Plans for the week of February 19-23

Dear all, the topic this week is a discussion of various gradient methods in order to find the optimal parameters for  the large VMC runs.

We will discuss various methods and discuss the pros and cons and outline computational strategies. The topics this week deal thus with various gradient optimization methods and we will cover

a. Semi-Newton methods (Broyden's algorithm, most used for our type of problems) and plain gradient descent

b. Steepest descent and conjugate gradient descent

c. Stochastic gradient descent

d. We will wrap up (see end of the slides for this week and link below) with how we can implement the plain gradient descent approach and quasi-newton methods.

Recommended background literature if you wish to dig deeper, Convex Optimization by Boyd and Vandenberghe. Their lecture slides  at https://web.stanford.edu/~boyd/cvxbook/bv_cvxslides.pdf are very useful (warning, these are some 300 pages).

The weekly jupyter-notebook with codes and more is at https://github.com/CompPhysics/ComputationalPhysics2/blob/gh-pages/doc/pub/week6/ipynb/week6.ipynb

Best wishes to you all,

Daniel, H?kon and Morten

p.s. Next week we will have lab only in order to focus on the various programming elements we need to deal with. On March 8 we will discuss how to perform a proper statistical analysis of the outcomes from a VMC calculation. This leads to a statistically "sound" estimate of the errors (standard deviation) in the calculation of the energies. After that we discuss how to include parallelization and that is our last programming element.  Thus, next week we will have lab only, and we start from 1015am and end at 3pm.