35. a new machine learning based data-driven computational framework in the mechanics of solids and structures

Department: Structural Engineering
Research Institute Affiliation: Center for Extreme Events Research
Faculty Advisor(s): Jiun-Shyan Chen

Primary Student
Name: Qizhi He
Email: q9he@ucsd.edu
Phone: 310-383-8989
Grad Year: 2018

Abstract
Data­ driven computing in computational mechanics integrates well­ established physical laws with experimental material data directly and, therefore, avoids the necessity of empirical constitutive models that remain difficult in characterizing complex material behavior. A new data ­driven approach based on machine learning techniques, termed locally convex data­driven (LCDD) computing, is proposed for elasticity problems, aiming to enhance robust against noise/outliers presented in data sets and prevent unexpected suboptimal convergence. Different from existing data ­driven methods based on minimizing the distance to a single data point, LCDD seeks for optimum data solutions from a convex subset built upon a cluster of k nearest neighbor (k­NN) points, which leads to less sensitivity to noisy data and ensures convergence stability. In addition to robustness, it is shown that LCDD still performs satisfactorily for high­-dimensional noisy data sets where data points are relatively sparse in the high­dimensional phase space. This is because the inherent manifold learning can capture the underlying material manifold of the data structure with the reproducibility of locally linear approximation. Numerical tests in truss problems and 2D elasticity mechanics are given to validate the robustness, accuracy, and convergence properties of the proposed approach.

Industry Application Area(s)
Civil/Structural Engineering | Life Sciences/Medical Devices & Instruments | Materials

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