# The Art of Devising Thumbnail Models'An Introduction to Modeling'

## from Problems to Numbers and Back

Title Description/
Lecture notes Introduction to Modeling 'From Problems to Numbers and Back' This is the complete document (Chapters 1 .. 7 + appendices) lecture notes
Glossary and Index to 'Introduction to Modeling' The lecture notes introduce much terminology. All terms are defined and illustrated with examples. These definitions and examples are compiled into a glossary / index, which is part of the lecture notes. it can also be accessed by means of an interactive web page. For easy use of the glossary / index, the web page can be accessed by means of auto-completion on a full text search engine. glossary
ACCEL This is the interactive modeling environment, including dozens of demo scipts and an extensive help-system, a tutorial and auxiliary tooling. ACCEL
ACCEL tutorial
Errata for the Video Lectures -- errata

# Chapter 1

No Model Without a Purpose
Introduction; Purposes; Dimensions of Modeling; the Modeling Process

lecture notes

#### Video Lecture 1 (Dutch)Video Lecture 1 (English)

No model without a purpose
Before making a model, you should ask yourself what that model is supposed to do for you.
studio lecture 1
We start with the invitation to develop the model of a yoyo.

#### Video Lecture 2 (Dutch)Video Lecture 2 (English)

Purposes for Models
You learn how to find out what the purpose of a model should be. You learn how to distinguish purposes, and you learn the terminology to name and distinguish purposes.
studio lecture 2
You find out what the purpose of something is by pretending that it does not exist: what do you miss then?
studio lecture 3
Three dimensions for purposes are:
• Is there something to choose? If so, what?
• Should there be a numerical outcome? If so, what should the number(s) represent?
• Should the model produce value or knowledge? What value, or what knowledge?
We give the terminology for the most frequently occurring purposes.

#### Video Lecture 3 (Dutch)Video Lecture 3 (English)

Dimensions for Distinguishing Models
Apart from their purposes, modeling methods themselves can also be distinguished. You learn a set of dimensions for distinguishing models, and you learn how to use these to formulate your modeling purpose more precisely.
studio lecture 4
The various dimensions of modeling are introduced and applied to a model for a concrete example.

#### Video Lecture 4 (Dutch)Video Lecture 4 (English)

The Modeling Process
The five phases of the modeling process are introduced.
studio lecture 5
The five phases of the modeling process are introduced.

#### Video Lecture 5 (Dutch)Video Lecture 5 (English)

The Street Illumination Example: the Definition Phase.
As a running example in this course, we elaborate the problem of making a model for street illumination. This lecture explains the purpose for the street illumination model.
studio lecture 6
The purpose and the dimensions of the street illumination example are given.

#### Homework Assignment Chapter 1

Assignment chapter 1

#### Example Elaboration Homework Assignment Chapter 1

Assignment chapter 1

#### Materials for 0LDB0 (modeling from scratch)

PowerPoint presentation week1

# Chapter 2

The Art of Omitting
The Conceptual Model; Concepts, Properties, Values; Quantities; Units and Dimensions

lecture notes

#### Video Lecture 6 (Dutch)Video Lecture 6 (English)

You learn the notions 'entity', 'concept', 'property', 'value' and 'relation'.
studio lecture 7
The terminology for conceptual modeling is introduced.

#### Video Lecture 7 (Dutch)Video Lecture 7 (English)

Notation I: Conventions for Uniquely Denoting Conceptual Models
You learn how to write down a conceptual model such that its meaning is uniquely determined.
voice-over lecture 1
This lecture explains the proper use of various types of brackets, colons and semi colons and their meaning.

#### Video Lecture 8 (Dutch)Video Lecture 8 (English)

Notation II: Graphical Notation
You learn how to draw schematic diagrams for conceptual models with blocks and arrows. You learn that some choices for grouping properties are more convenient than others, given the purpose.
voice-over lecture 2
This lecture gives the rules for well-formed diagrams for conceptual models.

#### Video Lecture 9 (Dutch)Video Lecture 9 (English)

Notation III: the Script Language of ACCEL
If your model should be processed by a computer, you need to obey certain rules for denotation. You learn these rules and how to apply them.
voice-over lecture 3
This lecture explains the denotation of quantities, concepts and properties in ACCEL.

