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Physics-constrained data-driven computing is an emerging hybrid approach thatintegrates universal physical laws with data-driven models of experimental datafor scientific computing. A new data-driven simulation approach coupled with alocally convex reconstruction, termed the local convexity data-driven (LCDD)computing, is proposed to enhance accuracy and robustness against noise andoutliers in data sets in the data-driven computing. In this approach, for agiven state obtained by the physical simulation, the corresponding optimumexperimental solution is sought by projecting the state onto the associatedlocal convex manifold reconstructed based on the nearest experimental data.This learning process of local data structure is less sensitive to noisy dataand consequently yields better accuracy. A penalty relaxation is alsointroduced to recast the local learning solver in the context of non-negativeleast squares that can be solved effectively. The reproducing kernelapproximation with stabilized nodal integration is employed for the solution ofthe physical manifold to allow reduced stress-strain data at the discretepoints for enhanced effectiveness in the LCDD learning solver. Due to theinherent manifold learning properties, LCDD performs well for high-dimensionaldata sets that are relatively sparse in real-world engineering applications.Numerical tests demonstrated that LCDD enhances nearly one order of accuracycompared to the standard distance-minimization data-driven scheme when dealingwith noisy database, and a linear exactness is achieved when localstress-strain relation is linear.

A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database