## Distinguished Seminar Series in Computational Science and Engineering

**October 13, 2022, 12:30 PM**

**Geometric Shallow Learning
(for interatomic potentials and other particle systems)**

Christoph Ortner

Professor, Department of Mathematics

University of British Columbia

**Abstract:
**I will outline a geometric learning framework, the atomic cluster expansion (ACE), which focuses on linear and shallow models. The framework is particularly well-suited for studying particle systems where it often achieves state-of-the-art accuracy and performance. The main focus will be on learning interatomic potentials: I will explain how ACE models arise naturally from a few systematic modelling and approximation steps, and how this gives a new dimension to established geometric deep learning frameworks.

Linear ACE variants are particularly well-suited to integrate with Bayesian and active learning ideas. I will explain how we adapt these ideas to construct a general scheme for generating training sets that brings us close to an end-to-end workflow for producing robust and fast machine learned (interatomic potential) models with only minimal user-intervention. A particular highlight is the fully-automated prediction of phase diagrams for high-entropy alloys.

Time permitting I will also mention how the ACE framework can be applied in other contexts such as parameterising hamiltonians, wave functions, or for jet tagging.

**Bio:**

Christoph Ortner is Professor of Mathematics at the University of British Columbia. He works on models, algorithms and the mathematical theory for atomistic and multi-scale simulation. A main focus of his research has been on bridging the scales from quantum to atomistic to continuum descriptions of materials and material defects. Nowadays the focus has shifted to the development of hybrid mechanistic and machine-learned interaction models for particle systems, in particular atoms, molecules and electrons.

CO received a DPhil (PhD) in Numerical Analysis in 2007 from the University of Oxford, where he also held his first permanent position. He moved to the University of Warwick in 2011 and to the University of British Columbia in 2020. His work on the mathematics of atomistic multi scale models was recognized by a Leverhulme Prize (2012), ERC Starting Grant (2014), LMS Whitehead Prize (2015), MFO John Todd Award (2017), ERC Consolidator Grant (2019), and membership of the college of the Royal Society of Canada (2022).

Geometric Shallow Learning

(for interatomic potentials and other particle systems)

Christoph Ortner

University of British Columbia