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SUMMARY:Some mathematical aspects of uncertainty quantification for intera
 tomic potentials - Maciej Buze (Heriot-Watt University)
DTSTART:20230726T130000Z
DTEND:20230726T140000Z
UID:TALK203527@talks.cam.ac.uk
DESCRIPTION:Interatomic potentials (IPs) approximate the potential energy 
 surface of systems of atoms as a function of their positions and are seen 
 as a computationally feasible alternative to electronic structure calculat
 ions\, which additionally model the motion of electrons around atomic nucl
 ei. IPs form a basis of molecular mechanics and molecular dynamics simulat
 ions in computational chemistry\, computational physics and computational 
 materials science and have proven useful in explaining and predicting mate
 rials properties\, such as lattice parameters\, surface energies\, interfa
 cial energies\, adsorption\, cohesion\, thermal expansion\, and elastic an
 d plastic material behaviour\, as well as chemical reactions.\nEmpirical I
 Ps have between 2 and 11 parameters\, rising to >1000 parameters for moder
 n machine-learning potentials\, and the highly nonlinear and nonconvex nat
 ure of the overall model necessitates quantifying the uncertainty in their
  choice and how this propagates to quantities of interest\, such as mechan
 ical or chemical properties of materials. Usually\, this is achieved by em
 ploying a Bayesian approach\, whereby one assumes some prior probability d
 istribution for the parameters defining a given interatomic potential\, wh
 ich are subsequently updated using available data originating from experim
 ents or higher-level theories.\nIn this talk I will discuss ongoing work o
 n advancing the mathematical understanding of how uncertainty quantificati
 on for IPs should be conducted. In particular\, I will discuss (i) how the
  vast literature on the topic of continuum stochastic elasticity can be le
 veraged to provide an information-theoretic approach to deriving prior dis
 tributions for the IP parameters \; (ii) how polynomial approximation theo
 ry can be leveraged to reduce the uncertainty. 
LOCATION:Seminar Room 2\, Newton Institute
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