Machine Learning in Modeling and Simulation : Methods and Applications.

Format:

Book

Author/Creator:

Rabczuk, Timon.

Contributor:

Bathe, Klaus-Jürgen.

Series:

Computational Methods in Engineering and the Sciences Series

Language:

English

Subjects (All):

Machine learning.

Computer simulation.

Physical Description:

1 online resource (456 pages)

Edition:

1st ed.

Place of Publication:

Cham : Springer International Publishing AG, 2023.

Summary:

This book focuses on the application of machine learning techniques in engineering and the sciences, emphasizing their role in modeling and simulation. Edited by Timon Rabczuk and Klaus-Jürgen Bathe, it covers a wide range of topics including solid structural mechanics, fluid dynamics, heat transfer, and more. The book highlights the potential of machine learning to solve complex engineering problems, reduce computational costs, and innovate in fields like digital twins and new material design. This comprehensive volume is intended for professionals and researchers in engineering and applied sciences, offering both theoretical insights and practical applications. Generated by AI.

Contents:

Intro

Preface

Contents

About the Editors

1 Machine Learning in Computer Aided Engineering

1.1 Introduction

1.2 Machine Learning Procedures Employed in CAE

1.2.1 Machine Learning Aspects and Classification of Procedures

1.2.2 Overview of Classical Machine Learning Procedures Used in CAE

1.3 Constraining to, and Incorporating Physics in, Data-Driven Methods

1.3.1 Incorporating Physics in, and Learning Physics From, the Dataset

1.3.2 Incorporating Physics in the Design of a ML Method

1.3.3 Data Assimilation and Correction Methods

1.3.4 ML Methods Designed to Learn Physics

1.4 Applications of Machine Learning in Computer Aided Engineering

1.4.1 Constitutive Modeling and Multiscale Applications

1.4.2 Fluid Mechanics Applications

1.4.3 Structural Mechanics Applications

1.4.4 Machine Learning Approaches Motivated in Structural Mechanics and by Finite Element Concepts

1.4.5 Multiphysics Problems

1.4.6 Machine Learning in Manufacturing and Design

1.5 Conclusions

References

2 Artificial Neural Networks

2.1 Introduction

2.2 Biological Motivation and Pre-history

2.2.1 Memory

2.2.2 Learning

2.2.3 Parallel Distributed Processing Paradigm

2.2.4 The Artificial Neuron

2.2.5 The Perceptron

2.3 The First Age-The Multi-layer Perceptron

2.3.1 Existence of Solutions

2.3.2 Uniqueness of Solutions

2.3.3 Generalization and Regularization

2.3.4 Choice of Output Activations Functions

2.4 A First-Age Case Study: Structural Monitoring of an Aircraft Wing

2.5 The Second Age-Deep Learning

2.5.1 Convolutional Neural Networks (CNNs)

2.5.2 A Little More History

2.5.3 Other Recent Developments

2.6 Conclusions

3 Gaussian Processes

3.1 Introduction

3.1.1 A Visual Introduction To Gaussian Processes

3.1.2 Gaussian Process Regression.

3.1.3 Implementation and Learning of the GP

3.2 Beyond the Gaussian Process

3.2.1 Large Training Data

3.2.2 Non-Gaussian Likelihoods

3.2.3 Multiple-Output GPs

3.3 A Case Study with Wind Turbine Power Curves

3.4 Conclusions

4 Machine Learning Methods for Constructing Dynamic Models From Data

4.1 Introduction

4.2 Modeling Viewpoints

4.3 Learning Paradigms: Burgers' Equation

4.4 Dynamic Models From Data

4.4.1 Dynamic Mode Decomposition

4.4.2 Sparse Identification of Nonlinear Dynamics

4.4.3 Neural Networks

4.5 Joint Discovery of Coordinates and Models

4.6 Conclusions

5 Physics-Informed Neural Networks: Theory and Applications

5.1 Introduction

5.2 Basics of Artificial Neural Networks

5.2.1 Feed-Forward Neural Networks

5.2.2 Activation Functions

5.2.3 Training

5.2.4 Testing and Validation

5.2.5 Optimizers

5.3 Physics-Informed Neural Networks

5.3.1 Collocation Method

5.3.2 Energy Minimization Method

5.4 Numerical Applications

5.4.1 Forward Problems

5.4.2 Inverse Problems

5.5 Conclusions

6 Physics-Informed Deep Neural Operator Networks

6.1 Introduction

6.2 DeepONet and Its Extensions

6.2.1 Feature Expansion in DeepONet

6.2.2 Multiple Input DeepONet

6.2.3 Physics-Informed DeepONet

6.3 FNO and Its Extensions

6.3.1 Feature Expansion in FNO

6.3.2 Implicit FNO

6.3.3 Physics-Informed FNO

6.4 Graph Neural Operators

6.4.1 Graph Neural Networks

6.4.2 Integral Neural Operators Through Graph Kernel Learning

6.5 Neural Operator Theory

6.6 Applications

6.6.1 Data-Driven Neural Operators

6.6.2 Physics-Informed Neural Operators

6.7 Summary and Outlook

