Bayesian Analysis Code for SLI

Introduction

This code base is complementary to our End2End shaken lattice project. The C++ component uses shaking sequences that were previously learned using RL to simulate the shaken lattice and record the final momentum space probability distributions $P(p|a,V_0)$, where $p$ is momentum and $a,V_0$ are the acceleration and lattice depths for the system specifically. The Python notebooks are then used to do Bayesian and statistical analysis.

General Notes:

• The shaking sequences are currently hard-coded as constant std::vectors into the source files. While not programmatically elegant, this is partly because for the purposes of this project, the shaking sequences should never be changed, even in error, and there are only three sequences.
• The shaking sequences are generated via RL code, which for privacy purposes isn't public yet. It however uses a version of the Environment and Wavepacket classes shown here.
• The Bayesian updating, Jenson-Shannon divergence calculation and other statistical analyses are all in the Python notebooks. The Python code reads in the files generated by the C++ simulations.
• Despite Github marking this as solely a Jupyter project, the core simulations and physics of the shaken lattice are encapsulated in the C++ code.

Structure of the code

The code is structured in the following folders:

• src contains the source main files
  • Compare was used to compare the accuracy of our probability distributions to those from the Python code.
  • Generate is used to generate the final momentum probability files for different $(a,V_0)$ values. It does so by directly evolving the Wavepacket class.
  • Simulate_Momentum uses the shaking sequences to evolve the Momentum class, thus recording the evolution of different observables with time. (This file is in progress).
• include contains the class files: Environment and Wavepacket.
• Python includes the Python code .py files for doing Bayesian Updating and calculating Jenson-Shannon Divergences. Jupyter notebooks used for generating plots for figures.
• Output is where the files generated by Generate and Simulate_Momentum are stored as the code runs.
• Data contains past runs from Output.
• build is for using CMake to build the C++ program, and contains binaries. The CMakeLists.txt is modified whenever we pick a different target and src/ file.