Plans for the week of April 13-17

Dear all welcome to FYS4411/9411 and please have me excused for this late update.

The plan this week is to discuss codes and implementations of restricted Boltzmann machines and neural networks to quantum mechanical many-body systems. The lecture this week develops the theory and implementation of Neural Quantum States (NQS), starting from the probabilistic foundations of Boltzmann machines and ending with fully-trained deep neural-network wave functions for the quantum harmonic oscillator.

We will also discuss project 2 and its variants. The jupyter-notebook for this week is at https://github.com/CompPhysics/ComputationalPhysics2/blob/gh-pages/doc/pub/week12/ipynb/week12.ipynbLinks to an external site.

There are also additional notes on stochastic reconfiguration at https://github.com/CompPhysics/ComputationalPhysics2/blob/gh-pages/doc/pub/week12/ipynb/sg1.pdf

Outline:

Section Topic

1 Boltzmann Machines ¡ª probabilistic foundations

2 Restricted Boltzmann Machine (RBM)

3 RBM as a Neural Quantum State

4 Wave function derivation and cost function

5 Variational gradient ¡ª derivation and formulas

6 Implementation: RBM-VMC for the 2-electron quantum dot

7 Neural-network wave functions ¡ª beyond the RBM

8 Bosonic and fermionic wave functions

9 Local energy, VMC estimator, and optimisation

10 Stochastic Reconfiguration ¡ª full derivation

11 Implementation: bosonic quantum harmonic oscillator

12 Implementation: fermionic quantum harmonic oscillator

Best wishes to you all,

Aleksander and Morten