Author: Joseph W. Abbott, PhD Student @ Lab COSMO, EPFL

A proof-of-concept workflow for torch-based electron density learning. Equivariant structural representations, that is those that transform equivariantly under rotation with the irreducible spherical components of the target property (i.e. whether they be invariant or covariant), can be constructed using the xyz coordinates of a set of training molecules. As part of a supervised machine learning scheme, these structural representations form inputs to the machine learning model, while reference electron densities calculated by quantum chemical methods are given as target outputs.

Model training is performed using PyTorch, but various other parts of the workflow are performed with a number of open source packages from the software stacks of labs COSMO and LCMD at EPFL. The main ones are outlined below.

Q-Stack: lcmd-epfl/Q-stack

A software stack dedicated to pre- and post-processing tasks for quantum machine learning. In rholearn, its equistore-interfacing module equio is used to pre-process electron density coefficients generated from quantum chemical calculations into TensorMap format, ready for input into a equistore/torch-based ML model. Its fields module is also used to post-process electron densities into a format suitable for visualization.

rascaline: Luthaf/rascaline

This is used to generate equivariant structural representations for input into ML models. In rholearn, rascaline is used to build an atom-centered density descriptor of the molecules in the training data, which is then used to generate an equivariant $\lambda$-SOAP representation.

equistore: lab-cosmo/equistore

This is a storage format for atomistic machine learning, allowing an efficient way to track data and associated metadata for a wide range of atomistic systems and objects. In rholearn, it is used to store $\lambda$-SOAP structural representations, ground and excited state electron densities, and Coulomb overlap matrices.

equisolve: lab-cosmo/equisolve

Concerned with higher-level functions and classes built on top of equistore, this package is used to prepare data and build models for machine learning. However, it is still in a very early alpha development stage. In rholearn, it is used to split TensorMap objects storing structural representations and electron densities into train, test, and validation data.

chemiscope: lab-cosmo/chemiscope

This package is used a an interactive visualizer and property explorer for the molecular data from which the structural representations are built.

The only requirements to begin installation are git, conda and rustc:

• git >= 2.37
• conda >= 22.9
• rustc >= 1.65

conda

Is used as a package and environment manager. It allows a virtual environment will be created within which the appropriate version of Python (== 3.10) and required packages will be installed.

If you don't already have conda, the latest version of the lightweight miniforge can be downloaded from here, for your specific operating system. After downloading, change the execute permissions and run the installer, for instance as follows:

chmod +x Miniforge3-Linux-x86_64.sh
./Miniforge3-Linux-x86_64.sh

and follow the installation instructions.

When starting up a terminal, if the (base) label on the terminal user prompt is not seen, the command bash might have to be run to activate conda.

rustc

Is used to compile code in rascaline and equistore. To install rustc, run the following command, taken from the 'Install Rust' webpage:

curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh

and follow the installation instructions.

Clone this repo and create a conda environment using the environment.yml file. This will install all the required base packages, such as ase, numpy, torch and matplotlib, into an environment called rho.

1. Clone the rholearn repo and create a virtual environment.

git clone https://github.com/jwa7/rho_learn.git
cd rho_learn
conda env create -f environment.yml
conda activate rho

Then, some atomistic ML packages from the lab COSMO and LCMD software stacks can be installed in the rho environment. Ensure you install these in the order shown below (this is very important) and with the exact commands, as some development branches are required for this setup.

2. rascaline: pip install git+https://github.com/m-stack-org/rascaline.git@rholearn

3. equisolve: pip install git+https://github.com/m-stack-org/equisolve.git@rholearn

4. qstack: pip install git+https://github.com/jwa7/Q-stack.git

5. chemiscope: pip install chemiscope

6. rholearn: ensure you're in the rho_learn/ directory then pip install .

In order to run the example notebooks (see Examples section below), you'll need to work within the rho conda environment. If the env doesn't show up in your jupyter IDE, you can run the terminal command ipython kernel install --user --name=rho and restart the jupyter session.

