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SUMMARY:Scaling up the solving of large biological systems of ordinary dif
 ferential equations with mixed-precision arithmetic.
DTSTART:20251203T143000Z
DTEND:20251203T151000Z
DTSTAMP:20260504T084600Z
UID:indico-event-15503@indico.math.cnrs.fr
DESCRIPTION:Speakers: Arsène Marzorati (ICJ - INRIA)\n\nIn computational 
 biology\, agent-based models (ABM) are a computational modelling approach 
 for complex living systems\, enabling heterogeneity across agents. ABMs ar
 e often better aligned with data from real large systems. However\, the co
 mputational cost\, which can increase supra-linearly with size\, is a majo
 r challenge that limits applicability. In our work\, we suggest to tackle 
 this problem with the use of mixed-precision. Mixed-precision methods cons
 ist in using two or more numerical formats\, usually floating point number
 s\, inside a single numerical method\, to find a good trade-off between t
 he accuracy and speed. These methods are developed in several fields that 
 encounter similar dimensional computing problems such as machine-learning\
 , linear algebra or meteorology.Here\, we consider an ABM of N heterogenou
 s agents\, and we assume that the dynamical dependence is split into two p
 arts\, an agent-centered term and another term accounting for complex pair
 wise interactions. We make no assumption on the form of the interaction te
 rm\, except that all the N agents can interact heterogeneously with each o
 ther. This leads to an ODE system with a right-hand side presenting a comp
 lexity in N^2 that is difficult to reduce.We show that accuracy of numeric
 al scheme is improved with the mixed-precision tuning as the system size i
 ncreases. As the size of the population increases\, rounding errors coming
  from low precision terms are absorbed by the large number of interactions
 . In addition\, the complexity of non-linear functions used in modeling an
 d the increasing size tend to increase the speed-up of low precision. This
  leads to an interesting gain in performance with a limited degradation in
  accuracy\, particularly for interaction evaluations.\n \n\nhttps://indic
 o.math.cnrs.fr/event/15503/
LOCATION:Fokko (ICJ)
URL:https://indico.math.cnrs.fr/event/15503/
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