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      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

3 A Core Course on Modeling      Various Kinds of Modeling Purposes      Explanation Prediction (2) Compression Abstraction Unification Analysis Verification Communication Documentation Week 1- No Model Without a Purpose ‘why…’, ‘how comes …’ ‘Why do we sometimes see a rainbow?’ ‘when …’ ‘When will fossile fuel end?’ ‘what …’, ‘what if …’ ‘What is the effect of CO 2 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      Various Kinds of Modeling Purposes      Exploration Decision Optimization Specification Realization Steering and Control Training Week 1- No Model Without a Purpose ‘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      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’ Week 1- No Model Without a Purpose

6 A Core Course on Modeling      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, …) Week 1- No Model Without a Purpose 19th century brain model, Boerhaave Museum 20th century brain model (Wang & Chiew, UofCalgary, 2010) a material object requires an immaterial story to become a model

7 A Core Course on Modeling      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 matter a dynamical model typically assumes a statical model first Week 1- No Model Without a Purpose

8 A Core Course on Modeling 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      Modeling Approaches: continuous / discrete      Week 1- No Model Without a Purpose

9 A Core Course on Modeling 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      Week 1- No Model Without a Purpose

10 A Core Course on Modeling 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      Week 1- No Model Without a Purpose

11 A Core Course on Modeling 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     deterministicstochastic Week 1- No Model Without a Purpose

12 A Core Course on Modeling 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      Week 1- No Model Without a Purpose

13 A Core Course on Modeling 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      Week 1- No Model Without a Purpose

14 A Core Course on Modeling     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? Week 1- No Model Without a Purpose

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

16 A Core Course on Modeling     The modeling process     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. Week 1- No Model Without a Purpose

17 A Core Course on Modeling     The modeling process     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 Week 1- No Model Without a Purpose

18 A Core Course on Modeling     The modeling process     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 Week 1- No Model Without a Purpose

19 A Core Course on Modeling     The modeling process     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 relations formalize relations Week 1- No Model Without a Purpose

20 A Core Course on Modeling     The modeling process     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 relations obtain values obtain values formalize relations formalize relations operate model operate model obtain result obtain result Week 1- No Model Without a Purpose

21 A Core Course on Modeling     The modeling process     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 values formalize relations formalize relations operate model operate model obtain result obtain result present result present result interpret result interpret result Week 1- No Model Without a Purpose

22 A Core Course on Modeling     The modeling process     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 r e f l e c t i n g Week 1- No Model Without a Purpose

23 A Core Course on Modeling     The modeling process     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? (problem validation) Week 1- No Model Without a Purpose

24 A Core Course on Modeling     The modeling process     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? (problem validation) Week 1- No Model Without a Purpose Right concepts? ( concepts validation)

25 A Core Course on Modeling     The modeling process     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 Week 1- No Model Without a Purpose Right problem? (problem validation) Right concepts? ( concepts validation) Right model? ( model verification )

26 A Core Course on Modeling     The modeling process     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 Week 1- No Model Without a Purpose Right problem? (problem validation) Right concepts? ( concepts validation) Right model? ( model verification ) Right outcome? (outcome verification)

27 A Core Course on Modeling     The modeling process     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 Week 1- No Model Without a Purpose Right problem? (problem validation) Right concepts? ( concepts validation) Right model? ( model verification ) Right outcome? (outcome verification) Right answer? ( answer verification ) Right answer? ( answer verification )

28 A Core Course on Modeling     The modeling process     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 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 Week 1- No Model Without a Purpose

29 A Core Course on Modeling     Example     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 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?’ Week 1- No Model Without a Purpose

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

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

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

33 A Core Course on Modeling 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 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     Week 1- No Model Without a Purpose

34 A Core Course on Modeling 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 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     Week 1- No Model Without a Purpose

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

36 A Core Course on Modeling 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 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     Week 1- No Model Without a Purpose

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

38 A Core Course on Modeling 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? (problem validation) 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     Week 1- No Model Without a Purpose

39 A Core Course on Modeling 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     Week 1- No Model Without a Purpose

40 A Core Course on Modeling 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     Week 1- No Model Without a Purpose

41 A Core Course on Modeling 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 outcome? ( outcome verification) 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     Week 1- No Model Without a Purpose

42 A Core Course on Modeling 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 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     Week 1- No Model Without a Purpose

43 A Core Course on Modeling 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 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     Week 1- No Model Without a Purpose

44 A Core Course on Modeling after the party…    Summary     Week 1- No Model Without a Purpose 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