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Data-driven finite element method

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conference contribution
posted on 13.05.2021, 13:49 by Adriana Kuliková, Andrei G. Shvarts, Lukasz Kaczmarczyk, Chris J. Pearce
The standard approach to mechanical problems requires the solution to the mathematical equations that describe both the conservation laws and the constitutive relationships, where the latter is obtained after fitting experimental data to a certain material model. In this work, we follow an alternative approach, and develop a Data-Driven (DD) framework for mechanical problems. The conservation laws are satisfied by means of the finite element method; instead of a constitutive relationship we can use experimental data directly, thereby avoiding the need for material model parameters. In this paper, the DD approach is applied to a flow problem in porous media. We present the solution algorithm, demonstrate its efficiency with numerical examples, and, finally, study the influence of the noise present in the data on the results. The framework has been implemented in the open-source finite element software MoFEM.

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