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An investigation on the coupling of data-driven computing and model-driven computing

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2022年 393卷

作者： Yang, Jie Huang, Wei Huang, Qun Hu, Heng Wuhan Univ Sch Civil Engn 8 South Rd East Lake Wuhan 430072 Peoples R China

The aim of this work is to investigate the coupling of data-driven (DD) computing and model-driven (MD) computing for the analyses of engineering structures. The data-driven computing was initially introduced by Kirchdoerfer and Ortiz (2016), the main idea of which is to directly embedding the experimental material data into mechanical simulations, thus bypassing the empirical material constitutive modeling. The model-driven computing in this work refers to the standard constitutive model-based simulations, which allows to benefit from its computational efficiency. The idea of this proposed DD-MD solver is to employ the data-driven computing for the local region of the solution domain where the material constitutive models are difficult to be determined, whilst the model-driven computing is applied to the remaining regions where the material models can be easily accessed. Several numerical examples are presented to demonstrate the robustness and reliability of the proposed method.(c) 2022 Elsevier B.V. All rights reserved.

关键词： data-driven computing Model-driven computing Coupling

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data-driven computing WITH CONVOLUTIONAL NEURAL NETWORKS FOR TWO-PHASE FLOWS: APPLICATION TO WAVE-STRUCTURE INTERACTION 37

DATA-DRIVEN COMPUTING WITH CONVOLUTIONAL NEURAL NETWORKS FOR...

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37th ASME International Conference on Ocean, Offshore and Arctic Engineering

作者： Mao, X. Joshi, V. Miyanawala, T. P. Jaiman, Rajeev K. Natl Univ Singapore Dept Mech Engn Singapore 117575 Singapore

ISBN: (纸本)9780791851210

Fluctuating wave force on a bluff body is of great significance in many offshore and marine engineering applications. We present a Convolutional Neural Network (CNN) based data-driven computing to predict the unsteady wave forces on bluff bodies due to the free-surface wave motion. For the full-order modeling and high-fidelity data generation, the air-water interface for such wave-body problems must be captured accurately for a broad range of physical and geometric parameters. Originated from the thermodynamically consistent theories, the physically motivated Allen-Cahn phase-field method has many advantages over other interface capturing techniques such as level-set and volume-of-fluid methods. The Allen-Cahn equation is solved in the mass-conservative form by imposing a Lagrange multiplier technique. While a tremendous amount of wave-body interaction data is generated in offshore engineering via both CFD simulations and experiments, the results are generally underutilized. Design space exploration and flow control of such practical scenarios are still time-consuming and expensive. An alternative to semi-analytical modeling, CNN is a class of deep neural network for solving inverse problems which is efficient in parametric data-driven computation and can use the domain knowledge. It establishes a model with arbitrarily generated model parameters, makes predictions using the model and existing input parametric settings, and adjusts the model parameters according to the error between the predictions and existing results. The computational cost of this prediction process, compared with high-fidelity CFD simulation, is significantly reduced, which makes CNN an accessible tool in design and optimization problems. In this study, CNN-based data-driven computing is utilized to predict the wave forces on bluff bodies with different geometries and distances to the free surface. The discrete convolution process with a non-linear rectification is employed to approximate the ma

关键词： data-driven computing CNN-based deep learning Allen-Cahn phase-field Parametric deep kernel learning Wave-structure interaction

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Coupling of data-driven and model-driven computing within non-matching meshes

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2025年 441卷

作者： Bai, Xiaowei Yang, Jie Huang, Qun Huang, Wei Li, Huicui Damil, Noureddine Hu, Heng Wuhan Univ Sch Civil Engn 8 South Rd East Lake Wuhan 430072 Peoples R China Ningxia Univ Sch Math & Stat Yinchuan 750021 Peoples R China Hassan II Univ Casablanca Fac Sci Ben MSik Lab Ingn Mat LIMAT BP7955 Casablanca Morocco Ctr Rech Syst Complexes & Interact Cent Casablanca Bouskoura 27182 Morocco

This work aims to couple distance-minimizing data-driven computing with model-driven computing (standard constitutive model-based simulations), allowing for non-matching interfaces between computational regions meshed with both full and reduced finite elements. Specifically, data-driven (DD) computing is employed for regions where the material constitutive models are difficult to determine, whilst model-driven (MD) computing is applied to the remaining regions to take advantage of its computational efficiency. To connect non-matching interfaces, a penalty-based technique is utilized to ensure the continuity of displacements and the accurate transfer of interaction forces across these interfaces. In this manner, the proposed method becomes more versatile and practical for engineering applications, enabling separate modeling of data-driven and model-driven regions with different mesh refinements or types of elements (e.g., coarse and fine meshes, full and reduced finite elements) based on their specific needs. Several examples are provided to illustrate the effectiveness and robustness of the proposed method.

