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Hybrid Modelling of Interatomic Forces (Physics+Data+Mathematics)

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Accurate molecular simulation requires quantum chemistry models that accurately capture the interaction between nuclei and electrons. Unfortunately, their high computational cost makes these models unsuitable for simulating complex material phenomena or large molecules. On the other hand, interatomic potentials (IPs) are largely empirical models with poor accuracy and narrow applicability. The past decade has seen a revival of IPs, re-casting their construction as a “machine learning” instead of a “modelling” problem.

In this talk I will backtrack from this trend by returning to simple functional forms, motivated by physics (and somewhat justified by mathematics), but retain a key feature of the data-driven/ML approach: models must be systematically improvable. I will demonstrate how a combination of elementary ideas from analysis, approximation theory, and representation theory leads to a very competitive construction (in terms of fitting error/cost) that has a range of additional advantages, for example that it can be effectively regularised. While my talk will focus specifically on interatomic potentials, the ideas should in principle be applicable to a much wider range of particle models, and at a more conceptual level also to continuum models.

This talk is part of the SIAM-IMA Cambridge Student Chapter series.

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