Computationally efficient and noise resilient data-driven mechanics via a continuous data space

Abstract

In this study, a continuous data space driven computational mechanics framework that enhances the original data-driven methodology is presented. The traditional data-driven approach relies on finite, discrete datasets and direct projections between the dataset and the constraint space dictated by the problem settings. The use of a discrete dataset entails accuracy problems as the dataset is inherently subject to noise and outliers. Moreover, finding the optimal datapoint in the dataset is computationally demanding especially for large sized datasets and geometrically higher dimensional problems. The proposed framework addresses these limitations by leveraging a continuous data space constructed via Gaussian mixture modeling to replace the discrete dataset. The continuous data space can be interpreted as a data density field that can be used to assess the likelihood of a point capturing the underlying material behavior. Hence the effect of noise and outlier on the solution accuracy is reduced. By eliminating search queries in the discrete dataset, the computational cost is significantly reduced as well. Moreover, the data-to-constraint space projection is conducted efficiently via a search direction deduced from the continuous data space. Numerical experiments demonstrate the capability of the framework to enhance accuracy and computational efficiency.