关键词： data-driven computing Non-matching meshes Coupling

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GPM-PeNN: A generalized plasticity model-based data-driven constitutive modeling framework using physics-encoded neural network

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2025年 436卷

作者： Wang, Jingzhou Ma, Gang Qu, Tongming Guan, Shaoheng Zhou, Wei Chang, Xiaolin Wuhan Univ State Key Lab Water Resources Engn & Management Wuhan Peoples R China Wuhan Univ Inst Water Engn Sci Wuhan Peoples R China Wuhan Univ Key Lab Rock Mech Hydraul Struct Engn Minist Educ Wuhan Peoples R China Hong Kong Univ Sci & Technol Dept Civil & Environm Engn Kowloon Hong Kong Peoples R China Graz Univ Technol Inst Theoret Phys Computat Phys A-8010 Graz Styria Austria

data-driven surrogate modeling provides a new way to characterize and predict the mechanical behavior of materials. However, pure data-driven models tend to suffer from problems with stress path generalization ability. The model's performance is not stable enough especially when dealing with boundary value problems because of the various loading paths and historical influences. In this study, a physics-encoded data-driven constitutive modeling framework based on generalized plasticity, known as GPM-PeNN (Generalized Plasticity Model-based Physics-encoded Neural Network), is proposed, aiming to improve the stress path generalization ability and robustness of the model for extrapolated predictions. In this framework, the theory of generalized plasticity model is encoded as the physical priori. By leveraging generalized plasticity knowledge for task decomposition, the complex relationships of materials have been transformed into subrelations that are more easily discernible by neural networks. Additionally, the generalized plasticity theory-consistent information flow structure limits the scope of fitting in traditional constitutive modeling, enhancing the robustness. Considering the assumptions like elastoplastic decomposition and associated flow rule, this framework is suitable for the modeling of small strain elastoplastic materials. The GPM-PeNN is also embedded into the general finite element program Abaqus through UMAT subroutine to solve boundary value problems and accurately reproduce ground truth solutions. Sensitivity analysis of data quantity and noise level is conducted to evaluate the model's performance on small datasets and resistance to noise. The results show that the GPM-PeNN trained with even limited data or noisy datasets can still provide stable solutions against boundary value problems, which unequivocally demonstrates its stress path generalization ability and robustness.

关键词： Physics-encoded neural networks Constitutive modeling data-driven computing Generalized plasticity Boundary value problem

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A physics-informed GAN framework based on model-free data-driven computational mechanics

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2024年 424卷

作者： Ciftcei, Kerem Hackl, Klaus Ruhr Univ Bochum Inst Mech Mat Univ Str 150 D-44801 Bochum Germany

Model -free data -driven computational mechanics, first proposed by Kirchdoerfer and Ortiz, replace phenomenological models with numerical simulations based on sample datasets in strain-stress space. In this study, we integrate this paradigm within physics -informed generative adversarial networks (GANs). We enhance the conventional physics -informed neural network framework by implementing the principles of data -driven computational mechanics into GANs. Specifically, the generator is informed by physical constraints, while the discriminator utilizes the closest strain-stress data to discern the authenticity of the generator's output. This combined approach presents a new formalism to harness data -driven mechanics and deep learning to simulate and predict mechanical behaviors.

关键词： Model-free data-driven Generative adversarial networks data-driven computing Physics-informed neural networks

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data-driven micromorphic mechanics for materials with strain localization

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2024年 429卷

作者： Ulloa, Jacinto Stainier, Laurent Ortiz, Michael Andrade, Jose E. CALTECH Div Engn & Appl Sci Pasadena CA 91125 USA Nantes Univ GeM CNRS Ecole Cent NantesUMR 6183 F-44000 Nantes France

This paper explores the role of generalized continuum mechanics, and the feasibility of model-free data-driven computing approaches thereof, in solids undergoing failure by strain localization. Specifically, we set forth a methodology for capturing material instabilities using data-driven mechanics without prior information regarding the failure mode. We show numerically that, in problems involving strain localization, the standard data-driven framework for Cauchy/Boltzmann continua fails to capture the length scale of the material, as expected. We address this shortcoming by formulating a generalized data-driven framework for micromorphic continua that effectively captures both stiffness and length-scale information, as encoded in the material data, in a model-free manner. These properties are exhibited systematically in a one-dimensional softening bar problem and further verified through selected plane-strain problems.

关键词： data-driven computing Micromorphic continuum Strain localization Softening materials

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data-driven confidence bound for structural response using segmented least squares: a mixed-integer programming approach

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JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2024年第3期41卷 1501-1534页

作者： Kanno, Yoshihiro Univ Tokyo Math & Informat Ctr Hongo 7-3-1 Tokyo 1138656 Japan

As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures.

