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Data driven computing with noisy material data sets. (English) Zbl 07186068
Summary: We formulate a Data Driven Computing paradigm, termed max-ent Data Driven Computing, that generalizes distance-minimizing Data Driven Computing and is robust with respect to outliers. Robustness is achieved by means of clustering analysis. Specifically, we assign data points a variable relevance depending on distance to the solution and on maximum-entropy estimation. The resulting scheme consists of the minimization of a suitably-defined free energy over phase space subject to compatibility and equilibrium constraints. Distance-minimizing Data Driven schemes are recovered in the limit of zero temperature. We present selected numerical tests that establish the convergence properties of the max-ent Data Driven solvers and solutions.

62G99 Nonparametric inference
62B10 Statistical aspects of information-theoretic topics
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62R07 Statistical aspects of big data and data science
68T10 Pattern recognition, speech recognition
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