1 A Core Course on Modeling Week 1- No Model Without a Purpose Contents Models that Everybody Knows Various Kinds of Modeling Purposes.

1

A Core Course on ModelingWeek 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)

2

A Core Course on Modeling

Models that Everybody Knows

• Question

• Data, Measurements

• Calculations, Approximations

• Conclusion

• Consequences

• Question

• Data, Measurements

• Calculations, Approximations

• Conclusion

• Consequences

Week 1- No Model Without a Purpose

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Various Kinds of Modeling Purposes • 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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Various Kinds of Modeling Purposes • 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 driver’s alertness?

purposes from design

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Various Kinds of Modeling Purposes

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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Modeling Approaches: material / immaterial

• 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 (ink+paper, computer screen, …)


19th century brain model, Boerhaave Museum19th century brain model, Boerhaave Museum20th century brain model (Wang & Chiew, UofCalgary, 2010)20th century brain model (Wang & Chiew, UofCalgary, 2010)

a material object requires an immaterial story to become a model

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Modeling Approaches: static / dynamic

• loads (or other quantities) are invariant in time

• no causality

• d/dt doesn’t matter

• loads (or other quantities) vary in time

• causality: cause precedes effect

• d/dt may mattera dynamical model typically assumes a statical model first


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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 (t:=t+1, , …)

• Examples: jumpy or singular mechanical & chemical processes, particles, business processes, …

• Newton’s cradle: a simple machanical device showing the interplay between continuous and discrete motion behaviorsampling turns continuous behaviour into a series of discrete ones

Modeling Approaches: continuous / discrete


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• manipulate numbers: 3*5+6*3=3*(5+6)=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: ab+ca=a(b+c) = ?

• 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

Modeling Approaches: numerical / symbolic


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two locations can be close or distant

shortest path between two points

a straight path

lines that intersect in

what parallel lines have in common

to measure difference between directions

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

intuitions relating to perception of space (Euclid):

• location

• distance

• straight

• line (segment)

• parallel

• direction

• angle

• … if these notions matter geometric modeling

geometry may mean:

•continuous geometry (mechanical engineering, physics)

•sampled geometry (civil engineering, BMT, mechanical engineering)

•discrete geometry (electronics, urban studies, games, …)

Modeling Approaches: geometric / non geometric


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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.

Modeling Approaches: deterministic / stochastic


http://www.youtube.com/watch?v=1YjJqfL3vZQ

http://www.youtube.com/watch?feature=endscreen&v=PM7z_03o_kk&NR=1

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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

logic: connecting and founding both calculating and reasoning

• 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.

Modeling Approaches: calculating / reasoning


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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

Modeling Approaches: black box/ glass box


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The modeling process

define

conceptualize

conclude

execute

formalize

context initial problem

initial problem conceptual model

conceptual model formal model

formal model result

result resolve initial problem?


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define

conceptualize

conclude

execute

formalize sometimes, all modeling phases may be skipped


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define

conceptualize

conclude

execute

formalize sometimes, the formal phases may be skipped

A geographic map and/or a compass are examples of conceptual models that may help to solve problems without further need for formal manipulations.


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define

conceptualize

conclude

execute

formalize

• What problem are we solving?

• What context?

• What purpose?

• What will be done with the results?

formulate

purpose

formulate

purpose


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define

conceptualize

conclude

execute

formalize

• 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

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

relations


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define

conceptualize

conclude

execute

formalize

• 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

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

relations

obtain

values

obtain

values

formalize

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formalize

relations


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define

conceptualize

conclude

execute

formalize

• What can we / must we do with the model?

• How can we do that?

• What result do we get out?

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

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obtain

values

obtain

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formalize

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define

conceptualize

conclude

execute

formalize

• 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

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

relations

obtain

values

obtain

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formalize

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formalize

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operate

model

operate

model

obtain

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obtain

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present

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present

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interpret

result

interpret

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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

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choose

relations

choose

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obtain

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obtain

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formalize

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present

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present

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r e f l e c t i n g


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

relations

obtain

values

obtain

values

formalize

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formalize

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operate

model

operate

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obtain

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obtain

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present

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present

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interpret

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interpret

result

Right problem?

(problem validation)


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

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obtain

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obtain

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formalize

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operate

model

operate

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obtain

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obtain

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present

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present

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Right problem?



