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

2. A Core Course on Modeling
Chapter 1- No Model Without a Purpose
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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… 2

3. A Core Course on Modeling
Chapter 2- The Art of Omitting
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Conceptual model consists of concepts, representing entities;
Concept: bundle of properties, each consisting of a name and a set of values (type):
Concepts + relations = conceptual model (entity-relationship graph)
establish concepts;
establish properties;
establish types of properties;
establish relations.
Quantities are 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 ordering or total ordering, interval scale, ratio scale;
Measuring =counting the number of units in the measured item.
Sets of units with fixed ratio: dimension is 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.) 3

4. A Core Course on Modeling
Chapter 3- Time for Change
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State = snapshot of a conceptual model at some time point;
State space = collection of all states;
Change = transitions between 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 exposed and hidden properties 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 recursive function Qi+1 = F(Qi , Qi-1 , Qi-2, …. , Pi , Pi-1 , Pi-2 , …) can be used to unroll a 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: continuous time, DE’s (examples: mass-spring system); 4

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 quantities drive this mechanism?
What is the qualitative behavior 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 Wizard can help finding appropriate fragments of mathematics;
the Function Selector can help finding an appropriate expression for a desired behavior;
wisdom of the crowds can help improve the accuracy of guessed values; 5

6. A Core Course on Modeling
Chapter 5-Roles of Quantities in a Functional Model 6
functional model helps distinguish input (choice) and output (from purpose);
Building a functional model as a graph shows roles of 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 lumping and penalty functions;
The distinction between requirements, desires, and wishes;
The notion of dominance to 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. 6

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 uncertainty because of different causes:
Differences between accuracy, precision, error;
Uncertainty  distributions of values rather than a single value (normal, uniform);
Confidence for black box models:
Common features of aggregation: average, standard deviation and correlation;
Validation of 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 analysis and the propagation of uncertainty in input data;
Sensitivity analysis to decide if a model should be improved. 7

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: Input or output side? Modeled system or stakeholders? Qualitative or 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. 8