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Model-free Data-Driven inference in computational mechanics

Prume, E. and Reese, S. and Ortiz, M. (2023) Model-free Data-Driven inference in computational mechanics. Computer Methods in Applied Mechanics and Engineering, 403 . Art. No. 115704. ISSN 0045-7825. doi:10.1016/j.cma.2022.115704.

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We extend the model-free Data-Driven computing paradigm to solids and structures that are stochastic due to intrinsic randomness in the material behavior. The behavior of such materials is characterized by a likelihood measure instead of a constitutive relation. We specifically assume that the material likelihood measure is known only through an empirical point-data set in material or phase space. The state of the solid or structure is additionally subject to compatibility and equilibrium constraints. The problem is then to infer the likelihood of a given structural outcome of interest. In this work, we present a Data-Driven method of inference that determines likelihoods of outcomes from the empirical material data and that requires no material or prior modeling. In particular, the computation of expectations is reduced to explicit sums over local material data sets and to quadratures over admissible states, i.e., states satisfying compatibility and equilibrium. The complexity of the material data-set sums is linear in the number of data points and in the number of members in the structure. Efficient population annealing procedures and fast search algorithms for accelerating the calculations are presented. The scope, cost and convergence properties of the method are assessed with the aid selected applications and benchmark tests.

Item Type:Article
Related URLs:
URLURL TypeDescription
Prume, E.0000-0002-2227-7540
Reese, S.0000-0003-4760-8358
Ortiz, M.0000-0001-5877-4824
Additional Information:All authors gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG) and French Agence Nationale de la Recherche (ANR) through the project “Direct Data-Driven Computational Mechanics for Anelastic Material Behaviours” (ANR-19-CE46-0012-01, RE 1057/47-1, project number 431386925) within the French-German Collaboration for Joint Projects in Natural, Life and Engineering (NLE) Sciences, Germany. SR gratefully acknowledges the funding of the DFG, Germany projects “Model order reduction in space and parameter dimension - towards damage-based modeling of polymorphic uncertainty in the context of robustness and reliability” (SPP 1886, project number 312911604) and “Coupling of intrusive and non-intrusive locally decomposed model order reduction techniques for rapid simulations of road systems” (TP B05/TRR 339, Germany, project number 453596084). MO is grateful for support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via project 211504053 - SFB 1060; project 441211072 - SPP 2256; and project 390685813 - GZ 2047/1 - HCM.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)312911604
Agence Nationale de la Recherche (ANR)312911604
Agence Nationale de la Recherche (ANR)431386925
Agence Nationale de la Recherche (ANR)453596084
Agence Nationale de la Recherche (ANR)ANR-19-CE46-0012-01
Deutsche Forschungsgemeinschaft (DFG)453596084
Deutsche Forschungsgemeinschaft (DFG)441211072 - SPP 2256
Deutsche Forschungsgemeinschaft (DFG)390685813 - GZ 2047/1 - HCM
Record Number:CaltechAUTHORS:20221128-494241100.30
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ID Code:118069
Deposited By: Research Services Depository
Deposited On:16 Dec 2022 18:40
Last Modified:16 Dec 2022 21:41

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