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SUMMARY:When the loss is not enough: misspecification uncertainty in atomi
 c simulations - Dr Thomas Swinburne\, Centre Interdisciplinaire de Nanosci
 ence de Marseille\, CNRS
DTSTART:20241023T133000Z
DTEND:20241023T143000Z
UID:TALK216568@talks.cam.ac.uk
CONTACT:Lisa Masters
DESCRIPTION:Atomic simulations employ interatomic potentials as a surrogat
 e model for electronic structure calculations of atomic energies and force
 s. \nIn practice\, interatomic potentials are always misspecified - no one
  choice of parameters can exactly match training data. Model parameters ar
 e thus intrinsically uncertain\, and any scheme to propagate uncertainty t
 o simulation results of interest should capture this uncertainty. \n\nThe 
 posterior distribution from Bayesian inference would appear to be ideal fo
 r this purpose\, but in fact the posterior is completely blind to misspeci
 fication uncertainty. This is most problematic when the underlying data is
  deterministic- the same input gives the same output\, as is the case for 
 electronic structure calculations and many other settings in computational
  science. As a result\, Bayesian parameter uncertainties are severe undere
 stimates\, rapidly decaying to zero as the number of training points incre
 ases. \n\nWith analogy to the Gibbs-Bogoliubov bound in free energy estima
 tion\, I will discuss how the loss is only an upper bound to the true gene
 ralisation error. I will derive a condition any minimiser of the generalis
 ation error must obey\, and design a simple ansatz that can be variational
 ly minimised[1]. The variational minimum can be found analytically for hig
 h dimensional linear models\, giving efficient estimation and very useful 
 bounding of worse-case errors. Importantly\, model prediction errors are n
 ow directly related to uncertainties in model parameters\, essential to ca
 pture correlations present when propagating uncertainty through multi-scal
 e simulations. If time allows\, I will discuss how parameter uncertainty c
 an be efficiently propagated when simulation results are stationary points
  on the atomic energy landscape[2].\n\n[1] https://arxiv.org/abs/2402.0181
 0v3 (with Danny Perez\, Los Alamos National Laboratory)\n[2] https://arxiv
 .org/abs/2407.02414 (with Ivan Maliyov and Petr Grigorev\, CNRS/Aix-Marsei
 lle U)\n
LOCATION:Unilever Lecture Theatre\, Yusuf Hamied Department of Chemistry
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