#### Video Lecture 10 (Dutch)Video Lecture 10 (English)

Quantities and Order
You learn the notion of scale type, or 'level of ordering', for a quantity; you learn that, depending on the type of scale, a quantity may admit only limited kinds of mathematical operations .
studio lecture 8
The four levels of ordering are explained (nominal, ordinal, difference and ratio scales). Partial and total ordering are introduced, and the operations for various ordering levels are given.

#### Video Lecture 11 (Dutch)Video Lecture 11 (English)

Quantities and Units
You learn that computing with quantities always involves computing with units; various rules apply to what you can and cannot do with quantities given their units.
studio lecture 9
A value is a number multiplied with a unit. From this observation, rules follow that dictate what is permitted when performing mathematical operations on quantities.

#### Video Lecture 12 (Dutch)Video Lecture 12 (English)

Units in ACCEL
Units can be verified automatically, which can prevent serious mistakes in models that otherwise could go unnoticed. You learn how to verify units in a mathematical model using ACCEL.
voice-over lecture 4
This lectures explains how ACCEL can perform automatic checking of units.

#### Video Lecture 13 (Dutch)Video Lecture 13 (English)

Computing with Dimensions
By using dimensions and units, it is often possible to 'guess' the form of mathematical expressions.
studio lecture 10
Dimensions are introduced and explained. By means of some examples, the construction of expressions using dimensions is illustrated.
studio lecture 11
(empty).

#### Video Lecture 14 (Dutch)Video Lecture 14 (English)

The Street Illumination Example: the Conceptual Model
You learn the concepts, their properties and values and their relations that occur in the street illumination example.
studio lecture 12
The concepts for the street illumination example are chosen; the types are determined, and a graphical diagram for the relations is developed.

#### Homework Assignment Chapter 2

Assignment chapter 2 Notice: assignment 2 is an example only. In the 'example elaboration', below, it is fully elaborated. You only should work on assignment 1.

#### Example Elaboration Homework Assignment Chapter 2

Assignment chapter 2

#### Materials for 0LDB0 (modeling from scratch)

PowerPoint presentation week2

# Chapter 3

Time for Change
States and Transitions; Discrete Time Models, Sampling and Continuous Time Models

lecture notes

#### Video Lecture 15 (Dutch)Video Lecture 15 (English)

Time and Change
You are introduced to the notion of 'states' which form an adequate way to deal with a changing system.
studio lecture 13
States form a representation of a changing system.
studio lecture 14
The state space, which is a collection of all states of a process, is introduced; the notion of state space explosion is explained, and 'hiding' and 'exposing' as possible strategies to avoid state space explosion are discussed. A detailed example of a process with its permitted state transitions is elaborated.

#### Video Lecture 16 (Dutch)Video Lecture 16 (English)

Multiple Flavors of Time
In this lecture you learn that various modeling purposes require various ways to represent time: partially or totally ordered time, various forms of sampling, and continuous time.
studio lecture 15
The various flavors of time are introduced.

#### Video Lecture 17 (Dutch)Video Lecture 17 (English)

Time and Recursive Functions
For systems with totally ordered time, there is a generic approach to modeling time: using so called recursive functions. In this lecture you learn what recursive functions are, by means of an example for constructing a model for a simple system involving change over time.
studio lecture 16
Recursive functions for dealing with time are explained and illustrated with an example.

#### Video Lecture 18 (Dutch)Video Lecture 18 (English)

Dynamical Systems: Sampling vs. Analytic Approaches
Dynamic systems, described with continuous time, can be modeled either by means of sampling or - in rare cases - by analytic means. Both approaches are illustrated, and the advantages and disadvantages of each are explained.
voice-over lecture 5
A mass-spring system, with and without damping, is described both using sampling and using an analytic approach.

#### Video Lecture 19 (Dutch)Video Lecture 19 (English)

Elementary Examples of Dynamical Systems
Simple examples of dynamical systems are: a differentiator, an integrator, a damper and a delay. You learn how to model these systems in ACCEL.
voice-over lecture 6
This lecture contains the implementation of simple dynamic systems in ACCEL.

#### Video Lecture 20 (Dutch)Video Lecture 20 (English)

More Realistic Examples of Dynamical Systems
Using differentiators, integrators, dampers and delays, a variety of more or less realistic systems can be modeled. This lecture demonstrates a model for a moving cannon ball with air friction, for a combat, for an ecological system and for billiards.
voice-over lecture 7
This lecture contains the implementation of some more realistic dynamic systems in ACCEL.

