
conflicting signal settings ?
how can a known audience be informed? How to
explain nuclear fusion to an ESSENT
representative?
how can an unknown audience be informed? How to
describe this new pathological condition (BMT)?
purposes from research
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? ? Various Kinds of Modeling Purposes ? ?
? ? ?
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• Exploration
• Decision
• Optimization
• Specification
• Realization
• Steering and Control
• Training

what are the options ? In what ways can we
connect A to B?
which of these is the best option Which of
these is the best material to choose for
component X?
what is the best value for these
parameter(s)? What should the dimensions of X be?
what external properties should some artefact
have ? What should a (machine, system,
component, process, ) do?
what internal properties should some artefact
have? What should a blueprint (recipe,
algorithm), to realize this artefact, look like?
what (real time, online) interventions should
this system do? What should a smart thermostat
automatic pilot pacemaker do?
how does a trainee learn to do X? How can a
driving simulator improve drivers alertness?
purposes from design
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? ? Various Kinds of Modeling Purposes ? ?
? ? ?
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• Q Why is purpose important for the modeler?
• A The answer to almost any question in modeling
  will be check your purpose

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? ? Modeling Approaches material /
immaterial ? ? ? ? ?
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19th century brain model, Boerhaave Museum
20th century brain model (Wang Chiew,
UofCalgary, 2010)

• can be construct e.g., scale model (wind tunnel,
  towing tank)
• can be natural object (e.g. guinee pig for
  medical purposes)

• material representation is irrelevant (inkpaper,
  computer screen, )

a material object requires an immaterial story to
become a model
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? ? Modeling Approaches static / dynamic ?
? ? ? ?
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• loads (or other quantities) are invariant in time
• no causality
• d/dt doesnt matter

• loads (or other quantities) vary in time
• causality cause precedes effect
• d/dt may matter

a dynamical model typically assumes a statical
model first
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? ? Modeling Approaches continuous /
discrete ? ? ? ? ?
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• Measuring rather than counting
• Quantities have full range of values (no holes,
  no jumps real numbers)
• Limits, functions calculus (d/dt, d/dx, ?dx,
  )
• Examples smooth mechanical chemical processes,
  fields, waves, circuits, averages,

• Counting rather than measuring
• Quantities have countably many values integers
• Enumeration, graphs algorithms (tt1, ?, )
• Examples jumpy or singular mechanical chemical
  processes, particles, business processes,

• Newtons cradle a simple machanical device
  showing the interplay between continuous and
  discrete motion behavior

sampling turns continuous behaviour into a series
of discrete ones
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? ? Modeling Approaches numerical /
symbolic ? ? ? ? ?
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• manipulate numbers 35633(56)33
• one expression accounts for 1 single instance
• computers can do numbers better than symbols
• approximations, inc. round-off errors (may
  explode)
• continuum problems need sampling

• manipulate symbols abcaa(bc) ?
• one formula represents ? numeric expressions but
  no outcome
• people can do symbols better than numbers
• exact, but symbolic manipulation is not always
  possible (Mathematica)
• continuum problems do without 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.

eventually, numerical outcomes are typically
needed anyway
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? ? Modeling Approaches geometric / non
geometric ? ? ? ? ?
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• geometry may mean
• continuous geometry (mechanical engineering,
  physics)
• sampled geometry (civil engineering, BMT,
  mechanical engineering)
• discrete geometry (electronics, urban studies,
  games, )

• intuitions relating to perception of space
  (Euclid)
• location
• distance
• straight
• line (segment)
• parallel
• direction
• angle
• if these notions matter ? geometric modeling

• Geometry is the language to talk about
  situations where spatial configurations are
  relevant.

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? ? Modeling Approaches deterministic /
stochastic ? ? ? ? ?
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• 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.

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? ? Modeling Approaches calculating /
reasoning ? ? ? ? ?
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• number-valued quantities (numbers) 1,2,3,4,
• operations ,-,,/
• outcome numbers
• calculating with expressions
• applications physics, chemistry, electrical
  engineering

• truth-valued quantities (propositions) TRUE,
  FALSE
• operations AND, OR, IMPLIES,
• outcome the truth or non-truth of a proposition
• deriving consequences (e.g., database queries,
  expert systems)
• applications ICT, business engineering

• Some see logic as a model for natural language.
  Natural reasoning seems to follow certain rules
  logic tries to formulate and analyse these rules,
  and even to propose alternative ones.

logic connecting and founding both calculating
and reasoning
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? ? Modeling Approaches black box/ glass
box ? ? ? ? ?
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• only known what comes out perhaps manipulate
  inputs
• model follows from finding patterns in data
• techniques data fitting, extrapolation, data
  mining
• typically empirical research (ID, IE IS, urban
  studies, BMT)

