Inverse Computational Methods

Classical Approaches, Bayesian Inference, and Machine Learning
Erscheinungsjahr 2027
ISBN: 978-981-9286-98-0
Verlag: Springer

Buch, Englisch, Format (B × H): 155 mm x 235 mm

This book presents a unified, engineering-oriented treatment of inverse problems for graduate students, researchers, and computational engineers. It develops the subject from ill-posedness, identifiability, regularization, optimization, and numerical validation through Bayesian inversion, uncertainty quantification, and likelihood-free inference, and then explains how surrogate models, conditional generative models, operator learning, and physics-informed neural networks extend or accelerate these foundations. Rather than surveying these topics in isolation, the book organizes them within a common solution workflow and compares their assumptions, accuracy, uncertainty estimates, computational cost, robustness, and domains of applicability. Inverse heat conduction and material and structural parameter identification serve as recurring case studies, allowing classical, Bayesian, and scientific-machine-learning approaches to be evaluated on shared engineering problems. Mathematical derivations are combined with algorithmic descriptions, approximately 100 figures, comparative tables, and reproducible computational implementations. Readers will gain both a rigorous framework for selecting and assessing inverse methods and practical guidance for applying them responsibly to complex engineering data.

Zielgruppe

Research

Autoren/Hrsg.

Li, Guangyao

Wang, Hu

Lin, Sen

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Bayesianische Inferenz
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen

Inhaltsverzeichnis

Preface.- Theoretical Foundations of Inverse Problems.- Overview of Inverse Problems and a Unified Analytical Framework.- Regularization, Optimization, and Validation.- Bayesian Inversion Computation.- Bayesian Inverse Problems and Uncertainty Quantification.- Approximate Bayesian Computation.- Efficient Bayesian Inversion: Dimension Reduction and Surrogate Models.- Scientific Machine Learning for Engineering Inverse Problems.- Conditional Generative Models and Posterior Approximation.- Operator Learning and Forward-Model Acceleration.- Physics-Informed Neural Networks for Inverse Problems.- Engineering Case Studies and Method Selection.- Inverse Heat Conduction.- Material and Structural Parameter Identification.- Method Selection, Reproducibility, and Outlook for Engineering Inverse Problems.- Appendices.- References.

Über Autor(innen)

Guangyao Li is Professor and Doctoral Supervisor in the College of Mechanical and Vehicle Engineering at Hunan University, China, with a B.S. from Huazhong University of Science and Technology, an M.S. from Hunan University, and a Ph.D. from Hohai University. His research spans computational mechanics, vehicle engineering, engineering optimization, CAE simulation, and software development. He provides overall academic leadership and develops the unified framework linking classical regularization with Bayesian inference, uncertainty quantification, and data-driven learning. He has received National Science and Technology Progress Awards and the China Patent Excellence Award.

Hu Wang is Professor and Doctoral Supervisor in the College of Mechanical and Vehicle Engineering at Hunan University with research covering computational mechanics, engineering optimization, inverse parameter identification, Bayesian methods, surrogate modelling, and machine-learning-assisted analysis. He established a research program in uncertainty-aware inverse problems and scientific machine learning and leads the book's Bayesian and data-driven components. He has held visiting appointments at the National University of Singapore, Simon Fraser University, the University of Florida, and the University of Cincinnati.

Sen Lin is Associate Professor and Doctoral Supervisor in the College of Mechanical and Vehicle Engineering at Hunan University with research focusing on bio-inspired intelligence, computational mechanics, structural optimization, and CAD/CAE-integrated simulation. He organizes and synthesizes the book's research results and ensures consistency of technical style throughout. He has led five national and provincial research projects and serves as subproject leader in China's National Key R&D Program on Industrial Software.