#### Homework Assignment Chapter 3

Assignment chapter 3

#### Example Elaboration Homework Assignment Chapter 3

Assignment chapter 3

#### Materials for 0LDB0 (modeling from scratch)

PowerPoint presentation week3

# Chapter 4

The Function of Functions
Deriving Functional Models; the To-Do List; Expressions as Graphs

lecture notes

#### Video Lecture 21 (Dutch)Video Lecture 21 (English)

From Conceptual Model to Formal Model
You learn that a formal model is constructed from back to front, starting with the quantities you are interested in.
studio lecture 17
• short introduction on the necessity of translating a conceptual model to a formal model;
• the use of the to-do list by means of an example;
• using units to construct formulas;
• the notion that formulas can be represented by graphs.
studio lecture 18
You learn that the usefulness of the numerical outcome of a model can only be assessed in relation to the purpose of that model.

#### Video Lecture 22 (Dutch)Video Lecture 22 (English)

How to Make a Formula
You learn how a formula that does not follow from reasoning with units and dimensions can be made, either via a glass box approach or via a black box approach.
studio lecture 19
The two routes to constructing a formal relation are explained and demonstrated.

#### Video Lecture 23 (Dutch)Video Lecture 23 (English)

Getting Assistance when Searching for Useful Notions from Mathematics
You learn the 'inside-out' approach to mathematics.
voice-over lecture 8
The working of the Relation Wizard is explained.

#### Video Lecture 24 (Dutch)Video Lecture 24 (English)

Getting Assistance when Searching for Functional Relations
Given the graphical behavior of a functional relation it is often possible to suggest expressions for a function that should give this behavior.
voice-over lecture 9
The working of the Function Selector is introduced.

#### Video Lecture 25 (Dutch)Video Lecture 25 (English)

The Street Illumination Example: the Formalisation Phase
You learn how the functional relations, necessary to model street illunmination, are obtained.
studio lecture 20
The derivation of the functions needed in the street illumination example are presented.

#### Homework Assignment Chapter 4

Assignment chapter 4

#### Example Elaboration Homework Assignment Chapter 4

Assignment chapter 4

#### Materials for 0LDB0 (modeling from scratch)

PowerPoint presentation week4

# Chapter 5

Roles of Quantities in a Functional Mode
Using Functional Models; Four Categories; Optimization; Dominance; SPEA

lecture notes

#### Video Lecture 26 (Dutch)Video Lecture 26 (English)

Quantities in Four Categories
You learn that quantities in models always belong to one of four categories; you learn what these categories are, and how to use them.
studio lecture 21
• an introduction to the 4 categories;
• connection to the to-do list from Chapter 4.
voice-over lecture 10
The four categories are demonstrated in ACCEL by means of an implementation of a model for an optimization problem.

#### Video Lecture 27 (Dutch)Video Lecture 27 (English)

Requirements, Desires and Wishes
In four categories-models, requirements, desires and wishes are often represented in terms of so-called penalties. You learn how to make and use penalties in mathematical modeling.
studio lecture 22
• introduction to using penalties;
• examples of a number of different penalties;
studio lecture 23
• The importance of choosing exactly the right category-II quantity is illustrated by means of an example;
• a fully elaborated 4-catories model for a practical situation is presented.

#### Video Lecture 28 (Dutch)Video Lecture 28 (English)

Optimality
You learn that (biological) evolution is a promising source of inspiration for developing optimization models.
studio lecture 24
• dominance: the property that a concept is entirely better than an other concept;
• the so-called Pareto-front: the collection of concepts that are not dominated by any other concept.
studio lecture 25
• The SPEA algorithm is explained: an algorithm to help approximating the Pareto Front in a functional model.
voice-over lecture 11
• An application of the SPEA algorithm on the problem of Video Lecture 26 is shown.

#### Video Lecture 29 (Dutch)Video Lecture 29 (English)

The Street Illumination Example: the Execution Phase
You learn that the initial model, derived in Video Lecture 25, needs modifications in order to be processed by the SPEA algorithm.
voice-over lecture 12
The following problems with the naive implementation are addressed:
• the naive implementation asks too much computer resources;
• requirements and wishes are not translated very well into penalties;
• optimal solutions systematically occur at the borders of domains of quantities in category I.
.

