Square Well Emulators

This repository contains code used to test and generate preliminary results in Efficient emulators for scattering using eigenvector continuation (arXiv:2301.05093). It also contains code for the bound-state problem.

Getting Started

• This project relies on python=3.10. It was not tested with different versions. To view the entire list of required packages, see environment.yml.
• Clone the repository to your local machine.
• Once you have cd into this repo, create a virtual environment (assuming you have conda installed) via

conda env create -f environment.yml

• Enter the virtual environment with conda activate square-well-env
• Install the emulate package in the repo root directory using pip install -e . (you only need the -e option if you intend to edit the source code in emulate/).

Example

The two main classes for the KVP-based emulators are KVP_emulator_scattering for scattering and KVP_emulator_bound for bound states.

The code snippet below shows how the scattering emulator should be used:

from emulator_scattering import KVP_emulator_scattering

# Setup
V_exact = ... # The potential depth where we want to make our prediciton
V_b = ...  # The potential used to train the emulator
ps, ws = ...   # The momentum and integration measure in units of inverse fm, corresponding to the potential mesh
k0 = ...   # The wave number where we are making the prediction. Proportional to the square root of the energy.

# Initialize object.
emu = KVP_emulator_scattering(k=k0, ps=ps, ws=ws)

# Train the emulator
emu.train(psi_b, V_b, V_exact)

# Predict phase shifts at validation parameter values using the emulator
emu_pred = emu.prediction(tau_b, nugget) # Emulator

The code snippet below shows how the bound state emulator should be used:

from emulator_bound import KVP_emulator_bound

# Setup
V_exact = ... # The potential depth where we want to make our prediciton
Vr = ...  # The potential used to train the emulator
psi_b = ...  # The wave functions used to build the basis
T_b = ...  # The the kinetic energy for psi_b
ps, ws = ...   # The momentum and integration measure in units of inverse fm, corresponding to the potential mesh

# Initialize object.
KVP_emulator_bound(ps, ws, Vr)

# Predict phase shifts at validation parameter values using the emulator
emu_pred = emu.energy_pred(psi_b, T_b) # Emulator

Citing this work

Please cite this work as follows:

Title: KVP emulators for the square well problem
Author: A.J. Garcia
Date: 05/18/2023
Code version: 2.0
Availabilty: https://github.com/AJG91/square-well-emulators