W₀: What are Models?

CS300b – Agent Modeling

Eric Araújo

Boids Model

Boids Model

• Created by Craig Reynolds, a computer scientist working on motion picture graphics in the mid-1980s
• He tried to code the path of each individual bird, which showed impossible to be done
• The amount of thinking from the birds is independent to the number of birds in the flock
• Each bird has a simple heuristics in order to stay together with the other birds nearby

Boids Model

Reynolds came up with the three rules that describe the decision-making mechanism of each bird (or boid) within the flock:

• Separation: If there are other boids immediately in front of you, turn away from them to avoid collisions and crowding.
• Alignment: Turn to align with the average heading of nearby boids.
• Cohesion: Attempt to stay close to nearby flockmates by steering toward the average position of neaby boids.

Boids Model

Boids is an example of an Agent-based Model.

• Individuals are represented as computational entities (agents)
• Agents behave and interact locally

What is a Model?

• A simplified representation of a real-world phenomenon.
• Scientific models help us understand, explain, and predict.
• Not just about fashion! 😉

Joan Miro Art print : “The red sun (1972)”

Define what a scientific model is and how it’s used. Distinguish between the general concept of models and the specific focus on scientific models.

What is a model?

[…] a model is an abstract or physical structure that can potentially represent a real-world phenomenon.

If you are studying the mass of a rock, you weigh it. If you are studying a cell, you use a microscope.

Sometimes our object of study is not so directly accessible due to constraints of time, space, budget, or ethics. On those cases, we use models.

When a single failure of a system can be life-threatening, such models are invaluable.

This figure shows the U.S. Army Corps of Engineers Bay Model, built in the 1950s to assess the likely impacts of building dams and rerouting various channels.

Why model?

Formal models offer advantages over verbal descriptions:

• Precise communication: Reduce ambiguity inherent in language.
• Hypothesis generation: Reveal unexpected consequences of assumptions.
• Counterfactual exploration: Simulate “what if” scenarios.

Why model?

“All models are wrong, but some are useful.”

Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 424, Wiley. ISBN 0471810339.

Why model?

“[…] the apparent stupidity of a model can be a strength. By focusing only on some key aspects of a real-world system (i.e.,those aspects instantiated in the model), we can investigate how such a system would work if, in principle, we really could ignore everything we are ignoring.”

Paul Smaldino (page 8)

Decomposition

• What are the parts of the system we are interested in?
• What are their properties?
• What are the relationships between the parts and their properties?
• How do those properties and relationships change?

Decomposition

• Breaking down a system into essential parts, properties, and relationships.
• Driven by the research question: What do we want to understand?
• Different decompositions yield different models.
• No one “right” way: Choose the level of detail that suits your needs.

Types of Models

Equation-Based Models

• Describe system dynamics using mathematical equations.
• Often used for systems with well-defined relationships.

Agent-Based Models (ABMs):

• Simulate individual entities (“agents”) and their interactions.
• Capture emergent patterns from complex behaviors.

Fine-Grained vs. Coarse-Grained Models

Fine-grained models:

• High level of detail, aiming for accurate predictions.
• Can be complex and computationally demanding.

Coarse-grained models:

• Simplified representations, focusing on key mechanisms.
• Prioritize understanding over precise prediction.

Fine-Grained vs. Coarse-Grained Models

Choose the level of detail appropriate for your research question.

• Fine-grained means that there are data in the world that can be used to precisely parameterize and test the models.
• Coarse-grained models focus on broad, qualitative patterns in the data, not on reproducing exact measurements.

Many models in physics are like this; the model parameters are precisely measurable quantities like mass, pressure, or voltage. In epidemiology, some agent-based models are calibrated using high-precision data on demographics, geography, schools, travel matrices,and so forth, with the goal of predicting the time course of an epidemic. In neuroscience, biophysical models might exactly predict the dynamics of action potentials or motor behaviors.

Coarse-grained models focus on broad, qualitative patterns in the data, not on repro- ducing exact measurements.

