Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Polyatomic Complexes: A topologically-informed learning representation for atomistic systems

Rahul Khorana, Marcus Noack, Jin Qian

TL;DR

A representation of atomistic systems that satisfies all structural, geometric, efficiency, efficiency, and generalizability constraints is presented and a general algorithm to encode any atomistic system is provided.

Abstract

Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our representation satisfies all structural, geometric, efficiency, and generalizability constraints. Afterward, we provide a general algorithm to encode any atomistic system. Finally, we report performance comparable to state-of-the-art methods on numerous tasks. We open-source all code and datasets. The code and data are available at https://github.com/rahulkhorana/PolyatomicComplexes.

Polyatomic Complexes: A topologically-informed learning representation for atomistic systems

TL;DR

A representation of atomistic systems that satisfies all structural, geometric, efficiency, efficiency, and generalizability constraints is presented and a general algorithm to encode any atomistic system is provided.

Abstract

Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our representation satisfies all structural, geometric, efficiency, and generalizability constraints. Afterward, we provide a general algorithm to encode any atomistic system. Finally, we report performance comparable to state-of-the-art methods on numerous tasks. We open-source all code and datasets. The code and data are available at https://github.com/rahulkhorana/PolyatomicComplexes.
Paper Structure (59 sections, 11 theorems, 20 equations, 2 figures, 10 tables, 3 algorithms)

This paper contains 59 sections, 11 theorems, 20 equations, 2 figures, 10 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. SMILES
  3. DeepSMILES
  4. ECFP Fingerprints
  5. SELFIES
  6. GroupSELFIES
  7. Graphs
  8. Atomic Cluster Expansion (ACE)
  9. Behler-Parrinello Descriptor
  10. Bartók/SOAP Descriptor
  11. e3nn/Euclidean Neural Networks
  12. Motivation and Representation Criteria
  13. Invariances
  14. Uniqueness
  15. Continuity and Differentiability
  16. ...and 44 more sections

Key Result

Lemma 2.9

Atomic complexes are finite $n$-connected CW-complexes. The full proof can be found in the Appendix proof:atomicNConnectedFinite.

Figures (2)

  • Figure 1: We graphically describe, with the example of $\mathrm{H_2O}$, how to construct a Polyatomic complex. The first step is to encode each individual atom in detail (protons, neutrons, electrons). We view protons, neutrons and electrons as $n$-spheres. Afterward we combine our representations of each individual atom together to form molecules/atomistic systems. One can choose to further augment the representation at this step. Finally, one can feed the representation into a machine learning model.
  • Figure 2: Materials project: materials mp-626062, mp-5489, and mp-3301 MaterialsProject

Theorems & Definitions (45)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • proof
  • Remark 2.6
  • Definition 2.7
  • Remark 2.8
  • Lemma 2.9
  • ...and 35 more