🧠 Neil's Brain

Computational Science - Methods

3 min read

Week 8 - Computational Science

General Concepts

  1. Explain: “Everything should be made as simple as possible, but not simpler.” What are the repercussions in modeling? It demonstrates that abstraction is done to simplify things, but making it more simple defeats the purpose of modeling. Simply reduce a complex problem to a level at which a computer or human can analyze it and provide an answer to your specific problem.

  2. “The same system can be modeled at different scales.” Provide a concrete example of an object/system modeled on 3 different scales. A system is composed of different elements, and you can create different models with different scales based on what elements you’re trying to understand. The famous example of modeling in different scales is the atom model which is represented by different model such as 1. Solid Sphere Model (Dalton) 2. Plum Pudding Model (Thomson) 3. Nuclear Model (Rutherford) 4. Planetary Model (Bohr) 5. Electron Cloud Model (Schrodinger)

  3. Explain: “All models are wrong, but some are useful.” How do we validate a model? When creating a model, one must know that it is wrong until validated so to validate/benchmark a model, it is required to have an initial knowledge of the field, known phenomena, previous model to validate the model performance. A newly created model in a field that has no known phenomena is hard to validate thus, physical and traditional experimentation is prerequisite before the creation of models.

  4. Differentiate the Eulerian vs Lagrangian approach to modeling space in terms of point of view (POV) and representation. In Eulerian point of view, the regions observed is put in a cell which is fixed due to a specific observed position. The regions differs in intensity of colors based on the whole time of observation. While in a Langrangian point of view the regions observed is plotted in a cartesian plane and is not fixed since the observer is moving together with the systems. The regions specifies the space and time of the observed phenomena.

  5. Complex networks can be represented by a graph to show the interaction of components as in the case of a social system. Explain how this can be used to study social engineering experiments which aims to propagate an ideology/propaganda over social media platforms. In social engineering experiments on social media platforms, a circle represents a person, and a larger circle indicates that it has a larger network of individuals, while a color can represent their opinion. In this case, you can understand their point of view and how it evolves over time.

  6. The Monte-Carlo simulation is a random sampling process that can determine some statistical properties which cannot be predicted by probability theory. How can we employ this to determine the average duration of the card game called “war” or “battle”? Similar with a dice, the card game war is based on “Luck and Randomness”, which can be computed statistically but cannot be predicted since it is purely random. This shows that you can produce a probability of chances of winning but can’t predict it due to its high randomness.

  7. How is Markov-Chain Monte-Carlo (MCMC) simulation different from the regular Monte-Carlo simulation? Differentiate clearly Regular Monte-Carlo simulation relies on a repeated random sampling method which you will created a model based on continuous randomness, while Markov-Chain Monte-Carlo simulation uses the temporal and spatial dimension as well as the previous iteration of random sampling to create a model.

Graph View