7 Digital Twin for Dynamical Systems

7.1 Introduction

7.2 Building Blocks and Nominal Model in Digital Twin.

7.3 Physics-Based Digital Twin for SDOF System

7.3.1 Nominal Model

7.3.2 The Digital Twin Framework

7.3.3 Formulating the Digital Twin

7.3.4 Numerical Experiment

7.4 Physics ML Fusion: Towards a Predictive Digital Twin

7.4.1 Gaussian Process

7.4.2 Numerical Experiment

7.5 Digital Twin for Nonlinear Stochastic Dynamical Systems

7.5.1 Stochastic Nonlinear MDOF System: The Nominal Model

7.5.2 Problem Statement

7.5.3 The Digital Twin Framework

7.5.4 Numerical Examples

7.6 Digital Twin for Systems with Misspecified Physics

7.6.1 Model Updating Using Input-Output Measurement

7.6.2 Model Updating Using Output-Only Measurements

7.6.3 Sparse Bayesian Regression

7.6.4 Numerical Examples

7.7 Conclusions

8 Reduced Order Modeling

8.1 Introduction

8.2 Proper Orthogonal Decomposition

8.2.1 Proper Orthogonal Decomposition Applied to Partial Differential Equations

8.2.2 Singular Value Decomposition

8.3 Reduced Order Modeling Using Proper Orthogonal Decomposition

8.3.1 Galerkin Projection

8.3.2 Hyperreduction

8.3.3 Stabilization Using Variational Multiscale Methods

8.4 Non-intrusive Reduced Order Models

8.4.1 The General Concept

8.4.2 Dynamic Mode Decomposition

8.5 Parametric Reduced Order Models

8.5.1 Global Basis

8.5.2 Local Basis with Interpolation

8.6 Machine Learning-Based Reduced Order Models

8.6.1 Nonlinear Dimension Reduction

8.6.2 Machine Learning Based Non-intrusive Reduced Order Models

8.6.3 Closure Modeling

8.6.4 Correction Based on Fine Solutions

8.6.5 Machine Learning Applied to Parametric Reduced Order Models

8.6.6 Physics Informed Machine Learning for Reduced Order Models

8.6.7 Reduced System Identification

8.7 Concluding Remarks

9 Regression Models for Machine Learning

9.1 Introduction.

9.2 Parametric Regression: A Non-Bayesian Perspective

9.2.1 Least Square Regression

9.2.2 Support Vector Regression

9.2.3 Kernel Trick

9.3 Regression: A Bayesian Perspective

9.3.1 Gaussian Process Regression: A Parametric Space Perspective

9.3.2 Gaussian Process Regression: A Functional Space Perspective

9.4 Active Learning

9.4.1 Active Learning for Bayesian Cubature

9.4.2 Active Learning for Bayesian Reliability Assessment

9.5 Conclusions

10 Overview on Machine Learning Assisted Topology Optimization Methodologies

10.1 Introduction

10.2 Background

10.2.1 Topology Optimization

10.2.2 Artificial Intelligence and Neural Networks

10.3 Literature Survey

10.3.1 Density-Based Methods

10.3.2 Image-Based Methods

10.4 Conclusions

11 Mixed-Variable Concurrent Material, Geometry, and Process Design in Integrated Computational Materials Engineering

11.1 Introduction

11.2 Mixed-Variable and Constrained Bayesian Optimization

11.2.1 Gaussian Processes and Bayesian Optimization

11.2.2 Latent Variable Gaussian Process (LVGP) Modeling

11.2.3 Constrained Bayesian Optimization

11.3 Application to Concurrent Structure and Material Design

11.3.1 The Integrated Material-Structure Model

11.3.2 Design Variables, Constraints, and Objectives

11.3.3 LVGP Modeling and Validation

11.3.4 LVGP-CBO Setup and Design Results

11.4 Application to Concurrent Material and Process Design

11.4.1 The Integrated Process-Structure-Property Model

11.4.2 Design Variables, Constraints, and Objectives for SFRP Design

11.4.3 LVGP Modeling and Validation

11.4.4 LVGP-CBO Setup and Design Results

11.5 Conclusions

12 Machine Learning Interatomic Potentials: Keys to First-Principles Multiscale Modeling

12.1 Introduction.

12.2 Methods for Exploring Interatomic Forces

12.2.1 Quantum Mechanics

12.2.2 Empirical Interatomic Potentials

12.2.3 Machine Learning Interatomic Potentials

12.3 Developing a Machine Learning Interatomic Potential

12.3.1 Popular Machine Learning Interatomic Potentials

12.3.2 Training of Machine Learning Interatomic Potentials

12.3.3 Passive or Active Fitting

12.3.4 Current Challenges of MLIPs

12.4 Quantum Mechanics and Empirical Interatomic Potentials Challenges

12.4.1 Thermal Transport

12.4.2 Mechanical Properties

12.5 First-Principles Multiscale Modeling

12.6 Concluding Remark

References.

Notes:

Description based on publisher supplied metadata and other sources.

Part of the metadata in this record was created by AI, based on the text of the resource.

Other Format:

Print version: Rabczuk, Timon Machine Learning in Modeling and Simulation

ISBN:

9783031366444

3031366441

OCLC:

1402028815