TetrisCNN_for_spin_systems

This is a repository containing code for the NeurIPS ML4PS workshop paper:
"Speak so a physicist can understand you! TetrisCNN for detecting phase transitions and order parameters" by K. Cybiński, J. Enouen, A. Georges, and A. Dawid

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The data we use are snaphots of various physical 1D systems in the ground state, generated using the Julia programming language.
The ground state is calculated using Density Matrix Renormalization Group (DMRG) algorithm, using the ITensors.jl library.
The datasets are saved to the TFIM_datasets.

The physical system implementedin this demonstration repository is the 1-D Transverse Field Ising (TFIM) model
Hamiltonian (in Planck units, so $c = G = \hbar = k_B = 1$) reads:

$$\hat{H}_{\rm TFIM} = -J \left( \sum_{i} \hat{S}^z_i \,\hat{S}^z_{i + 1} + g \sum_i \hat{S}^x_i \right)$$

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For the machine learning part we use PyTorch ML library.
All auxiliary and helper functions are in /src/ folder. In particular:

• TetrisCNN architecture is located /src/architectures.py,
• data loaders are in /src/loaders.py,
• functions for unified performance metrics calculations are in /src/metrics.py,
• functions for combinatorial generation of all possible n-site correlations within a given kernel are in /src/combinatorics.py file,
• general auxiliary functions are in /src/auxiliary_functions.py.

File 1D_TFIM_train.py is developed for NN training and saving it into Models folder. This file also plots the training history analogous to Fig. 2 from submission text, along with loss and $R^2$ history.

The analysis pipeline is exectuted with analysis_pipeline_1D.py file. This file also plots the detailed report from linear and symbolic regression fittings, along with a report in a format matching Fig. 6 from the submission.

Both the training file (1D_TFIM_train.py) and analysis pipeline file (analysis_pipeline_1D.py) allow for a very detailed control, all governed by their CLI arguments, so do not hesitate to call them with -h flag, in order to see all customization options.

The fittings are all done using Symbolic Regression - we use PySR Python package for this, which is a wrapper around SymbolicRegression.jl Julia backend.

The code was written by Kacper Cybiński (University of Warsaw) and James Enouen (University of South California) with help of Anna Dawid (Leiden University).

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The packages needed for proper execution are listed below. Some of them are as of writing this documentation only pip-installable, and therefore indicated separately below.

Conda-Installable Packages

• torch
• numba
• sympy
• numpy
• matplotlib
• scikit-learn (sklearn)
• termcolor
• tqdm
• pandas
• networkx
• scipy
• pysr

Only Pip-Installable Packages

• prettytable
• latex2sympy2
• trimesh
• humanize