This Open Access book reviews recent theoretical and numerical developments in nonlinear model order reduction in continuum mechanics, being addressed to Master and PhD students, as well as to researchers, lecturers and instructors. The aim of the authors is to provide tools for a better understanding and implement reduced order models by using: physics-based models, synthetic data forecast by these models, experimental data and deep learning algorithms. The book involves a survey of key methods of model order reduction applied to model-based engineering and digital twining, by learning linear or nonlinear latent spaces.
Projection-based reduced order models are the projection of mechanical equations on a latent space that have been learnt from both synthetic data and experimental data. Various descriptions and representations of structured data for model reduction are presented in the applications and survey chapters. Image-based digital twins are developed in a reduced setting. Reduced order models of as-manufactured components predict the mechanical effects of shape variations. A similar workflow is extended to multiphysics or coupled problems, with high dimensional input fields. Practical techniques are proposed for data augmentation and also for hyper-reduction, which is a key point to speed up projection-based model order reduction of finite element models.
The book gives access to python libraries available on gitlab.com, which have been developed as part of the research program [FUI-25] MORDICUS funded by the French government. Similarly to deep learning for computer vision, deep learning for model order reduction circumvents the need to design parametric problems prior reducing models. Such an approach is highly relevant for image-base modelling or multiphysics modelling.
Conditions of Use
This book is licensed under a Creative Commons License (CC BY). You can download the ebook Manifold Learning for free.
- Title
- Manifold Learning
- Subtitle
- Model Reduction in Engineering
- Publisher
- Springer
- Author(s)
- David Ryckelynck, Fabien Casenave, Nissrine Akkari
- Published
- 2024-02-21
- Edition
- 1
- Format
- eBook (pdf, epub, mobi)
- Pages
- 117
- Language
- English
- ISBN-10
- 3031527666
- ISBN-13
- 9783031527647
- License
- CC BY
- Book Homepage
- Free eBook, Errata, Code, Solutions, etc.
Foreword Contents Acronyms 1 Structured Data and Knowledge in Model-Based Engineering 1.1 Nomenclature 1.2 Model-Based Engineering 1.3 Motivation References 2 Learning Projection-Based Reduced-Order Models 2.1 Motivation and Basic Assumptions 2.2 High-Fidelity Model (HFM) 2.3 Linear Manifold Learning for Projection-Based … 2.3.1 Approaches Preceding the Use of Machine Learning 2.3.2 Online Phase: Galerkin Projection 2.3.3 Offline Phase 2.3.4 Hyper-Reduction via a Reduced Integration Domain 2.3.5 Hyper-Reduction via Empirical Cubature 2.3.6 Computational Complexity 2.4 Nonlinear Manifold Learning for Projection-Based Reduced-Order Modeling 2.4.1 Nonlinear Dimensionality Reduction via Auto-Encoder 2.4.2 Piecewise Linear Dimensionality Reduction via Dictionary-Based ROM-Nets 2.5 Iterative and Greedy Strategies References 3 Error Estimation 3.1 Confidence and Trust in Model-Based Engineering Assisted by AI 3.2 In Linear Elasticity and for Linear Problems 3.3 In Nonlinear Mechanics of Materials 3.4 In Computational Fluid Dynamics 3.5 A Note on Accuracy of a Posteriori Error Bounds and Round-Off Errors References 4 Resources: Software and Tutorials 4.1 Mordicus: Reduced-Order Methods Designed for Industrial Usage 4.1.1 Mordicus Project and Consortium 4.1.2 Mordicus Library 4.1.3 Mordicus Datamodel 4.2 GenericROM Library 4.2.1 Main Available Methods 4.2.2 Noninstrusivity and Nonparametrized Variability 4.2.3 Precomputations for Efficiency 4.2.4 Tutorials and Datasets References 5 Industrial Application: Uncertainty Quantification in Lifetime Prediction of Turbine Blades 5.1 Industrial Context 5.1.1 Thermomechanical Fatigue of High-Pressure Turbine Blades 5.1.2 Industrial Dataset and Objectives 5.1.3 Modeling Assumptions 5.1.4 Stochastic Model for the Thermal Loading 5.2 ROM-net Based Uncertainty Quantification Applied to an Industrial … 5.2.1 Design of Numerical Experiments 5.2.2 ROM Dictionary Construction 5.2.3 Automatic Model Recommendation 5.2.4 Surrogate Model for Gappy Reconstruction 5.2.5 Uncertainty Quantification Results 5.2.6 Workflow 5.2.7 Verification References 6 Applications and Extensions: A Survey of Literature 6.1 Linear Manifold Learning 6.2 Nonlinear Dimensionality Reduction via Auto-Encoder 6.3 Piecewise Linear Dimensionality Reduction via Dictionary-Based … 6.4 Extension: Manifold Learning of Physics Problems Assisted … References
