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Dear all, welcome back to FYS4411/9411. We hope you've had a great weekend.
This week we start with one of the final ingredients for project 1, namely a proper statistical analysis of the errors (including a proper evaluation of the standard deviation of the mean value). This means that we will dive into resampling methods like the bootstrap and jackknife methods and finally the so-called blocking methods. These are all methods which are very popular in the statistical analysis. We will, for our purposes focus on the so-called blocking methods as this is very suitable for the type of Monte Carlo simulations we do in project 1.
The only missing item is then parallelization. With that included we will have a close to professional code for doing Monte Carlo simulations of quantum mechanical systems. Concerning the deadline for project (March 21), in case more time is needed, we can extend it by one week.
The plan next week is to focus ma...
Dear all, welcome back to FYS4411/9411.
This week we will try to wrap up our discussion of optimization methods, repeating some of the basic approaches and then discussing so-called quasi-Newton methods, which aim at circumventing the calculation of the second derivative of energy.
The plan is as follows:
Gradient methods:
Semi-Newton methods (Broyden's algorithm and Broyden-Farberg-Goldberg-Shanno algorithm)
Steepest descent and conjugate gradient descent
Stochastic gradient descent and variants thereof
Automatic differentiation
- Discussion of implementations and work on codes
Teaching Material, videos and written material.
These lecture notes
Recommended background literature, ...
Dear all, we hope all is well and we look forward to see you all again this coming Friday. Here are the plans with the link to the jupyter-notebook for this week, see https://github.com/CompPhysics/ComputationalPhysics2/blob/gh-pages/doc/pub/week6/ipynb/week6.ipynb
Topics.
Reminder from last week and derivation of equations for the gradients of the energy
Gradient methods:
a. Semi-Newton methods (Broyden's algorithm) and gradient descent
b. Steepest descent and conjugate gradient descent
c. Discussion of codes for VMC calculations
Teaching Material, videos and written material.
These lecture notes, see attachment
Dear all, welcome back to FYS4411/9411. The plans this week are to discuss:
Reminder on Fokker-Planck equation and Langevin equations (partly from last week)
Programming elements of correlation function (needed later)
Start optimization: Expressions for derivatives as functions of the variational parameters
and if we get time, we start discussing Newton's method and gradient descent. Methods like Steepest descent and Conjugate Gradient Descent will be discussed next week.
The slides (jupyter-notebook) are at https://github.com/CompPhysics/ComputationalPhysics2/blob/gh-pages/doc/pub/week5/ipynb/week5.ipynbLinks to an external site.
Best wishes to you all,
Morten
Dear all, welcome back to FYS4411.
The plans for this week are
Topics.
Short repetition from last week
Mathematical and computational details of importance sampling and Fokker-Planck and Langevin equations
- For the lab session we will continue our discussions on how to build a VMC code for project 1
The jupyter-notebook is attached and we will cover some of the mathematical details on how to compute the trial wave functions with importance sampling as well as the more mathematical (technicalities) of importance sampling such as the Fokker-Planck equation and how we derive the actual expression for the quantum force.
You can also find the jupyter-notebook at https://github.com/CompPhysics/ComputationalPhysics2/blob/gh-pages/doc/pub/week4/ipynb/week4.ipynb
To read more about Metropolis, Markov Chains, im...
Dear all and welcome back to Comp Phys 2.
Our plans this week are
- Markov Chain Monte Carlo and repetition from last week
- Metropolis-Hastings sampling and introducing importance sampling
Importance sampling will allow us to sample more reliably from a transition probability that mimics the physics at play. This will lead us to a discussion of what is called the Fokker-Plank equation and the Langevin equation in actual implementations of importance sampling.
We start with a top-down approach first where we present the equations we have to implement and show how to program this. Thereafter we will discuss the mathematical foundation. In the lab session we continue on implementing the variational Monte Carlo algorithm for a system of non-interacting bosons first.
To read more about Metropolis, Markov Chains, importance sampling, Fokker-Planck and Langevin equations, we recommend Becca...
Dear all, welcome back to FYS4411/9411. Here are the plans for the lecture tomorrow.
Note first that I have changed the zoom link to my UiO address. The permanent link for the rest of the semester is
https://uio.zoom.us/my/mortenhj
Please use this link if you cannot attend in person.
Note also that there are no lectures 815-10. The lectures start at 1015-12 and our lab sessions follow thereafter.
You will find the lecture notes for this week at https://github.com/CompPhysics/ComputationalPhysics2/blob/gh-pages/doc/pub/week2/ipynb/week2.ipynb
The topics this week are
Repetition from last week and discussions of code templates in python and C++
Essential ingredients: Variational Monte Carlo methods, Metropolis Algorithm, statistics and Markov Chain theory
How to structure the VMC code
Sections 3.1-3.9 of Sorella and Becca's t...
Dear all, welcome to a new semester and FYS4411/9411.
Our first session is January 24 (this Friday) at 10.15am, room FV172 at the Department of Physics, UiO.
After the lectures we move to room F?434 for the lab sessions. Note that there is a strange error in the online schedule at the official UiO website.
There is no lecture at 815am at F?434. We have lectures from 1015am-12pm in FV172 and then move to F?434 for the lab sessions.
All lectures will be recorded and the videos will be posted asap online here. Our first lab session follows right after the first lecture.
For those of you who cannot attend in person, the permanent zoom link is https://msu.zoom.us/j/93770363466 (with meeting ID...
Dear all, welcome to a new semester and FYS4411/9411.
Our first session is January 24 at 10am, room F?434 at the Department of Physics, UiO.
All lectures will be recorded and the videos will be posted asap online here. Our first lab session follows right after the first lecture.
The link to the teaching material is at https://github.com/CompPhysics/ComputationalPhysics2/blob/gh-pages/doc/pub/week1/ipynb/week1.ipynb or as a PDF file at https://github.com/CompPhysics/ComputationalPhysics2/blob/gh-pages/doc/pub/week1/pdf/week1.pdf
Note that for codes the jupyter-notebook is better suited than the pdf file.
...