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Thermodynamically Consistent Physics-Informed Data-Driven Computing and Reduced-Order Modeling of Nonlinear Materials


Physical simulations have influenced the advancements in engineering, technology, and science more rapidly than ever before. However, it remains challenging for effective and efficient modeling of complex linear and nonlinear material systems based on phenomenological approaches which require predefined functional forms. The goal of this dissertation is to enhance the predictivity and efficiency of physical simulations by developing thermodynamically consistent data-driven computing and reduced-order materials modeling methods based on emerging machine learning techniques for manifold learning, dimensionality reduction, sequence learning, and system identification.

For reversible mechanical systems, we first develop a new data-driven material solver built upon local convexity-preserving reconstruction to capture anisotropic material behaviors and enable data-driven modeling of nonlinear anisotropic elastic solids. A material anisotropic state characterizing the underlying material orientation is introduced for the manifold learning projection in the material solver. To counteract the curse of dimensionality and enhance the generalization ability of data-driven computing, we employ deep autoencoders to discover the underlying low-dimensional manifold of material database and integrate a convexity-preserving interpolation scheme into the novel autoencoder-based data-driven solver to further enhance efficiency and robustness of data searching and reconstruction during online data-driven computation. The proposed approach is shown to achieve enhanced efficiency and generalization ability over a few commonly used data-driven schemes.

For irreversible mechanical systems, we develop a thermodynamically consistent machine learned data-driven constitutive modeling approach for path-dependent materials based on measurable material states, where the internal state variables essential to the material path-dependency are inferred automatically from the hidden state of recurrent neural networks. The proposed method is shown to successfully model soil behaviors under cyclic shear loading using experimental stress-strain data.

Lastly, we develop a non-intrusive accurate and efficient reduced-order model based on physics-informed adaptive greedy latent space dynamics identification (gLaSDI) for general high-dimensional nonlinear dynamical systems. An autoencoder and dynamics identification models are trained simultaneously to discover intrinsic latent space and learn expressive governing equations of simple latent-space dynamics. To maximize and accelerate the exploration of the parameter space for optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for optimal training samples on the fly, which outperforms the conventional predefined uniform sampling. Compared with the high-fidelity models of various nonlinear dynamical problems, gLaSDI achieves 66 to 4,417x speed-up with 1 to 5% relative errors.

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