fast-few-body-bayesing

The corresponding arXiv publication can be found here.

This package is built to calculate posterior probability distributions for three-body low-energy constants at next-to-next-to-leading order (NNLO) in chiral nuclear forces. Eigenvector continuation (EC/ Ritz Method) is used as an efficient emulator for few-body bound-state observable calculations to make both Markov Chain Monte Carlo (MCMC) sampling possible.

Getting started

• This project relies on python=3.8. It was not tested with different versions. To view the entire list of required packages, see environment.yaml.
• 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 fit-3bf
• Install the fit3bf 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 /fit3bf.

Using your own chiral interaction

The inputs needed to use this package are Hamiltonians and operators for few-body systems. The workflow is the following

1. Package your Hamiltonian and operators for observables in the appropriate format.
2. Train EC emulator for observables and output an emulator file for each observable.
3. Use these emulator files to efficiently sample posterior pdfs for $c_D$ and $c_E$.

Following are details of how to perform these steps for your own chiral interaction to get posterior pdfs for $c_D$ and $c_E$.

Step 1: package operators in appropriate format

In order to train the EC emulators for the observables, you must construct files that the training script can use. This will involve separating your operators into a constant part and any parts proportional to the LECs being sampled. Please see reference for mathematical details and why this is necessary.

Fitting cD and cE only (no pi-N or NN LEC uncertainty included)

The simplest case is the one in which you have optimal values for the pi-N and NN LECs, and wish to keep these fixed in the analysis. If you have covariance matrices or posterior pdfs available for these other sectors and want to also include this information, please move to the next section.

Fitting cD and cE (pi-N or NN LEC uncertainty included)

If you have covariance matrices or posterior pdfs available for the pi-N and NN sectors and want to include this information when fitting cD and cE, the approach will be similar to the one above, except that you should place EC training points near the likely values of these LECs as well.

What to do next

Assuming you have followed the directions in the Getting Started section, to create the emulators used in this work:

1. Ensure the matrix element files are available (# TODO). The parameters files (discussed below) will have to point to the locations of these files.
2. cd to scripts/ and then run python train_emulators.py --parameters=parameters/NNLO_450.yaml. This will generate emulators in the full NN+3N space of 13 dimensions. The output directory name will be unique based on the contents of the parameter file fed into train_emulators.py
3. Again while in scripts/, run python train_emulators.py --parameters=parameters/NNLO_450_3bf_only.yaml. This will generate emulators in the 2d 3N space.

To sample the emulators (only done for the NN+3N emulators in this work) do the following: again while in scripts run python sample_emulators.py --parameters=parameters/sampling.yaml, ensuring the directory of the emulators matches what is in sampling.yaml.

To create the plots from these emulators and samples, check out the following in notebooks/:

• plot_samples.ipynb
• latin_hypercube_samples.ipynb
• gridded_posteriors.ipynb