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IRTG Lecture

Thursday, October 10, 2019 10:30 AM;

JGU Mainz, Physics, Newton-Raum


Christoph Ortner, University of Warwick: Hybrid Modelling of Interatomic Forces

Accurate molecular simulation requires computationally expensive quantum chemistry models that makes simulating complex material phenomena or large molecules intractable. The past decade has seen a revival of interatomic potentials (IPs), fast but traditionally inaccurate surrogate models, re-casting their construction as an approximation and data-fitting problem. I will give an introduction to this problem, from a mixed modelling / data / mathematics perspective. In particular I want to show how it can be formalised as a high-dimensional approximation problem, with many structures that can be exploited to make it tractable. I will introduce two approximation schemes, both using different symmetric polynomials, targeting in particular efficiency and transferability, some preliminary simulation results, and the beginnings of a rigorous numerical analysis. Joint work with Geneviève Dusson (CNRS Besançon), Markus Bachmayr (Mainz), Gabor Csanyi and Cas van der Oord (Cambridge), Simon Etter (NU Singapur).


Geneviève Dusson, University of Warwick: Atomic Permutation-Invariant Polynomials (aPIPs) for Materials and Molecules

I will present the practical construction of interatomic potentials for materials and molecules based on a body-order expansion (ANOVA, HDRM), each body order being represented by polynomials satisfying the rotation and permutation symmetry of the "exact" potential energy surface. These polynomials are determined in a data-driven fashion from linear fits trained with ab initio data. I will report convergence tests on training sets for materials and molecules, illustrating the accuracy, the low computational cost, and the systematic improvability of the potential. I will then outline a range of the regularisation procedures that we incorporate into the polynomial fits to achieve transferability of the potentials. Finally, I will outline a testing framework to stress-test the generalisation capabilities of new potentials far from the training set. Joint work with Alice Allen (Cambridge), Gábor Csányi (Cambridge), Christoph Ortner (Warwick), and Cas van der Oord (Cambridge).


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