Data-driven computational mechanics

By Trenton Kirchdoerfer, Magdalena Ortiz. 2015

738 citations recorded by the source corpus.

We develop a new computing paradigm, which we refer to as data-driven computing, according to which calculations are carried out directly from experimental material data and pertinent constraints and conservation laws, such as compatibility and equilibrium, thus bypassing the empirical material modeling step of conventional computing altogether. Data-driven solvers seek to assign to each material point the state from a prespecified data set that is closest to satisfying the conservation laws. Equivalently, data-driven solvers aim to find the state satisfying the conservation laws that is closest to the data set. The resulting data-driven problem thus consists of the minimization of a distance function to the data set in phase space subject to constraints introduced by the conservation laws. We motivate the data-driven paradigm and investigate the performance of data-driven solvers by means of two examples of application, namely, the static equilibrium of nonlinear three-dimensional trusses and linear elasticity. In these tests, the data-driven solvers exhibit good convergence properties both with respect to the number of data points and with regard to local data assignment. The variational structure of the data-driven problem also renders it amenable to analysis. We show that, as the data set approximates increasingly closely a classical material law in phase space, the data-driven solutions converge to the classical solution. We also illustrate the robustness of data-driven solvers with respect to spatial discretization. In particular, we show that the data-driven solutions of finite-element discretizations of linear elasticity converge jointly with respect to mesh size and approximation by the data set.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4724e3ab99251b50e4a20e180f840aa18d97c82d

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Citations in the corpus

Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity (2020, background): “Frame invariance requires that (Borja, 2013; Kirchdoerfer and Ortiz, 2016) , The above is automatically satisﬁed when the response is modeled as an equivalent function of the right Cauchy-Green deformation tensor C , since: By training all the models in this work as a function of the right…”
A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database (2019, methodology): “It has been observed that distance minimizing data-driven (DMDD) computing solver [41] with distance measure in (7) - (9) is sensitive to data noise and outliers [42,54] because”
An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications (2019, background): “For instance, [12] replaces the constitutive model for a data-driven model.”
Deep convolutional neural networks for eigenvalue problems in mechanics (2018, background): “There has admittedly been a recent push towards purely data driven mechanics computing [11, 12, 13, 14, 15].”
A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality (2017, methodology): “Kirchdoerfer and Ortiz [15] developed a variational approach and applied it to linear elastic truss structures, where the goal was to pair specific data points to local material states such that essential constraints and conservation laws were satisfied while minimizing the distance between these…”
A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning (2018, methodology): “) or recently varia-83 tional principles (cf. Kirchdoerfer and Ortiz [2016]).”