关键词： data-driven computing Mixed-integer programming Global optimization Order statistics Reliability with unknown distribution

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Three-dimensional data-driven magnetostatic field computation using real-world measurement data

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COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING 2022年第2期41卷 615-627页

作者： Galetzka, Armin Loukrezis, Dimitrios De Gersem, Herbert Tech Univ Darmstadt Inst Accelerator Sci & Electromagnet Fields Darmstadt Germany Tech Univ Darmstadt Ctr Computat Engn Darmstadt Germany

Purpose The purpose of this paper is to present the applicability of data-driven solvers to computationally demanding three-dimensional problems and their practical usability when using real-world measurement data. Design/methodology/approach Instead of using a hard-coded phenomenological material model within the solver, the data-driven computing approach reformulates the boundary value problem such that the field solution is directly computed on raw measurement data. The data-driven formulation results in a double minimization problem based on Lagrange multipliers, where the sought solution must conform to Maxwell's equations while at the same time being as close as possible to the available measurement data. The data-driven solver is applied to a three-dimensional model of a direct current electromagnet. Findings Numerical results for data sets of increasing cardinality verify that the data-driven solver recovers the conventional solution. Additionally, the practical usability of the solver is shown by using real-world measurement data. This work concludes that the data-driven magnetostatic finite element solver is applicable to computationally demanding three-dimensional problems, as well as in cases where a prescribed material model is not available. Originality/value Although the mathematical derivation of the data-driven problem is well presented in the referenced papers, the application to computationally demanding real-world problems, including real measurement data and its rigorous discussion, is missing. The presented work closes this gap and shows the applicability of data-driven solvers to challenging, real-world test cases.

关键词： Electromagnetic fields Finite element method Computational electromagnetics Three-dimensional electromagnetic field simulation data-driven computing data science Finite element analysis Magnetic materials Scientific computing

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Model-free data-driven simulation of inelastic materials using structured data sets, tangent space information and transition rules

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COMPUTATIONAL MECHANICS 2022年第2期70卷 425-435页

作者： Ciftci, Kerem Hackl, Klaus Ruhr Univ Bochum Inst Mech Mat D-44801 Bochum Germany

Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the data set is minimized, subject to equilibrium and compatibility constraints. Although this method operates well for non-linear elastic problems, there are challenges dealing with history-dependent materials, since one and the same point in stress-strain space might correspond to different material behaviour. In recent literature, this issue has been treated by including local histories into the data set. However, there is still the necessity to include models for the evolution of specific internal variables. Thus, a mixed formulation of classical and data-driven modeling is obtained. In the presented approach, the data set is augmented with directions in the tangent space of points in stress-strain space. Moreover, the data set is divided into subsets corresponding to different material behaviour. Based on this classification, transition rules map the modeling points to the various subsets. The approach will be applied to non-linear elasticity and elasto-plasticity with isotropic hardening.

关键词： data-driven computing Tangent space information Transition rules Inelasticity data science

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data-driven multiscale method for composite plates

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COMPUTATIONAL MECHANICS 2022年第5期70卷 1025-1040页

作者： Yan, Wei Huang, Wei Huang, Qun Yang, Jie Giunta, Gaetano Belouettar, Salim Hu, Heng Wuhan Univ Sch Civil Engn 8 South Rd East Lake Wuhan 430072 Peoples R China Luxembourg Inst Sci & Technol 5 Ave Hauts Fourneaux L-4362 Esch Sur Alzette Luxembourg

Composite plates are widely used in many engineering fields such as aerospace and automotive. An accurate and efficient multiscale modeling and simulation strategy is of paramount importance to improve design and manufacture. To this end, we propose an efficient data-driven computing scheme based on the classical plate theory for the multiscale analysis of composite plates. In order to accurately describe the relationship between the macroscopic mechanical properties and the microscopic architecture, the multiscale finite element method (FE2) is adopted to compute the generalized strain and stress fields. These data are then used to construct a database for data-driven computing. Since the database is offline populated, the data-driven computing scheme allows for a reduced computational cost when compared to the traditional multiscale method, where the concurrent coupling of different scales is still a burden. And data are obtained from a reduced structural model for computational efficiency. The proposed scheme is therefore addressed as Structural-Genome-driven (SGD) modeling of plates. Compared to the general data-driven computational mechanics modeling of plates, SGD is found to be more efficient since the number of integration points is significantly reduced. This scheme provides a robust alternative computational tool for composite plate structures analysis.

关键词： data-driven computing Structural-Genome-driven Multiscale finite element method Composite plates

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