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SUMMARY:Model-Free Data-Driven Science: Cutting out the Middleman - Prof M
 ichael Ortiz\, California Institute of Technology 
DTSTART:20210219T160000Z
DTEND:20210219T170000Z
UID:TALK156577@talks.cam.ac.uk
CONTACT:Hilde Hambro
DESCRIPTION:We have developed a new computing paradigm\, which we refer to
  as Data-Driven Computing\, according to which calculations are carried ou
 t directly from experimental material data and pertinent kinematic constra
 ints and conservation laws\, such as compatibility and equilibrium\, thus 
 bypassing entirely the empirical material modeling step of conventional co
 mputing altogether. Data-driven solvers seek to assign to each material po
 int the state from a prespecified data set that is closest to satisfying t
 he conservation laws. Equivalently\, data-driven solvers aim to find the s
 tate satisfying the conservation laws that is closest to the data set. The
  resulting data-driven problem thus consists of the minimization of a dist
 ance function to the data set in phase space subject to constraints introd
 uced by the conservation laws. We demonstrate the data-driven paradigm and
  investigate the performance of data-driven solvers by means of several ex
 amples of application\, including statics and dynamics of nonlinear three-
 dimensional trusses\, linear and nonlinear elasticity\, dynamics and plast
 icity\, including scattered data and stochastic behavior. In these tests\,
  the data-driven solvers exhibit good convergence properties both with res
 pect to the number of data points and with regard to local data assignment
 \, including noisy material data sets containing outliers. The variational
  structure of the data-driven problem also renders it amenable to analysis
 . We find that the classical solutions are recovered as a special case of 
 Data-Driven solutions. We identify conditions for convergence of Data-Driv
 en solutions corresponding to sequences of approximating material data set
 s. Specialization to constant material data set sequences in turn establis
 hes an appropriate notion of relaxation. We find that relaxation within th
 e Data-Driven framework is fundamentally different from the classical rela
 xation of energy functions. For instance\, we show that in the Data-Driven
  framework the relaxation of a bistable material leads to effective materi
 al data sets that are not graphs. I will finish my presentation with highl
 ights on work in progress\, including experimental material data mining an
 d identification\, material data generation through multiscale analysis an
 d fast search and data structure algorithms as a form of ansatz-free learn
 ing.\n\n
LOCATION:Zoom Meeting ID: 819 1682 8857
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