SFU Applied & Computational Math Seminar Series: Christoph Ortner

Although my talk is arguably about machine-learning, I will use mostly ideas and language from mathematical modelling and numerical analysis. I will introduce a natural geometric learning framework, the atomic cluster expansion (ACE), which focuses on linear and shallow models, and adds a new dimension to the design space of geometric deep learning. ACE is particularly well-suited for parameterising surrogate models of particle systems where it is important to incorporate symmetries and geometric priors into models without sacrificing systematic improvability. My main focus will be on “learning” interatomic potentials (or, force fields): in this context, ACE models arise naturally from a few systematic modelling and approximation theoretic steps that can be made reasonably rigorous. However, the applicability is much broader and, time permitting, I will also show how the ACE framework can be adapted to other contexts such as electronic structure (parameterising Hamiltonians), quantum chemistry (wave functions), or elementary particle physics (e.g., jet tagging).