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)

2. 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

3. 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

4. A Core Course on Modeling Week 1- No Model Without a Purpose    Various Kinds of Modeling Purposes  4 • 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

5. A Core Course on Modeling Week 1- No Model Without a Purpose    Various Kinds of Modeling Purposes  5 Q: Why is purpose important for the modeler? A: The answer to almost any question in modeling will be: ‘check your purpose’

6. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches: material / immaterial  6 19th centurybrain model, Boerhaave Museum 20th centurybrain 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 (ink+paper, computer screen, …) a material object requires an immaterial story to become a model

7. 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 • no causality • d/dt doesn’t 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

8. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches: continuous / discrete  8 • 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 behavior sampling turns continuous behaviour into a series of discrete ones

9. A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches: numerical / symbolic  9 • 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 • 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 • 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

10. 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 A Core Course on Modeling Week 1- No Model Without a Purpose   Modeling Approaches: geometric / non geometric  10 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.

11. 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.

12. 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,… • 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

13. 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 • 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

14. define conceptualize initial problem  conceptual model formalize conceptual model  formal model execute formal model  result conclude result  resolve initial problem? A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  14 context  initial problem

15. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  15 sometimes, all modeling phases may be skipped

16. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  16 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

17. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  17 • What problem are we solving? • What context? • What purpose? • What will be done with the results? formulate purpose

18. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  18 • 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

19. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  19 • 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

20. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  20 • 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

21. define conceptualize formalize execute conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  21 • 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

22. define conceptualize formalize execute conclude 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

23. define Right problem? (problem validation) conceptualize formalize execute conclude 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

24. define Right concepts? (concepts validation) Right problem? (problem validation) conceptualize formalize execute conclude 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. define Right problem? (problem validation) Right concepts? (concepts validation) conceptualize Right model? (model verification) formalize execute conclude 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. define Right concepts? (concepts validation) Right problem? (problem validation) conceptualize Right model? (model verification) formalize Right outcome? (outcome verification) execute conclude 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

27. define Right concepts? (concepts validation) Right problem? (problem validation) conceptualize Right model? (modelverification) formalize Right outcome? (outcome verification) execute Right answer? (answer verification) conclude 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. define formulate purpose define formulate purpose identify entities conceptualize conceptualize choose relations identify entities choose relations obtain values formalize relations formalize formalize obtain values formalize relations operate model obtain result execute present result interpret result conclude operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   The modeling process  28

29. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  29 • 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?’

30. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  30 • What sort of entities do we need (cars, road, lanterns …)? • What properties of these entities do we need (speed, amount, height, … )

31. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  31 • What relations between properties come into play (e.g., light reflects on the road)?

32. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  32 • Do we need measurements (e.g., traffic statistics)? • How accurate do we need these values? • Can we lump / average them ?

33. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  33 • 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?

34. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  34 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?

35. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize operate model obtain result execute present result interpret result conclude Core Course on Modeling Week 1- No Model Without a Purpose   Example  35 How certain is our answer? • How stable is our answer?

36. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  36 • 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?

37. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  37 • Who should do the interpretation? • What are the consequences of the outcome?

38. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize Right problem? (problem validation) operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  38 • 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?

39. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize Right concepts? (concepts validation) operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  39 • 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?

40. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize Right model? (model verification) operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  40 • 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?

41. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize Right outcome? (outcome verification) operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  41 • 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%

42. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize Right answer? (answer verification) operate model obtain result execute present result interpret result conclude 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?

43. define formulate purpose identify entities conceptualize choose relations obtain values formalize relations formalize operate model obtain result execute present result interpret result conclude A Core Course on Modeling Week 1- No Model Without a Purpose   Example  43 • 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…

44. 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…