Then, working within the rho environment, rholearn and other modules can then be imported in a Python script as follows:

from rholearn.features import lambda_soap_vector
from rholearn.loss import MSELoss, CoulombLoss
from rholearn.models import EquiModelGlobal
from rholearn.training import train

import equistore
from equistore import Labels, TensorMap
from equisolve.utils import split_data

If you ever need to update rholearn, or any of the other packages for that matter, make sure you uninstall before git pull-ing and reinstalling:

pip uninstall rholearn
cd rho_learn
git pull
pip install .

If you ever receive the equistore error ValueError: Trying to set the EQUISTORE library path twice error it is probably due to a clash between rascaline and equistore. This will soon be fixed in equistore, but unitl then make sure that any rascaline modules are loaded before equistore ones. The main rholearn module you need to be careful of in this regard is features.py. If, for example, you are importing from this module in a notebook, i.e. from rholearn.features import lambda_soap_vector, make sure you place this import at the very top of the notebook. This is because features.py imports both rascaline and equistore (in that order), but thus needs to be placed first.

The functionality of this package is demonstrated in the example notebooks in the rho_learn/docs/example/azoswitch directory. This section will briefly the various parts of the workflow.

A demonstrative notebook is provided, implementing the key parts of the model-training workflow. This begins with the generation of a $\lambda£-SOAP structural representation for a 1000-water monomer database. The relationship to the electron density is then learned using a linear model, optimizing weights based on gradient descent of an $L^2$ loss function. The aim of this notebook is to be a concise introduction to the key components of torch-based learning of the electron density.

The open-source packge "Symmetry-Adapted Learning of Three-dimensional Electron Densities" (SALTED) is the source for this dataset and was used to generate reference electron densities, with outputs converted to equistore format.

Also included in the examples are a set of more pedagogical notebooks on a more complicated dataset. In order to be lightweight enough to run on a laptop, and with the emphasis being on the workflow as opposed to accurate results, a 10-molecule database of azoswitch dyes are provided.

This dataset is a 10-molecule subset of a database of molecular azoswitches used in the electron density learning paper entitled "Learning the Exciton Properties of Azo-dyes" DOI: 10.1021/acs.jpclett.1c01425.

There are 3 example notebooks for the azoswitch workflow.

The first notebook 1_data.ipynb outlines how to visualize the molecular data, construct a $\lambda$-SOAP representation, perform a train-test-validation split and partition data into training subsets of various sizes such that a learning exercise can be performed.

The second 2_models.ipynb goes through the construction of both a linear and nonlinear model, custom loss functions (based on the Coulomb metric), and how to use these in model training.

The third and final notebook 3_analysis.ipynb outlines plotting figures analysing model training, as well as making a prediction on a validation structure, visualizing this prediction and the associated error.

• Symmetry-Adapted Machine Learning for Tensorial Properties of Atomistic Systems, Phys. Rev. Lett. 120, 036002. DOI: 10.1103/PhysRevLett.120.036002

• SALTED (Symmetry-Adapted Learning of Three-dimensional Electron Densities), GitHub: github.com/andreagrisafi/SALTED, Andrea Grisafi, Alan M. Lewis.

• Transferable Machine-Learning Model of the Electron Density, ACS Cent. Sci. 2019, 5, 57−64. DOI: 10.1021/acscentsci.8b00551

• Atom-density representations for machine learning, J. Chem. Phys. 150, 154110 (2019). DOI: 10.1063/1.5090481

• Learning the Exciton Properties of Azo-dyes, J. Phys. Chem. Lett. 2021, 12, 25, 5957–5962. DOI: 10.1021/acs.jpclett.1c01425

• Impact of quantum-chemical metrics on the machine learning prediction of electron density, J. Chem. Phys. 155, 024107 (2021), DOI: 10.1063/5.0055393