• idea of the inner causality connecting inputs to
  outputs
• model follows by proposing math. representations
  for causal mechanisms
• techniques postulating functional relations,
  equations, algorithms
• typically simulation (physics, mechanical
  engineering, BMT)

• Illusionis David Blaine locked up for 44 days in
  a glass box without food this is my most
  difficult stunt ever

black ?glass postulate model based on data fit
parameters to data
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
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context ? initial problem
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
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sometimes, all modeling phases may be skipped
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
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A geographic map and/or a compass are examples of
conceptual models that may help to solve problems
without further need for formal manipulations.
sometimes, the formal phases may be skipped
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
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• What problem are we solving?
• What context?
• What purpose?
• What will be done with the results?

formulate purpose
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
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• What entities do we consider?
• What properties do we have per entity?
• What qualitative relations do these entities
  have?
• What do we already know about the values of
  properties?

formulate purpose
identify entities
choose relations
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
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• Which properties have known values (and which
  not)?
• How do we obtain (measure?) the required values?
• Which properties do we need to know?
• How do translate relations to formal relations?

formulate purpose
identify entities
choose relations
obtain values
formalize relations
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
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• What can we / must we do with the model?
• How can we do that?
• What result do we get out?

formulate purpose
identify entities
choose relations
obtain values
formalize relations
operate model
obtain result
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
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• In which context should we present the result?
• What presentation is appropriate?
• What does the result mean?
• What further conclusions can we draw from it?

formulate purpose
identify entities
choose relations
obtain values
formalize relations
operate model
obtain result
present result
interpret result
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
22
formulate purpose
identify entities
choose relations
obtain values
formalize relations
r e f l e c t i n g
operate model
obtain result
present result
interpret result
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
23
formulate purpose
identify entities
choose relations
obtain values
formalize relations
operate model
obtain result
present result
interpret result
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
24
formulate purpose
identify entities
choose relations
obtain values
formalize relations
operate model
obtain result
present result
interpret result
25
A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
25
formulate purpose
identify entities
choose relations
obtain values
formalize relations
operate model
obtain result
present result
interpret result
26
A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
26
formulate purpose
identify entities
choose relations
obtain values
formalize relations
operate model
obtain result
present result
interpret result
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
27
formulate purpose
identify entities
choose relations
obtain values
formalize relations
operate model
obtain result
present result
interpret result
28
A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? The modeling process ? ? ? ?
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• 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?

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• What sort of entities do we need (cars, road,
  lanterns )?
• What properties of these entities do we need
  (speed, amount, height, )

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• What relations between properties come into play
  (e.g., light reflects on the road)?

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• Do we need measurements (e.g., traffic
  statistics)?
• How accurate do we need these values?
• Can we lump / average them ?

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• What formal relations do we need?
• What does depend on what?
• Can we give mathematical expressions?
• If not, what else ?
• What are we going to do with the math.
  expressions?

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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This example deals with a calculation-type model.
For reasoning-type models, somewhat different
questions may apply

• Is a simulation necessary / helpful / fun /
  superfluous / misleading?
• Is performance an issue?
• How to deal with the precision / effort balance?

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Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• How certain is our answer?
• How stable is our answer?

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• Who will be using the (numeric) outcome?
• How will the outcome be used?
• What is a meaningful format?
• Is there need for interaction?
• How to show any uncertainties?

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• Who should do the interpretation?
• What are the consequences of the outcome?

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• Are we asking the right question?
• does our effort balance with the benefits?
• are we well-equipped to tackle this problem?
• has the problem been tackled before?
• are there related problems?
• are there alternative formulations?

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• Do we take the right things into account?
• We didnt talk about maintenance, is that OK?
• We did not consider the relation between cars, is
  that OK?

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• What simple cases can you think of?
• no traffic at all
• no adaptivity at all
• what traffic density gives 0 energy reduction?
• Is there ground truth data?
• Are there independent models?

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• Are results in correspondence with assumptions in
  the model?
• Are accuracy and stability sufficient?
• Do we need to REFINE the model?

Example in some design disciplines, there is a
6?-attitude irrespective of the problem
context, probabilities should be better than
99,99966
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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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?

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A Core Course on Modeling
Week 1- No Model Without a Purpose
? ? ? ? Example ? ? ? ?
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• What went really well?
• How do we consolidate?
• What went not so well?
• How can we improve?
• What lessons did we learn?
• take influence of remote lamp posts into account
• 1-D approximation to the 2-D model (ignore road
  width)

after the party
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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?
• 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

after the party