Is Simulated Annealing a Monte Carlo Method?

Image link: https://commons.wikimedia.org/wiki/File:Schematic_of_the_Metropolis_Monte_Carlo_Algorithm.png

C O N T E N T S:

- The FRAGFOLD method 2, 17, 18 also employed simulated annealing as its metaheuristic, with more recent versions making use of replica-exchange Monte Carlo trajectories 19.(More…)
- Simons, K. T., Kooperberg, C., Huang, E. & Baker, D. Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and Bayesian scoring functions.(More…)
- Standard numerical methods include modified genetic algorithms, annealing methods, and parallel tempered Monte Carlo.(More…)

- A similar approach, the quasi-Monte Carlo method, uses low-discrepancy sequences.(More…)

** Double click on a snippet to show in context, i.e. with its surrounding text Modes 1) double click snippet to see in context; 2) double click snippet to Share or Publish **

**KEY TOPICS**

** The FRAGFOLD method 2, 17, 18 also employed simulated annealing as its metaheuristic, with more recent versions making use of replica-exchange Monte Carlo trajectories 19.** [1] The Monte Carlo simulation results show that the average value of the power grid investment simulated by the Monte Carlo method in the next three years will reach 4837.6, 4980.2, and 5109.2 hundred million yuan, respectively. [2] Then the distribution data of the next year?s input variables are calculated on the basis of the growth rate results of each input variable simulated by the Monte Carlo method and the data of the input variables in this year, and the distribution data of the next year?s residue will be predicted based on the GA-SVM model and the next year?s variables data. [2] The residual component from 2018 to 2020 is dynamically simulated based on the GA-SVM model and the Monte Carlo method. [2]

It can be simulated directly, or its average behavior can be described by stochastic equations that can themselves be solved using Monte Carlo methods. [3]

Sawilowsky 48 distinguishes between a simulation, a Monte Carlo method, and a Monte Carlo simulation: a simulation is a fictitious representation of reality, a Monte Carlo method is a technique that can be used to solve a mathematical or statistical problem, and a Monte Carlo simulation uses repeated sampling to obtain the statistical properties of some phenomenon (or behavior). [3] Before the Monte Carlo method was developed, simulations tested a previously understood deterministic problem, and statistical sampling was used to estimate uncertainties in the simulations. [3]

Uses of Monte Carlo methods require large amounts of random numbers, and it was their use that spurred the development of pseudorandom number generators, which were far quicker to use than the tables of random numbers that had been previously used for statistical sampling. [3] In this paper, we use the Monte Carlo method to simulate the distributed data of these influencing factors in the next three years; then the distributed data of these influencing factors will be used to predict China?s power grid investment in 2018-2020 based on the EMD-GASVM-RBFNN hybrid prediction model. [2] Figure 10: Frequency distribution graph of the power grid investment demand based on the Monte Carlo method in the next three years (the unit is 100 million yuan). [2] The Monte Carlo method is used to simulate China?s power grid investment in 2018-2020. [2] Monte Carlo methods in finance are often used to evaluate investments in projects at a business unit or corporate level, or to evaluate financial derivatives. [3] After verifying the normal distribution of the growth rate of each input variable by K-S test, the Monte Carlo method will be used to create 100 thousand groups’ next year?s input variables. [2] Monte Carlo methods are mainly used in three problem classes: 1 optimization, numerical integration, and generating draws from a probability distribution. [3] Monte Carlo methods can be used to solve any problem having a probabilistic interpretation. [3] In astrophysics, they are used in such diverse manners as to model both galaxy evolution 59 and microwave radiation transmission through a rough planetary surface. 60 Monte Carlo methods are also used in the ensemble models that form the basis of modern weather forecasting. [3] Monte Carlo methods are widely used in engineering for sensitivity analysis and quantitative probabilistic analysis in process design. [3] Monte Carlo methods are used in various fields of computational biology, for example for Bayesian inference in phylogeny, or for studying biological systems such as genomes, proteins, 69 or membranes. 70 The systems can be studied in the coarse-grained or ab initio frameworks depending on the desired accuracy. [3] The Rand Corporation and the U.S. Air Force were two of the major organizations responsible for funding and disseminating information on Monte Carlo methods during this time, and they began to find a wide application in many different fields. [3] Monte Carlo methods were central to the simulations required for the Manhattan Project, though severely limited by the computational tools at the time. [3] Monte Carlo method: Pouring out a box of coins on a table, and then computing the ratio of coins that land heads versus tails is a Monte Carlo method of determining the behavior of repeated coin tosses, but it is not a simulation. [3] From 1950 to 1996, all the publications on Sequential Monte Carlo methodologies including the pruning and resample Monte Carlo methods introduced in computational physics and molecular chemistry, present natural and heuristic-like algorithms applied to different situations without a single proof of their consistency, nor a discussion on the bias of the estimates and on genealogical and ancestral tree based algorithms. [3] This can be accomplished by means of an efficient Monte Carlo method, even in cases where no explicit formula for the a priori distribution is available. [3] Monte Carlo methods are typically used to generate these users and their states. [3] The most common application of the Monte Carlo method is Monte Carlo integration. [3] The Intergovernmental Panel on Climate Change relies on Monte Carlo methods in probability density function analysis of radiative forcing. [3] In geostatistics and geometallurgy, Monte Carlo methods underpin the design of mineral processing flowsheets and contribute to quantitative risk analysis 14. [3] “Diffusion Monte Carlo Methods with a fixed number of walkers” (PDF). [3] Monte Carlo methods provide a way out of this exponential increase in computation time. [3] Monte Carlo method applied to approximating the value of ?. [3] Monte Carlo methods are also a compromise between approximate randomization and permutation tests. [3] The modern version of the Markov Chain Monte Carlo method was invented in the late 1940s by Stanislaw Ulam, while he was working on nuclear weapons projects at the Los Alamos National Laboratory. [3] “Stan Ulam, John von Neumann, and the Monte Carlo method” (PDF). [3] “The Manhattan Project, the first electronic computer and the Monte Carlo method”. [3]

