Deep autoencoders for physics-constrained data-driven nonlinear materials modeling

Abstract

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains difficult to deal with high-dimensional applications and extrapolative generalization. This paper introduces deep learning techniques under the data-driven framework to address these fundamental issues in nonlinear materials modeling. To this end, an autoencoder neural network architecture is introduced to learn the underlying low-dimensional representation (embedding) of the given material database. The offline trained autoencoder and the discovered embedding space are then incorporated in the online data-driven computation such that the search of optimal material state from database can be performed on a low-dimensional space, aiming to enhance the robustness and predictability with projected material data. To ensure numerical stability and representative constitutive manifold, a convexity-preserving interpolation scheme tailored to the proposed autoencoder-based data-driven solver is proposed for constructing the material state. In this study, the applicability of the proposed approach is demonstrated by modeling nonlinear biological tissues. A parametric study on data noise, data size and sparsity, training initialization, and model architectures, is also conducted to examine the robustness and convergence property of the proposed approach.

References in corpus (10)

• Data-driven computational mechanics
• A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials
• Model-Free Data-Driven Inelasticity
• Data Driven Computing with Noisy Material Data Sets
• Exploring the 3D architectures of deep material network in data-driven multiscale mechanics
• Data driven problems in elasticity
• Model-Free Data-Driven Methods in Mechanics: Material Data Identification and Solvers
• A hybrid approach to simulate the homogenized irreversible elastic-plastic deformations and damage of foams by neural networks
• A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database
• Model-free Data-Driven Computational Mechanics Enhanced by Tensor Voting

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• gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification
• Manifold embedding data-driven mechanics
• Data-driven micromorphic mechanics for materials with strain localization
• Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: application to planar soft tissues
• Knowledge-integrated AutoEncoder Model
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