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Aplikacije

Monte Carlo methde su vrlo korisne za simuliranje fenomena sa znacajnom nesigurnoscu kod ulaza i sistema sa velikim brojem uparenih stepena slobode. Polja primene ukljucuju:

Fizicke nauke

Monte Karlo metode su vrlo vazne u racunarskoj fizici, fizickoj hemiji, i srodnim primenjenim naukama, i imaju siroke primene od komplikovanih izracunavanja u kvantnoj hromodinamici do dizajniranja toplotnih stitova i aerodinamickih oblika. U statistickoj fizici Monte Karlo molekularno modeliranje je alternativa racunskoj molekularnoj dinamici, i Monte Karlo metode se koriste za izracunavanja u statistickoj teoriji polja jednostavnih cesticnih i polimernih sistema.^[1] Kvantne Monte Karlo metode resavaju probleme multi-tela za kvantne sisteme. U eksperimentalnoj fizici cestica, Monte Karlo methode se koriste za dizajn detektora, razumevanje njihovih ponasanja i poredjenje eksperimentalnih podataka sa teorijom. U astrofizici, koriste se na razlicite nacine, tako da modeliraju evoluciju galaksija^[2] i transmisiju mikrotalasnog zracenja kroz grubu planetarnu povrsinu.^[3] Monte Karlo metode se takodje koriste u Ansambl modelima koji formiraju temelje moderne prognoze vremena.

Engineering

Monte Carlo methods are widely used in engineering for sensitivity analysis and quantitative probabilistic analysis in process design. The need arises from the interactive, co-linear and non-linear behavior of typical process simulations. For example,

in microelectronics engineering, Monte Carlo methods are applied to analyze correlated and uncorrelated variations in analog and digital integrated circuits.
in geostatistics and geometallurgy, Monte Carlo methods underpin the design of mineral processing flowsheets and contribute to quantitative risk analysis.
in wind energy yield analysis, the predicted energy output of a wind farm during its lifetime is calculated giving different levels of uncertainty (P90, P50, etc.)
impacts of pollution are simulated^[4] and diesel compared with petrol.^[5]
In autonomous robotics, Monte Carlo localization can determine the position of a robot. It is often applied to stochastic filters such as the Kalman filter or Particle filter that forms the heart of the SLAM (Simultaneous Localization and Mapping) algorithm.
In Aerospace engineering, Monte Carlo methods are used to ensure that multiple parts of an assembly will fit into an engine component.

Computational biology

Monte Carlo methods are used in computational biology, such for as Bayesian inference in phylogeny.

Biological systems such as proteins^[6] membranes,^[7] images of cancer,^[8] are being studied by means of computer simulations.

The systems can be studied in the coarse-grained or ab initio frameworks depending on the desired accuracy. Computer simulations allow us to monitor the local environment of a particular molecule to see if some chemical reaction is happening for instance. We can also conduct thought experiments when the physical experiments are not feasible, for instance breaking bonds, introducing impurities at specific sites, changing the local/global structure, or introducing external fields.

Computer graphics

Path Tracing, occasionally referred to as Monte Carlo Ray Tracing, renders a 3D scene by randomly tracing samples of possible light paths. Repeated sampling of any given pixel will eventually cause the average of the samples to converge on the correct solution of the rendering equation, making it one of the most physically accurate 3D graphics rendering methods in existence.

Applied statistics

In applied statistics, Monte Carlo methods are generally used for two purposes:

To compare competing statistics for small samples under realistic data conditions. Although Type I error and power properties of statistics can be calculated for data drawn from classical theoretical distributions (e.g., normal curve, Cauchy distribution) for asymptotic conditions (i. e, infinite sample size and infinitesimally small treatment effect), real data often do not have such distributions.^[9]
To provide implementations of hypothesis tests that are more efficient than exact tests such as permutation tests (which are often impossible to compute) while being more accurate than critical values for asymptotic distributions.

Monte Carlo methods are also a compromise between approximate randomization and permutation tests. An approximate randomization test is based on a specified subset of all permutations (which entails potentially enormous housekeeping of which permutations have been considered). The Monte Carlo approach is based on a specified number of randomly drawn permutations (exchanging a minor loss in precision if a permutation is drawn twice – or more frequently—for the efficiency of not having to track which permutations have already been selected).

Artificial intelligence for games

Monte Carlo methods have been developed into a technique called Monte Carlo Tree Search that is useful for searching for the best move in a game. Possible moves are organized in a search tree and a large number of random simulations are used to estimate the long-term potential of each move. A black box simulator represents the opponent's moves.^[10]

The Monte Carlo Tree Search (MCTS) method has four steps:^[11]

Starting at root node of the tree, select optimal child nodes until a leaf node is reached.
Expand the leaf node and choose one of its children.
Play a simulated game starting with that node.
Use the results of that simulated game to update the node and its ancestors.

The net effect, over the course of many simulated games, is that the value of a node representing a move will go up or down, hopefully corresponding to whether or not that node represents a good move.

Monte Carlo Tree Search has been used successfully to play games such as Go,^[12] Tantrix,^[13] Battleship,^[14] Havannah,^[15] and Arimaa.^[16]

Design and visuals

Monte Carlo methods are also efficient in solving coupled integral differential equations of radiation fields and energy transport, and thus these methods have been used in global illumination computations that produce photo-realistic images of virtual 3D models, with applications in video games, architecture, design, computer generated films, and cinematic special effects.^[17]

Finance and business

Monte Carlo methods in finance are often used to calculate the value of companies, to evaluate investments in projects at a business unit or corporate level, or to evaluate financial derivatives. They can be used to model project schedules, where simulations aggregate estimates for worst-case, best-case, and most likely durations for each task to determine outcomes for the overall project.

Telecommunications

When planning a wireless network, design must be proved to work for a wide variety of scenarios that depend mainly on the number of users, their locations and the services they want to use. Monte Carlo methods are typically used to generate these users and their states. The network performance is then evaluated and, if results are not satisfactory, the network design goes through an optimization process.

[1] Baeurle 2009

[2] MacGillivray & Dodd 1982

[3] Golden 1979

[IntPanis1-4] Int Panis et al. 2001

[IntPanis2-5] Int Panis et al. 2002

[6] Ojeda & et al. 2009,

[7] Milik & Skolnick 1993

[8] Forastero et al. 2010

[9] Sawilowsky & Fahoome 2003

[10] ttp://sander.landofsand.com/publications/Monte-Carlo_Tree_Search_-_A_New_Framework_for_Game_AI.pdf

[11] ttp://mcts.ai/about/index.html

[12] ttp://link.springer.com/chapter/10.1007/978-3-540-87608-3_6

[13] ttp://www.tantrix.com:4321/Tantrix/TRobot/MCTS%20Final%20Report.pdf

[14] ttp://www0.cs.ucl.ac.uk/staff/D.Silver/web/Publications_files/pomcp.pdf

[15] ttp://link.springer.com/chapter/10.1007/978-3-642-17928-0_10

[16] ttp://www.arimaa.com/arimaa/papers/ThomasJakl/bc-thesis.pdf

[17] Szirmay-Kalos 2008

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