Right concepts?

(concepts validation)

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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

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obtain

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obtain

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formalize

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formalize

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operate

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operate

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obtain

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obtain

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present

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present

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interpret

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result


Right problem?

(problem validation)Right concepts?

(concepts validation)Right model?

(model verification)

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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

relations

obtain

values

obtain

values

formalize

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formalize

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operate

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operate

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obtain

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obtain

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present

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present

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interpret

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interpret

result


Right problem?



(model verification)Right outcome?

(outcome verification)

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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

relations

obtain

values

obtain

values

formalize

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formalize

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operate

model

operate

model

obtain

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obtain

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present

result

present

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interpret

result

interpret

result


Right problem?



(model verification)Right outcome?


Right answer?Right answer?

((answer verificationanswer verification))

Right answer?Right answer?

((answer verificationanswer verification))

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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

relations

obtain

values

obtain

values

formalize

relations

formalize

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operate

model

operate

model

obtain

result

obtain

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present

result

present

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interpret

result

interpret

result

define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

relations

obtain

values

obtain

values

formalize

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formalize

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operate

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Example

define

conceptualize

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execute

formalize

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result

• 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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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

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relations

choose

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obtain

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operate

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obtain

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obtain

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present

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present

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interpret

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interpret

result

• What sort of entities do we need (cars, road, lanterns …)?

• What properties of these entities do we need (speed, amount, height, … )

Example


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define

conceptualize

conclude

execute

formalize

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formulate

purpose

identify

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identify

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relations

choose

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result

• What relations between properties come into play (e.g., light reflects on the road)?

Example


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

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relations

choose

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operate

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interpret

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result

• Do we need measurements (e.g., traffic statistics)?

• How accurate do we need these values?

• Can we lump / average them ?

Example


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

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relations

choose

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obtain

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formalize

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operate

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obtain

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obtain

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present

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interpret

result

• 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?

Example


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

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values

obtain

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• 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 reasoning-type models, somewhat different questions may apply

Example


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Core Course on Modeling

define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

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obtain

values

obtain

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formalize

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formalize

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operate

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operate

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obtain

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obtain

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present

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interpret

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interpret

result

How certain is our answer?

• How stable is our answer?

Example


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

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obtain

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formalize

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formalize

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operate

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operate

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obtain

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obtain

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present

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present

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interpret

result

interpret

result

• 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?

Example


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

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obtain

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formalize

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operate

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obtain

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obtain

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present

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present

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interpret

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interpret

result

• Who should do the interpretation?

• What are the consequences of the outcome?

Example


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

relations

obtain

values

obtain

values

formalize

relations

formalize

relations

operate

model

operate

model

obtain

result

obtain

result

present

result

present

result

interpret

result

interpret

result

Right problem?


• 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?

Example


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

relations

obtain

values

obtain

values

formalize

relations

formalize

relations

operate

model

operate

model

obtain

result

obtain

result

present

result

present

result

interpret

result

interpret

result

Right concepts?

(concepts validation)

• Do we take the right things into account?

•We didn’t talk about maintenance, is that OK?

•We did not consider the relation between cars, is that OK?

Example


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

relations

obtain

values

obtain

values

formalize

relations

formalize

relations

operate

model

operate

model

obtain

result

obtain

result

present

result

present

result

interpret

result

interpret

result

Right model?

(model verification)

• 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?

Example


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

relations

obtain

values

obtain

values

formalize

relations

formalize

relations

operate

model

operate

model

obtain

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obtain

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present

result

present

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interpret

result

interpret

result

Right outcome?


• 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%

Example


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

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obtain

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formalize

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formalize

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operate

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operate

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obtain

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present

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present

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interpret

result

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Right answer?

(answer verification)

• To what extent does the presented and interpreted answer, after the formal outcome has been mappend back to the problem, really solve the problem?

Example


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define

conceptualize

conclude

execute

formalize

formulate

purpose

formulate

purpose

identify

entities

identify

entities

choose

relations

choose

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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…

Example


44


after the party…

Summary


• 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

1 A Core Course on Modeling Week 1- No Model Without a Purpose Contents Models that Everybody Knows Various Kinds of Modeling Purposes.

Documents

modeling modeling approaches

modeling models

core course

scale model wind tunnel

best material

material object

material immaterial

component x