Copy of S-CSPE001 Midterms.pdf

Module 1 Introduction to Computational Modeling - The Importance of Computational Sciences Computer Science vs Computational Science Simplified Comparison: Computer Science is about the science of computers. Computational Science is about the use of computers to solve science and engineerin...

Module 1 Introduction to Computational Modeling - The Importance of Computational Sciences Computer Science vs Computational Science Simplified Comparison: Computer Science is about the science of computers. Computational Science is about the use of computers to solve science and engineering problems. ○ It is a discipline concerned with the design, implementation and use of mathematical models to analyze and solve scientific problems. ○ The term refers to the use of computers to perform simulations or numerical analysis of a scientific system or process. Related Disciplines Definition of Terms - A model is an abstraction or simplification of a real-world object or phenomenon that helps us gain insights into the state or behavior of a complex system. - A mathematical model is a representation of a phenomenon or system that is used to provide insights and predictions about system behavior. - Simulation is the application of a model to imitate the behavior of the system under a variety of circumstances. Models and Simulations - Models and simulations have always been an essential part of the human experience: as we get up in the morning, we crank up our mental model of the little world around us, run a few simulations in our mind on how we are going to deal with the problems and people we will meet during the day, try out different approaches, evaluate the likely outcomes, and start the day with a plan.  - It will not protect us from failures and surprises, but it will have prepared us to deal more effectively with whatever tasks await us. Advantage of Computational Modeling and Simulations - The main advantage is that the computer can track the multitude of implications of complex relationships and their dynamic consequences much more reliably than the human mind. - Models and simulations of many kinds are tools for dealing with reality: they are as old as humanity itself. Contributions of Modeling to Advances in Science and Engineering Table 1. Timeline of Advances in Computer Power and Scientific Modeling  Table 2. Timeline of Advances in Computer Power and Scientific Modeling Some Contemporary Examples of Large-Scale Simulations The reports on global warming use comprehensive models of the earth’s climate including components on the atmosphere and hydrosphere (ocean circulation and temperature, rainfall, polar ice caps) to forecast the long-term impacts on our climate and ecosystems (Pachauri and Meyer, 2014) Modeling and Simulation Application - COVID-19 Pandemic Concerns - How simulation modeling can help reduce the impact of COVID-19. Journal of Simulation, 14(2), 83-97. - Currie, C. S., Fowler, J. W., Kotiadis, K., Monks, T., Onggo, B. S., Robertson, D. A., & Tako, A. A. (2020). Module 2 - The Modeling Process Each of us creates informal, mental models all the time as an aid to making decisions. - One example may be deciding on a travel route that gets us to several shopping locations faster or with the fewest traffic headaches. Some of our first formal models were physical models. Those include simplified prototypes of objects used to evaluate their characteristics an/d behaviors. - One of the most ambitious physical models ever built was a costly 200 acre model of the Mississippi River Basin used to simulate flooding in the watershed (U.S. Army Corp of Engineers, 2006). - Through theory and experimentation, scientists and engineers also developed mathematical models representing aspects of physical behaviors. - Over time, mathematical models that started as very simplistic representations of complex systems have evolved into systems of equations that more closely approximate real-world phenomena such as the large scale models.  - These became the basis of computer models by translating the mathematics into computer codes. Major Steps in the Modeling Process Concept Mapping Example Conceptual Models - Abstract, psychological representations of how tasks should be carried out. People use conceptual models subconsciously and intuitively as a way of systematizing processes. - These are a partially completed concept map and mind showing the component of a model of the time it takes to make a car trip between two points. Different Ways to Classify Models Classifications / Types of Models 1. Deterministic Model  -The Deterministic Model applies a set of inputs or initial conditions and uses one or more equations to produce model outputs. 2. Probabilistic or Stochastic Model - The Probabilistic Model includes one or more elements that might occur by chance or at random while the deterministic model does not. - Stochastic - A random process or a process, which occurs by chance - A Probabilistic Model will exhibit random effects that will produce different outputs for each model run. Another Way to Classify Models Classifications / Types of Models 1. Static Model - Static or steady-state model is a model that has gone through a transient state such as a start-up or warm-up period and arrived at an observed behavior that remains constant. Example: The flow of fluid through a pipe. In the initial, transient state period, the pipe is empty and will fill with fluid under pressure until the capacity of the pipe is reached. This will be its steady-state condition. In economics, a steady-state economy is one that has reached a relatively stable size. 2. Dynamic Model - Dynamic Model considers the state of a system over time while a static model does not. Dynamic Models may be characterized as being discrete or continuous. 1. Continuous Model would represent time as a continuous function. 2. The Discrete Model divides time into small increments and calculates its state for each time-period. In computer modeling, most (all?) dynamic models divide time into discrete increments to facilitate rapid calculations that mimic continuous systems. Examples of Different Simulation Approaches as they relate to various Model Types 1. Deterministic Models consist of one or more equations that characterize the behavior of a system. Most such models simplify the system by assuming that one or more casual variables or parameters are constant for a single calculation of the model outcomes. - Example: A map is an example of a deterministic model. It is a model of location, which can help us get from place to place. 2. Probabilistic or Stochastic Models - Most models really should be stochastic or probabilistic rather than deterministic, but this is often too complicated to implement. - Example: When planning a school formal, there are some elements of the model that are deterministic and some that are probabilistic. The cost to hire the venue is deterministic, but the number of students who will come is probabilistic.  3. Dynamic Models - The focus is on the behavior of the system over time and sometimes over space. Simulations calculate the changes in the state of the system over time. - Example: A model of ball being dropped from a bridge. As it is dropped, the ball accelerates due to the force of gravity. - At each time increment, the model will calculate the velocity of the ball and its position in space. That position will depend on where it was in the previous time period and how far it was dropped related to its velocity during that time period. The model will then predict when the ball will hit the water and at what velocity. 4. Stochastic Models typically will have characteristics in common with Dynamic Models. - The difference is that one or more of the governing parameters are probabilistic or could happen by random chance. - Example: The model of the spread of a disease that is passed by human contact. - A susceptible person may have contact with an infected person but will not necessarily become infected. - There is a probability of being infected that is related to the spread of the disease, the state of health of the susceptible person, and the nature of the contact. - A model of this system would simulate those probabilities to project the potential spread of a disease outbreak. ========================================================================