Metamodeling of constitutive model using Gaussian process machine learning

Wang, Jikun; Li, Tianjiao; Cui, Fan; Chen, Hui; Yeo, Jingjie; Zehnder, Alan T.

doi:10.1016/j.jmps.2021.104532

Cited by 25 publications

(12 citation statements)

References 28 publications

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“…Results for the growth condition check, Equation (33). The predicted energy is monotonically increasing as det F approaches 0.…”

Section: F I G U R E 17mentioning

confidence: 98%

“…Alternatives that may accelerate the modeling and material identification process are (1) bypassing the modeling process via distance‐minimization algorithms (e.g., References 20‐23); (2) handling these processes with supervised learning (e.g., References 24‐29); and (3) an indirect approach where subscale displacement and force data are used to deduce stress 30 . Our focus here is on the supervised approach where hyperelasticity free energy functionals can be deduced by models inferred from trained feed‐forward neural networks, support vector machines, symbolic regression (e.g., Reference 31), and Gaussian processes (e.g., References 32‐34).…”

Section: Introductionmentioning

confidence: 99%

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Molecular dynamics inferred transfer learning models for finite‐strain hyperelasticity of monoclinic crystals: Sobolev training and validations against physical constraints

Vlassis

Zhao

et al. 2022

Numerical Meth Engineering

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We present a machine learning framework to train and validate neural networks to predict the anisotropic elastic response of a monoclinic organic molecular crystal known as β$$ \beta $$‐HMX in the geometrical nonlinear regime. A filtered molecular dynamic (MD) simulations database is used to train neural networks with a Sobolev norm that uses the stress measure and a reference configuration to deduce the elastic stored free energy functional. To improve the accuracy of the elasticity tangent predictions originating from the learned stored free energy, a transfer learning technique is used to introduce additional tangential constraints from the data while necessary conditions (e.g., strong ellipticity, crystallographic symmetry) for the correctness of the model are either introduced as additional physical constraints or incorporated in the validation tests. Assessment of the neural networks is based on (1) the accuracy with which they reproduce the bottom‐line constitutive responses predicted by MD, (2) the robustness of the models measured by detailed examination of their stability and uniqueness, and (3) the admissibility of the predicted responses with respect to mechanics principles in the finite‐deformation regime. We compare the training efficiency of the neural networks under different Sobolev constraints and assess the accuracy and robustness of the models against MD benchmarks for β$$ \beta $$‐HMX.

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“…Results for the growth condition check, Equation (33). The predicted energy is monotonically increasing as det F approaches 0.…”

Section: F I G U R E 17mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Molecular dynamics inferred transfer learning models for finite‐strain hyperelasticity of monoclinic crystals: Sobolev training and validations against physical constraints

Vlassis

Zhao

et al. 2022

Numerical Meth Engineering

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show abstract

“…In finite element calculations of materials, the key issue is constructing a constitutive model for specific materials in a given service environment. Many ML models are able to construct a constitutive model from data, for example, Gaussian processing [272], Artificial Neural Networks [273][274][275][276][277][278] and symbolic regressions [279,280].…”

Section: Computational Materials Sciencementioning

confidence: 99%

Intelligent Computing: The Latest Advances, Challenges, and Future

Zhu

et al. 2023

Intell Comput

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Computing is a critical driving force in the development of human civilization. In recent years, we have witnessed the emergence of intelligent computing, a new computing paradigm that is reshaping traditional computing and promoting digital revolution in the era of big data, artificial intelligence, and internet of things with new computing theories, architectures, methods, systems, and applications. Intelligent computing has greatly broadened the scope of computing, extending it from traditional computing on data to increasingly diverse computing paradigms such as perceptual intelligence, cognitive intelligence, autonomous intelligence, and human–computer fusion intelligence. Intelligence and computing have undergone paths of different evolution and development for a long time but have become increasingly intertwined in recent years: Intelligent computing is not only intelligence oriented but also intelligence driven. Such cross-fertilization has prompted the emergence and rapid advancement of intelligent computing. Intelligent computing is still in its infancy, and an abundance of innovations in the theories, systems, and applications of intelligent computing is expected to occur soon. We present the first comprehensive survey of literature on intelligent computing, covering its theory fundamentals, the technological fusion of intelligence and computing, important applications, challenges, and future perspectives. We believe that this survey is highly timely and will provide a comprehensive reference and cast valuable insights into intelligent computing for academic and industrial researchers and practitioners.

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“…Li and Chen [174] developed an equilibrium-based CNN to extract local stress distribution based on strain measurement from DIC for hyperelastic materials. Wang et al [175] developed an ML algorithm based on singular value decomposition (SVD) and a Gaussian process to build metamodels of constitutive laws for time-dependent and nonlinear materials. This metamodeling method can be used to determine sets of material parameters that are best fit for experimental data.…”

Section: For Biomechanicsmentioning

confidence: 99%

Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review

Jin¹,

Zhang²,

Espinosa³

2023

Preprint

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For many decades, experimental solid mechanics has played a crucial role in characterizing and understanding the mechanical properties of natural and novel materials. Recent advances in machine learning (ML) provide new opportunities for the field, including experimental design, data analysis, uncertainty quantification, and inverse problems. As the number of papers published in recent years in this emerging field is exploding, it is timely to conduct a comprehensive and up-to-date review of recent ML applications in experimental solid mechanics. Here, we first provide an overview of common ML algorithms and terminologies that are pertinent to this review, with emphasis placed on physics-informed and physics-based ML methods. Then, we provide thorough coverage of recent ML applications in traditional and emerging areas of experimental mechanics, including fracture mechanics, biomechanics, nano-and micro-mechanics, architected materials, and 2D material. Finally, we highlight some current challenges of applying ML to multi-modality and multi-fidelity experimental datasets and propose several future research directions. This review aims to provide valuable insights into the use of ML methods as well as a variety of examples for researchers in solid mechanics to integrate into their experiments.

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Metamodeling of constitutive model using Gaussian process machine learning

Cited by 25 publications

References 28 publications

Molecular dynamics inferred transfer learning models for finite‐strain hyperelasticity of monoclinic crystals: Sobolev training and validations against physical constraints

Molecular dynamics inferred transfer learning models for finite‐strain hyperelasticity of monoclinic crystals: Sobolev training and validations against physical constraints

Intelligent Computing: The Latest Advances, Challenges, and Future

Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review

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