As characterization of complex material behaviors by phenomenological models remains challenging in complex material systems, data-driven computing that performs physical simulation directly from material data has attracted considerable attention. This study extends the local convexity data-driven framework [1] for nonlinear materials modeling by introducing autoencoder based deep manifold learning. An autoencoder is a special architecture of deep neural networks that allows a low-dimensional representation (embedding) of data and addresses the ‚Äúdimensionality curse‚Äù emerging from other conventional manifold learning-based methods. The data embeddings learned by the encoders provide enhanced noise filtering and extrapolation generalization. A local convexity-preserving scheme based on Shepard interpolation is introduced for the data-driven local solution. In this study,  investigation on data noisiness, data size, training initialization, and model architectures is conducted to examine the robustness of the proposed approach against noise and convergence of solutions with increasing material data size. Application to modeling biological tissue is performed to demonstrate the effectiveness of the proposed data-driven computing approach.

Reference
[1] He, Q., & Chen, J. S. (2020). A physics-constrained data-driven approach based on locally convex reconstruction for noisy database. Computer Methods in Applied Mechanics and Engineering, 363, 112791.

Deep Autoencoders for Physics-Constrained Data-Driven Nonlinear Materials Modeling

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