Description
- Abstract:
- This dissertation presents a comprehensive, systematic investigation of methods and applications of scientific machine learning (SciML) in mechanics and their broader implications for interdisciplinary research. The first study presents a method based on Physics-Informed Neural Networks (PINNs) for inverse problems in solid mechanics. PINNs incorporate conservation laws and material models in the neural network architecture. The method can handle nonlinear material properties and irregular, high-deformable geometries. We systematically validate the utility of our approach for material identification, geometry identification, and geometry design problems, for materials exhibiting linear elasticity, hyperelasticity, and plasticity. This general framework can be applied to various engineering applications, targeting material characterization, elasticity imaging, non-destructive detection, and topology design. The second study concentrates on SciML methods for multimodal constitutive modeling of biological tissues. We incorporate non-mechanical information, including material type and microstructure, into the modeling workflow. The first part of the study develops a novel genotype-to-biomechanical phenotype neural network for characterizing and classifying the biomechanical properties of soft tissues based on genotypes. The second part further improves the method by incorporating the microstructure of tissues. The method captures the correlation between material classes, microstructure, and biomechanical properties of tissues, capable of making inferences both within a single modality and across different modalities. This SciML framework is capable of correlating and integrating multimodal information associated with solid materials, promising a paradigm shift in our understanding of the mechanical properties of materials. Lastly, the third study aims to develop a fast solver for differential equations. We introduce HINTS, a hybrid, iterative, numerical, and transferable solver for solving differential equations. HINTS integrates the Deep Operator Network (DeepONet) with existing numerical solvers. Through several numerical examples, we demonstrate that HINTS is fast, accurate, and widely applicable to a wide range of differential equations and linear systems, including but not limited to problems related to solid mechanics. This method is flexible regarding differential equations, computational domains (shape and dimension), and discretization. HINTS holds immense potential to transform the fields of scientific computing and numerical analysis, benefiting all areas of science and engineering that involve differential equations.
- Notes:
- Thesis (Ph. D.)--Brown University, 2023
Citation
Zhang, Enrui,
"Scientific Machine Learning for Mechanics and Beyond"
(2023).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:ugqmvdt2/
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Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....