Computational Path Integration

In summary, when taking Feynman path integrals, it is recommended to use the Metropolis algorithm for Monte Carlo simulations. The VEGAS algorithm from the GNU Scientific Library may be useful for multi-dimensional integrals, but it can give large errors for Gaussian integrals. For high dimensional integrals, the two most commonly used Markov chain Monte Carlo methods are Gibbs sampling and the Metropolis-Hastings algorithm, with the latter being more advanced but also more complex.
  • #1
Trajito
6
0
Hello to all,

To take Feynman path integrals, which Monte Carlo algorithm do you think is best to use? I tried VEGAS algorithm as it is in GNU Scientific Library. It is pretty useful for many kinds of multi-dimensional integrals but since the path integral formulation includes Gaussian integrals, it gives really huge errors (I don't know why it isn't suitable for the Gaussians). So, do you think Metropolis works?
 
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  • #2
The answer was "yes." When calculating every kind of very high dimensional integrals, Markov chain Monte Carlo methods are widely employed. Two most common of these are Gibbs sampling and the Metropolis-Hastings algorithm. Both have advantages; the latter is, as far as I see, much more complicated and much more advanced.
 

1. What is Computational Path Integration?

Computational Path Integration is a process in which a computer or mathematical model is used to simulate or analyze the navigation and movement of an individual or object in an environment. It involves tracking and predicting the location and orientation of the individual/object based on sensory information and previous movements.

2. How is Computational Path Integration used in scientific research?

Computational Path Integration is widely used in various fields of scientific research such as neuroscience, psychology, robotics, and animal behavior. It helps in understanding the mechanisms and strategies involved in navigation and spatial cognition, as well as in developing and testing algorithms for autonomous navigation and path planning.

3. What are the benefits of using Computational Path Integration?

The use of Computational Path Integration allows for the exploration and analysis of complex spatial behaviors and environments that would be difficult or impossible to study in real-life scenarios. It also provides a quantitative and objective approach to studying navigation and can be used to make predictions and test hypotheses.

4. What are some commonly used models and algorithms in Computational Path Integration?

Some commonly used models and algorithms in Computational Path Integration include the Kalman filter, Bayes filters, and artificial neural networks. These models and algorithms are used to integrate sensory information and previous movements to predict the future location and orientation of an individual or object.

5. What are the potential applications of Computational Path Integration in the future?

Computational Path Integration has a wide range of potential applications in fields such as robotics, virtual reality, and spatial navigation aids for individuals with impaired spatial cognition. It can also be used in developing intelligent navigation systems for autonomous vehicles and drones.

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