Symmetry-Aware Neural Networks in Materials Science Tutorial

Tess Smith introduces the tutorial on Symmetry Aware Neural Networks, emphasizing their importance in materials science and machine learning applications.

### Symmetry Aware Neural Networks for Materials Science: MRS 2021 Fall Meeting Tutorial
* 👩 ‍🏫 Tess Smith introduces the tutorial on symmetry-aware neural networks, emphasizing the goal of making **equivariant neural networks more accessible** for applications in materials science.
* 📚 The tutorial will cover the **importance of symmetry** in machine learning models, the necessary **mathematics**, and examples of applications such as **molecular dynamics** and **material properties**.
* 🌐 Participants can access resources, including schedules, videos, and code, at **e3n.org/mrs**, and are encouraged to reach out via GitHub or email with questions.
* 🔍 The morning session will focus on **symmetry considerations**, with talks from Mario Geiger on **group theory** and Martin on using **equivariant functions in E3NN** for atomic geometry representations.
* ⚛ The afternoon will delve into applications of equivariant models, with presentations from Simon, Alby, Josh Rackers, and Nina Gentile on **molecular dynamics**, **electron densities**, and **phonon properties**.
* 📈 Tess highlights the significance of **symmetry** in achieving **high accuracy** in models, referencing DeepMind's AlphaFold2 and the Gordon Bell Prize-winning DeepMD model as examples of symmetry's **impact on performance**.
* 📊 Equivariant models are noted for their **data efficiency**, allowing for **accurate results with less data**, which is crucial for training on **expensive calculations** like coupled cluster methods.
* 📖 The tutorial aims to equip participants with the knowledge to develop computational tools that **understand and predict structure-property relationships** in atomic systems, ultimately **accelerating materials discovery and design**.

e3nn Tutorial MRS 2021 Fall Meeting -- Tutorial 1/6 -- Tess Smidt

e3nn

Introduction to the MRS 2021 Fall Meeting Tutorial on Symmetry Aware Neural Networks

Tess Smith introduces the tutorial on equivariant neural networks for materials science using the E3NN package.

The tutorial aims to make equivariant neural networks more accessible for materials science applications.

Topics covered include the benefits of symmetry in machine learning models, relevant mathematics, and applications in molecular dynamics and material properties.

Tutorial information, including schedule, videos, slides, and code, is available at e3n.org/mrs.

Questions can be submitted via GitHub or email to the tutorial instructors.

The morning session focuses on symmetry considerations and machine learning for physical sciences.

Mario Geiger will discuss group theory and equivariant interactions.

Martin will explain how to use equivariant functions in E3NN to create invariant representations of atomic geometry.

The afternoon session covers applications of equivariant models for molecular dynamics, electron densities, and phonon properties.

Importance of Symmetry in Machine Learning Models for Materials Science

AlphaFold2's success is attributed to its use of local and global reference frames preserving symmetry.

The DeepMD model, while considering symmetry, is not fully equivariant.

Equivariant models are significantly more data-efficient than DeepMD.

The afternoon session will discuss n-equip, an equivariant interatomic potential model.

The overall motivation is to build computational tools for understanding and designing structure-property relationships of atomic systems.

Representing Atomic Structures and Properties

Physical systems are described using coordinate systems in 3D space.

Coordinate systems are arbitrary and can be transformed using rotations, translations, and inversions.

The choice of coordinate system should not affect the physical meaning of the results.

Approaches to Creating Symmetry-Aware Models

Data augmentation is a brute-force approach that is inefficient for 3D data.

Invariant models compute invariant features and discard the coordinate system.

Equivariant models retain the coordinate system, and the output changes accordingly with coordinate system changes.

Euclidean Neural Networks: Combining Neural Networks and Representation Theory

Neural networks are differentiable functions that update weights using gradient descent.

Representation theory studies how objects transform under group actions (rotations, translations, etc.).

Equivariant neural networks must satisfy the condition that operations commute with group actions.

The models operate on geometry and geometric tensors using geometric tensor algebra.