Introduction to Modeling and Simulation

Introduction to Modeling and Simulation

• Advances in innovation have led to the development of more powerful computers.
• Supercomputers enable computations involving massive amounts of computing power.
• Supercomputers today can achieve petaflops in floating operations per second.
• Computational Science is an interdisciplinary field combining computer simulation, scientific visualization, mathematical modeling, computer programming, data structures, networking, database design, symbolic computation, and high-performance computing.
• Scientific computing enables improvements to weather forecasting, virology, ecology, seismology, and even allows the ability to backtrack languages.

Models

• Modeling is the process of creating a model, which represents the construction and workings of a system.
• A model is similar to, but simpler than, the system it represents.
• Models act as a representation of a real system, but are not expected to clone the entire system.
• Models are bounded by a specific field of interest.
• Models are not perfect.
• Defining interests help define the scope of a study.
• Simulation takes place when a full system is available and a curiosity needs to be satisfied.

Simulation

• Simulation of a system involves operating a model of that system.
• Models can be reconfigured and experimented with, unlike actual systems which are often impossible, too expensive, or impractical to manipulate.
• Using available variables, constants, and setups to 'simulate' allows for changes to behavior, values, for a certain outcome of a scenario.
• Simulation is essentially a digital laboratory.
• In this course, modeling and simulation is geared towards scientific applications exclusively.

Types of Models

• The three types of models are physical, mathematical, and computer models.

Physical Models

• Physical models are tangible representations of a system.
• An example of a physical model is a classroom Earth model.

Mathematical Models

• These models consist of equations and data.
• These models can model growth of population from an initial population size or how fast bacteria populate at a given period amount of time.

Computer Models

• Computer models run on a computer to simulate real-world phenomena or events.
• One example of a computer model is an agent-based model.

Model Classifications

• Models can be classified as stochastic vs. deterministic, static vs. dynamic, and continuous vs. discrete.

Stochastic vs. Deterministic

• Stochastic models exhibit random effects concerning initial parameter values and conditions.
• Deterministic models exhibit determined effects with respect to the initial parameter values and conditions.

Static vs. Dynamic

• Static models are not related to time, while dynamic models change with time.

Continuous vs. Discrete

• With continuous models time changes continuously, while with discrete models time changes in steps.

Steps of the Modeling Process

• The steps are: Analyze the Problem, Formulate a Model, Solve the model, Verify and Validate the model's solution, Report on the model, and Maintain the model.

Analyze the Problem

• Requires understanding the main motivation to design a model through precise knowledge of the problem.
• Important questions to ask are what the problem is about, and what the plan to achieve (specifying objectives)• Classification is.

Formulate a Model

• Important questions to ask are what the entities, variables, constants, behavior of the entities and equations.

Solve the Model

• Solve the model where the complexity of implementation, analysis of algorithms used, equations integrated, tools/software used take place.
• Treat it as a form of methodology.

Verify and Validate the Model's Solution

• Prove the integrity of the model once it is polished.
• With two things that needs to be done, report on the model.

Maintain the Model

• The model is enough to represent the model to co-learners, teachers, etc.
• Maintenance can include additional features, bug fixes, or corrections to components.
• Recalibrate the model after maintenance.