The Modeling Journey

• Models are tools for thinking: They help us refine our ideas, test our assumptions, and explore possibilities.
• “Doing violence to reality” allows for insight: Simplification can reveal essential mechanisms.

• Recap the key takeaway: Models are powerful tools for scientific thinking.
• Reiterate the importance of simplification in modeling and its potential to lead to deeper understanding.
• End with an encouraging note, inviting the audience to embark on their own modeling journey.

SIR Model

Equation-based Models

Advantages

• Precision
• Elegance

Disadvantages

• Ability to handle heterogeneity
• Explainability

SIR - Equation-based

\[ \frac{dS}{dt} = -\beta SI\] \[ \frac{dI}{dt} = \beta SI - \gamma I\] \[ \frac{dR}{dt} = \gamma I\]

SIR - Equation-based

\[ S(t+1) = S(t) - \beta S(t)I(t)\] \[ I(t+1) = I(t) + \beta S(t)I(t) - \gamma I(t)\] \[ R(t+1) = R(t) + \gamma I(t)\]

SIR

Preview

gamma = 0.07, beta =0.3 and 0.15

SIR - Agent-based Model

• agents are situated on a two-dimensional surface and move around using a random walk
• reduction of social contact flattens the curve

Netlogo Basics

Netlogo basics

Extracted from the book Modeling Social Behavior, by Paul E. Smaldino

Patches

• spatial organization
• discrete square cells laid out in two-dimensional retangular grid
• can be used as agents themselves
• used to represent properties of the agent’s environment

Turtles

• spatially embodied
• have a position in continuous space and a directional heading

Turtles history

• Neuroscientist and roboticis W. Grey Walker created a simple, programmable, mobile robot in the 1950s called tortoise
• Inspired the creators of Logo, developed in the 1960s. Logo permits to issue commands to move and draw with a small triangular figure on a computer monitor

Turtles history

Extracted from the book Modeling Social Behavior, by Paul E. Smaldino

Links

• Netlogo allows turtles to be connected through a class called links

Netlogo Tabs

• Interface
  • Create, delete and manipulate controllers
  • Inspect the model’s output and parameter manipulation
  • Settings of the patch grid

Netlogo Tabs

• Info
  • Description of the model
  • Documentation

Netlogo Tabs

• Code
  • Instructions for the model’s operation
  • The code for Netlogo is everything, not just the Code tab

Programming basics - variables

• no requirement for specifying the type of object to be represented by your variables
• we want our variables name to be both succint and easily identifiable
• Netlogo uses equal sign (=) only for logical test. Use set for changing the value of a variable

set value-win (0.1 * money-invested) - 1

Programming basics - variables

• models paramenters
  • global variables
  • agents variables
• local variables

remember that sliders and other elements at interface tab are also global variables

local variables have local scope, while parameters exist for the whole running

Programming basics - functions/procedures

• a label for a set of commands that are run together whenever the function is called
• may take arguments
• may need return values (reporters)
• Netlogo has build-in functions called primitives, which helps programmers a lot!
  • Netlogo Dictionary

Programming basics - loops

• the ability to perform the same computation over and over and over at great speed.
• for-loops and while-loops are the most common types.

while [any? other turtles-here]
    [forward 1]

anti-social turtles

Programming basics - loops

• Netlogo is very polite

ask agents [
    right 45
    forward 1
]

Programming basics - conditional statements

• allow for code to be executed only if specific conditions are met.
• Nelogo provides if and ifelse commands for that.

ask agents [
    ifelse energy > 1
    [
        right 45
        forward 1
    ]
    [
        forage
    ]
]

Programming basics - object-oriented programming (OOP)

• different types of variables for the program to work with.
• each class stores its own variables and procedures.
• all instantiations (objects) of this class will posses these variables and procedures.
• Netlogo is a special typo of OOP called agent-oriented programming
  • commands can be written as direct instructions to the agent