Wikiversity:Fellow-Programm Freies Wissen/Einreichungen/Open-access collection of advanced general-purpose Monte-Carlo algorithms
Open-access collection of advanced general-purpose Monte-Carlo algorithms[Bearbeiten]Projektbeschreibung[Bearbeiten]Monte-Carlo algorithms are an important tool to numerically solve complex problems in a variety of different fields. Application fields include mathematics (approximating complicated multidimensional integrals), physics (sampling the phase space of interacting many-body systems), and Bayesian statistics (sampling the posterior distribution) amongst others. Advanced Monte Carlo algorithms are, however, typically developed in a specific field or even for a specific model. As a consequence, advanced Monte Carlo algorithms are often inaccessible to other fields or it might be even unclear how to apply them to other models within the same field. With my project, I want to initiate an openly accessible collection of advanced, but general-purpose Monte-Carlo algorithms. This requires to (i) reduce advanced Monte-Carlo algorithms to their core function, (ii) construct a simple family of toy models that is illustrative to demonstrate the algorithms advantage, and (iii) to describe the algorithms in a uniform mathematical and programming language. The Monte-Carlo algorithms will be collected in a public GitHub repository, where each algorithm has a precise description and an example implementation on a toy model with a visualization (e.g. as animation). I will start with basic and advanced Monte Carlo algorithms from statistical physics, including Metropolis-Hastings, replica-exchange, and generalized-ensemble methods. I will apply them to the toy problem of sampling from multimodal distributions, which illustrates the three major applications of Monte Carlo methods: sampling, integration (summing the weighted samples), and optimization (estimating the maximum). With this baseline, I want to motivate others to contribute more algorithms and to improve the existing descriptions: I will motivate colleagues by presenting the project at international conferences and workshops; and I will motivate students by organizing two hackathons. The envisioned uniform description of advanced Monte-Carlo algorithms would not only serve as an encyclopedic tool to the community, it would also be a perfect resource for courses on any subject that involves Monte Carlo algorithms, for example for computational physics. I thus believe that there should be an appropriate way to include the resulting descriptions into Wikipedia, where they can be found easily by peers and students. Autor/in[Bearbeiten]
|
|