KIC is usually used in the context of a Monte Carlo algorithm with simulated annealing. [4] Extending results from the literature of particle filters and sequential Monte Carlo methods we can establish rigorous bounds on convergence properties of the cloning algorithm in continuous time, which are reported in this paper with details of proofs given in a further publication. [5]

Monte Carlo simulations are typically characterized by a large number of unknown parameters, many of which are difficult to obtain experimentally. 49 Monte Carlo simulation methods do not always require truly random numbers to be useful (although, for some applications such as primality testing, unpredictability is vital). 50 Many of the most useful techniques use deterministic, pseudorandom sequences, making it easy to test and re-run simulations. [3] The main structure of this article is arranged as follows: Section 2 introduces the methodology; Section 3 carries out empirical analysis to verify the validity of the proposed model for the power grid investment prediction in China; Section 4 uses the Monte Carlo dynamic simulation method to simulate the power grid investment in China from 2018 to 2020; Section 5 summarizes the whole paper. [2] The combination of the individual RF agents to derive total forcing over the Industrial Era are done by Monte Carlo simulations and based on the method in Boucher and Haywood (2001). [3] In signal processing and Bayesian inference, particle filters and sequential Monte Carlo techniques are a class of mean field particle methods for sampling and computing the posterior distribution of a signal process given some noisy and partial observations using interacting empirical measure s. [3] Being secret, the work of von Neumann and Ulam required a code name. 14 A colleague of von Neumann and Ulam, Nicholas Metropolis, suggested using the name Monte Carlo, which refers to the Monte Carlo Casino in Monaco where Ulam’s uncle would borrow money from relatives to gamble. 12 Using lists of “truly random” random numbers was extremely slow, but von Neumann developed a way to calculate pseudorandom numbers, using the middle-square method. [3] Another class of methods for sampling points in a volume is to simulate random walks over it ( Markov chain Monte Carlo ). [3] Low-discrepancy sequences are often used instead of random sampling from a space as they ensure even coverage and normally have a faster order of convergence than Monte Carlo simulations using random or pseudorandom sequences. [3] The critical value of the test statistic S used in the post-hoc procedure was calculated using 50,000 iterations of Monte Carlo simulation. [1] Table 10 shows the statistical test results of the Monte Carlo dynamic simulation results of the power grid investment distribution data in the next three years. [2] Ripley 47 defines most probabilistic modeling as stochastic simulation, with Monte Carlo being reserved for Monte Carlo integration and Monte Carlo statistical tests. [3]

