Chapter 2_Enumeration_Computational Modeling

Variables,

Parameters,

Equations/RulesWhy Do We Use Models?

Key Components of a Model (3)

Understand complex systems,

Predict future events,

Test different scenarios,

Reduce the cost of experiments,

Save time,

Improve decision-making,

Minimize risks associated with real-world experimentation

Why Do We Use Models? Models help us (7)

Describe how a system works,

Explain relationships among variables,

Predict future behavior,

Analyze different situations,

Support scientific and engineering decisions,

Test "what-if" scenarios safely

Major Purposes of Models (6)

Weather forecasting = Atmospheric simulation model

Disease spread = Epidemic model

Flood prediction = Hydrological model

Traffic management = Traffic flow model

Population growth = Population model

Problem = Computational Model Examples (5)

Simple but realistic,

Accurate,

Reliable,

Easy to understand,

Based on valid assumptions,

Flexible enough for different situations

Characteristics of a Good Model (5)

Deterministic,

Probabilistic / Stochastic

Types of Computational Models (2)

No randomness,

Predictable results,

Exact mathematical relationships,

Easier to analyze

Deterministic model characteristics (4)

Simple interest computation,

Projectile motion,

Population growth using fixed rates,

Newton's laws of motion

Deterministic model examples (4)

Easy to understand,

Easy to verify,

Produces consistent results

Deterministic Models Advantages (3)

Cannot represent uncertainty,

Less realistic for many natural systems

Deterministic Models Limitations (2)

β (Beta) – Infection/Transmission Rate,

γ (Gamma) – Recovery Rate

Parameters in the basic SIR model

Uses probability,

Includes random variables,

Models uncertainty,

Produces multiple possible outcomes

Probabilistic / Stochastic Models Characteristics (4)

Weather forecasting,

Stock market prediction,

Disease transmission,

Traffic congestion,

Insurance risk analysis

Probabilistic / Stochastic Models Examples (5)

More realistic,

Represents uncertainty,

Useful for complex systems

Probabilistic / Stochastic Models Advantages (3)

More difficult to analyze,

Results vary from one simulation to another

Probabilistic / Stochastic Models Limitations (2)

Email → Spam / Not Spam,

Review → Positive / Negative,

Disease symptoms → Disease A / Disease B,

News article → Sports / Politics / Business

Naïve Bayes Algorithm Examples (4)

Input data — left side,

Classifier — middle,

Possible classes — right side,

Final prediction

How to understand the diagram Naïve Bayes Classifier (4)

Build → Test → Refine → Reapply → Repeat

Modeling Process (5)

objectives,

questions,

boundaries

Step 1: Analyze the problem. (3)

assumptions,

variables,

relationships

Step 2: Formulate a model. (3)

algebra,

calculus,

graphs,

computer programs,

computer packages

Step 3: Solve the model (5)

Analysis of the problem,

Model design,

Model solution,

Results and conclusions

Step 5: Report on the model (4)

corrections,

improvements,

enhancements

Step 6: Maintain the model (3)

Analysis of the problem,

Model design,

Model solution,

Results and conclusions

Report components parallel the steps of the modeling process (4)

NumPy,

SciPy,

Matplotlib & Seaborn,

SimPy

Popular Libraries in Python for Computational Science

computational science,

engineering,

applied mathematics

SciPy adds a wide collection of algorithms and functions for more advanced tasks in (3)

2D plotting (line & scatter plots, histogram, bar charts)

Matplotlib uses (3)

distribution plots,

heatmaps,

regression,

pair plots

Seaborn uses specialized plots (4)

queueing systems,

logistics,

resource allocation,

operations research

SimPy is widely used for (4)

define the problem,

understand the system,

build and implement the model,

verify and validate it,

analyze the results,

refine the model as needed

Effective model development follows a structured process (6)

engineering,

healthcare,

environmental science,

business,

scientific research

Computational modeling is widely applied in (5)