A core course on Modeling kees van Overveld

1. A core course on Modelingkees van Overveld Week-by-week summary

2. A Core Course on Modeling Chapter 1- No Model Without a Purpose   Summary 2 • A model  clearly defined purpose; • purposes are: explanation, prediction (two cases!), compression, abstraction, unification, communication, documentation, analysis, verification, exploration, decision, optimization,specification, realization, steering and control. • Modeling dimensions: • static - dynamic: does time play a role? • continuous - 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: (often involves running a computer program) • conclude: adequate presentation and interpretion after the party…

3. A Core Course on Modeling Chapter 2- The Art of Omitting    Summary     3 • Conceptual model consists of concepts, representing entities; • Concept: bundle of properties, each consisting of a name and aset of values (type): • Concepts + relations = conceptual model (entity-relationship graph) • establish concepts; • establish properties; • establish types of properties; • establish relations. • Quantitiesare properties, disregarding the concept they are a property of; • Mathematical operations on quantities: what ordering is offered by the quantity’s type? • Nominal(no order), partial orderingor total ordering, interval scale, ratio scale; • Measuring=countingthe number of units in the measured item. • Sets of units with fixed ratio: dimensionis an equivalence class on units; • Using dimensions, the form of a mathematical relationships can often be checked or even derived (dimension anlysis or dimension synthesis.)

4. A Core Course on Modeling Chapter 3- Time for Change    Summary     4 • State= snapshot of a conceptual model at some time point; • State space= collection of all states; • Change = transitionsbetween states; state chart= graph; nodes (states) and arrows (transitions); • Behavior= path through state space; • State space explosion: number of states is huge for non trivial cases • Projection: given a purpose, distinguish exposedand hiddenproperties or value sets; • Multiple flavors of time: • partially ordered time, e.g. specification and verification; • totally ordered time, e.g. prediction, steering and control; • For totally ordered time, a recursivefunction Qi+1 = F(Qi , Qi-1 , Qi-2, …. , Pi , Pi-1 , Pi-2 , …) can be used to unrolla behavior • arbitrary intervals: just evaluate recursive functions • equal intervals: sometimes closed form evaluation is possible (e.g.,: periodic financial transactions); • equal, small intervals: approximation, sampling & sampling error (examples: moving point mass, … ); aliasing • infinitesimal intervals: continuoustime, DE’s (examples: mass-spring system);

5. A Core Course on Modeling Chapter 4-The Function of Functions 5 • Conceptual model formal model : not in a formally provable correct way; • Appropriate naming • Structure • Chain of dependencies: the formal model as a directed acyclic graph; • What mechanism? • What quantitiesdrive this mechanism? • What is the qualitativebehavior of the mechanism? • What is the mathematical expression to describe this mechanism? • To-do-list: all intermediate quantities are found and elaborated in turn; • Formation of mathematical expressions: • dimensional analysis mathematical expressions, e.g in the case of proportionality • the Relation Wizardcan help finding appropriate fragments of mathematics; • the Function Selectorcan help finding an appropriate expression for a desired behavior; • wisdom of the crowdscan help improve the accuracy of guessed values;

6. A Core Course on Modeling Chapter 5-Roles of Quantities in a Functional Model 6 • functional modelhelps distinguish input (choice) and output (from purpose); • Building a functional model as a graph shows rolesof quantities. These are: • Cat.-I: free to choose; • Models for (design) decision support: the notion of design space; • Choice of cat.-I quantities: no dependency-by-anticipation; • Cat.-II: represents the intended output; • The advantages and disadvantages of lumpingand penalty functions; • The distinction between requirements, desires, and wishes; • The notion of dominanceto express multi-criteria comparison; Pareto front; • Cat.-III: represents constraints from context; • Cat.-IV: intermediate quantities; • For optimization: use evolutionary approach; • Approximate the Pareto front using the SPEA algorithm; • Local search can be used for post-processing.

7. A Core Course on Modeling Chapter 6-Models and Confidence 7 • Validation and verification: is this the right model / is the model right? • Modeling involves uncertaintybecause of different causes: • Differences between accuracy, precision, error; • Uncertainty distributionsof values rather than a single value (normal, uniform); • Confidence for black box models: • Common features of aggregation: average, standard deviationand correlation; • Validationof a black box model: • Residual error: how much of the behavior of the data is captured in the model? • Distinctiveness: how well can the model distinguish between different modeled systems? • Common sense: how plausible are conclusions, drawn from a black box model? • Confidence for glass box models: • Structural validity: do we believe the behavior of the mechanism inside the glass box? • Quantitative validity: what is the numerical uncertainty of the model outcome? • Sensitivity analysisand the propagation of uncertainty in input data; • Sensitivity analysis to decide if a model should be improved.

8. A Core Course on Modeling Chapter 7-A working model – and then? 8 • Leading question: to what extent has the initial problem been solved? • Taxonomy of criteria for modeling: Inputor outputside? Modeled systemor stakeholders? Qualitativeor quantitative? • Resulting criteria: • Genericity: how many different modeled systems can we handle? • Scalability: how large can the size of the problem be? • Specialization: how much should the intended audience know? • Audience (size): how large can the intended audience be? • Convincingness: how plausible are the assumptions? • Distinctiveness: e.g., how accurate, how certain, how decisive can the model outcome be? • Surprise: to what extent can the model outcome give new insight? • Impact: how big can the consequences of the model outcome be? • Criteria for modeling quality are related to purposes.