#### Homework Assignment Chapter 5

Assignment chapter 5

#### Example Elaboration Homework Assignment Chapter 5

Assignment chapter 5

#### Materials for 0LDB0 (modeling from scratch)

PowerPoint presentation week5

# Chapter 6

Models and Confidence
Validation and Verification; Accuracy and Precision; Error Analysis and Sensitivity

lecture notes

#### Video Lecture 30 (Dutch)Video Lecture 30 (English)

Validation and Verification; Accuracy and Precision
You learn four central concepts to discuss confidence in models.
studio lecture 26
• assessing confidence requires knowledge of the model, the modeled system and the purpose;
• the difference between validation and verification;
• the difference between accuracy and precision.

#### Video Lecture 31 (Dutch)Video Lecture 31 (English)

Uncertainty in the Case of Black Box Models
You learn three central notions (average, spread and correlation) to discuss uncertainties in data.
studio lecture 27
The three notions, average, spread and correlation are explained by means of an example..
studio lecture 28
• The notion of linear least squares is introduced, and applied to a practical example.

#### Video Lecture 32 (Dutch)Video Lecture 32 (English)

Uncertainty in the Case of Glass Box Models (1): Qualitative Uncertainty
You learn how to test if the structure of a glass box model is plausible.
studio lecture 29
The methods for testing are:
• do the dependencies in the functional model behave as you expect?
• is the asymptotic behavior of the model as you expect?
• Is the behavior in singular points as you expect?
• Does the model outcome rely on convergence - and if so: has convergence been reached?

#### Video Lecture 33 (Dutch)Video Lecture 33 (English)

Uncertainty in the Case of Glass Box Models (2): Quantitative Uncertainty
You learn how the numerical precision of a glass box model can be assessed.
studio lecture 30
The intuitions of error propagation, sensitivity and stability are explained..
voice-over lecture 13
• This lecture explains the instruments for numerical analysis and error propagation in ACCEL.

#### Video Lecture 34 (Dutch)Video Lecture 34 (English)

The Street Illumination Example: Qualitative Assessment
You learn how much confidence you can have in the street illumination model.
voice-over lecture 14
The validity for the street illumination model is analysed by means of a number of tests, relating to the four criteria from Video Lecture 32.

#### Homework Assignment Chapter 6

Assignment chapter 6

#### Example Elaboration Homework Assignment Chapter 6

Assignment chapter 6

#### Materials for 0LDB0 (modeling from scratch)

PowerPoint presentation week6

# Chapter 7

A Working Model - And Then?
Quality Criteria for Modeling

lecture notes

#### Video Lecture 35 (Dutch)Video Lecture 35 (English)

Criteria for Quality in Models
You learn eight criteria that can be used to assess the quality of models.
studio lecture 31
• the eight criteria for quality in models;
• a cube representing these criteria and their internal structure.
voice-over lecture 15
• The criterion 'scalability' is explained in detail.
voice-over lecture 16
• The criterion 'plausibility' is explained in detail.

#### Video Lecture 36 (Dutch)Video Lecture 36 (English)

Iteration: a Better Model is Better
You learn how you can iteratively improve your model by using the criteria for quality.
studio lecture 32
This lecture explains the relation between purposes and criteria..

#### Video Lecture 37 (Dutch)Video Lecture 37 (English)

Improving the Street Illumination Model
You learn how critical analysis of the results of the street illumination model leads to a better model.
studio lecture 33
The analysis of the qualitative glass-box behavior shows that the ideal height of the street lamps is 0. This asks for a further investigation..

#### Homework Assignment Chapter 7

Assignment chapter 7

#### Example Elaboration Homework Assignment Chapter 7

Assignment chapter 7
sheets Introduction to Modeling - summary Overview of all chapters in key words link
Relation Wizard An interactive tool, comparable to a flora that helps determining plants, to help identify mathematical techniques or terminology that could be helpful when formalizing an intuititve notion. This is a draft version, subject to frequent but irregular updates. link
Function Selector An interactive tool, to help selecting a functional expression to meet with desired graphical behavior. link
Advanced Materials An increasing collection of presentations covering more advanced examples of functional modeling with ACCEL. optimal manufacturing