In Monte Carlo simulation, the distribution of the growth rate of each variable of the model inputs should be assumed, and different distribution assumptions will have different effects on the residue prediction result. [2] When the probability distribution of the variable is parametrized, mathematicians often use a Markov chain Monte Carlo (MCMC) sampler. 3 4 5 6 The central idea is to design a judicious Markov chain model with a prescribed stationary probability distribution. [3] By contrast, Monte Carlo simulations sample from a probability distribution for each variable to produce hundreds or thousands of possible outcomes. [3] Monte Carlo simulation: Drawing a large number of pseudo-random uniform variables from the interval at one time, or once at a large number of different times, and assigning values less than or equal to 0.50 as heads and greater than 0.50 as tails, is a Monte Carlo simulation of the behavior of repeatedly tossing a coin. [3] The average value of each input variable?s distribution data in 2018 obtained by Monte Carlo simulation will be the basis for the calculation of the distribution data of the variables in 2019, and the average value of the distribution data of each variable in 2019 will be the basis for the calculation of the distribution data of each variable in 2020. [2] Monte Carlo simulation allows the business risk analyst to incorporate the total effects of uncertainty in variables like sales volume, commodity and labour prices, interest and exchange rates, as well as the effect of distinct risk events like the cancellation of a contract or the change of a tax law. [3] Monte Carlo simulation is commonly used to evaluate the risk and uncertainty that would affect the outcome of different decision options. [3] In reliability engineering, Monte Carlo simulation is used to compute system-level response given the component-level response. [3] A Monte Carlo approach was used for evaluating the potential value of a proposed program to help female petitioners in Wisconsin be successful in their applications for harassment and domestic abuse restraining orders. [3] It was in 1993, that Gordon et al., published in their seminal work 30 the first application of a Monte Carlo resampling algorithm in Bayesian statistical inference. [3] “Sequential Monte Carlo samplers – Del Moral – Doucet – Jasra- 2006 – Journal of the Royal Statistical Society: Series B (Statistical Methodology) – Wiley Online Library”. [3] There are ways of using probabilities that are definitely not Monte Carlo simulations for example, deterministic modeling using single-point estimates. [3] The Monte Carlo simulation is in fact random experimentations, in the case that, the results of these experiments are not well known. [3] Swendsen RH, Wang J-S. Replica Monte Carlo simulation of spin-glasses. [1] “Fifty years of Monte Carlo simulations for medical physics”. [3] 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). [3] The classical model of spin-vector Monte Carlo is also analyzed, and we find it to have the same thermodynamic phase diagram as the quantum model in the ideal case, with deviations arising at non-zero temperature. [6] “Insertion of peptide chains into lipid membranes: an off-lattice Monte Carlo dynamics model”. [3] In contrast with traditional Monte Carlo and MCMC methodologies these mean field particle techniques rely on sequential interacting samples. [3] Path tracing, occasionally referred to as Monte Carlo ray tracing, renders a 3D scene by randomly tracing samples of possible light paths. [3] The use of Sequential Monte Carlo in advanced signal processing and Bayesian inference is more recent. [3] Shmygelska and Levitt 21 employed modified Rosetta frameworks with both temperature and Hamiltonian replica exchange Monte Carlo (TREM and HREM respectively) and demonstrate that HREM outperforms both standard Rosetta and the TREM framework in terms of locating lower-energy states. [1] Immediately after Ulam’s breakthrough, John von Neumann understood its importance and programmed the ENIAC computer to carry out Monte Carlo calculations. [3] The process of acceptance or rejection of moves is typically governed by a Metropolis Monte Carlo framework 9, 10. [1] There is no consensus on how Monte Carlo should be defined. [3] In autonomous robotics, Monte Carlo localization can determine the position of a robot. [3] “A Monte Carlo tool to simulate breast cancer screening programmes”. [3]

** Simons, K. T., Kooperberg, C., Huang, E. & Baker, D. Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and Bayesian scoring functions.** [1] AcceptanceCriterion compares energy or score values of consecutive LMin s using the usual Metropolis criterion, where the temperature parameter is set by a scheme of simulated annealing (details in Supplementary information). [1] J. Geng, M. -L. Huang, M. -W. Li, and W. -C. Hong, “Hybridization of seasonal chaotic cloud simulated annealing algorithm in a SVR-based load forecasting model,” Neurocomputing, vol. 151, no. 3, pp. 1362-1373, 2015. [2] J. Li, J. Liu, and J. Wang, “Mid-long term load forecasting based on simulated annealing and SVM algorithm,” Proceedings of the Chinese Society of Electrical Engineering, vol. 31, no. 16, pp. 63-66, 2011. [2]

** Standard numerical methods include modified genetic algorithms, annealing methods, and parallel tempered Monte Carlo.** [7] For this purpose, we perform ab initio calculations, develop a many-body interatomic potential (EAM formalism) for large-scale calculations, validate the potential and apply it using an atomistic kinetic Monte Carlo method to characterize the lifetime and diffusivity of vacancy clusters. [8]

In order to complement previous qualitative results, we devise a method based on Monte Carlo simulations. [5] In the past, he has developed advanced Monte Carlo simulation techniques and novel sampling methods to study chemical systems at the molecular level. [9] Minsley, B. J., 2011, A trans-dimensional Bayesian Markov chain Monte Carlo algorithm for model assessment using frequency-domain electromagnetic data: Geophysical Journal International, 187 (1), 252-272. [10] Green, P. J., 1995, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination: Biometrika, 82 (4), 711-732. [10] Malinverno, A., 2002, Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem: Geophysical Journal International, 151 (3), 675-688. [10] Agostinetti, N. P., and Malinverno, A., 2010, Receiver function inversion by trans-dimensional Monte Carlo sampling: Geophysical Journal International, 181 (2), 858-872. [10] His new interest is to utilize D-Wave2000Q to perform Monte Carlo Simulation efficiently. [9] There he studied the effects of barrier tunneling on quantum adiabatic optimization and quantum Monte Carlo. [9]

**POSSIBLY USEFUL**

** A similar approach, the quasi-Monte Carlo method, uses low-discrepancy sequences.** [3] Methods based on their use are called quasi-Monte Carlo methods. [3] These sequences “fill” the area better and sample the most important points more frequently, so quasi-Monte Carlo methods can often converge on the integral more quickly. [3]

“Monte Carlo sampling methods using Markov chains and their applications”. [3] “Monte Carlo sampling of solutions to inverse problems” (PDF). [3] “Monte carlo filter and smoother for non-Gaussian nonlinear state space models”. [3]

Bowman and Pande 20 describe the application of simulated tempering to Rosetta and report that this increases the explorative ability of the method, although improved predictive accuracy was not observed. [1] Bowman GR, Pande VS. Simulated tempering yields insight into the low-resolution Rosetta scoring functions. [1]

Use the results of that simulated game to update the node and its ancestors. [3]

We solve the mean-field-like p -spin Ising model under a spatio-temporal inhomogeneous transverse field to study the effects of inhomogeneity on the performance of quantum annealing. [6]

In practice, a combination of heuristic algorithms (such as hand-crafted annealing of KL-terms) is often used in order to achieve the desired results, but such solutions are not robust to changes in model architecture or dataset. [5] Our algorithm, which is based on Sequential Monte Carlo-Simulated Annealing, only relies on an indicator function that assesses whether or not the constraints are fulfilled, thus allowing us to enforce various complex constraints by specifying an appropriate indicator function without altering other parts of the algorithm. [5]

Monte-carlo based simulated quantum annealer is to get approximated solutions for problems with larger number of bits. [11] One can solve problems with thousands of bits for dense graph and bipartite graph with simulated quantum anneaers. [11]

We demonstrate how to conduct causal analyses using text classifiers on simulated and Yelp data, and discuss the opportunities and challenges of future work that uses text data in causal inference. [5]

**RANKED SELECTED SOURCES**(11 source documents arranged by frequency of occurrence in the above report)

1. (61) Monte Carlo method – Wikipedia

2. (13) A Hybrid Forecasting Model Based on EMD-GASVM-RBFNN for Power Grid Investment Demand

3. (9) Improved fragment-based protein structure prediction by redesign of search heuristics

4. (5) Whats new on arXiv | Data Analytics & R

5. (4) Transdimensional Bayesian inversion of time-domain airborne EM data | SpringerLink

6. (3) Quantum Computing Conference | Speakers

7. (2) sqaod PyPI

8. (2) https://journals.aps.org/pra/accepted/8907bNacI7015c1d75d26736b89e90a8d84ed2eb8