Data Driven Models In Inverse Problems

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Data Driven Models In Inverse Problems

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Author : Tatiana A. Bubba
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-11-18

Data Driven Models In Inverse Problems written by Tatiana A. Bubba and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-18 with Mathematics categories.

Advances in learning-based methods are revolutionizing several fields in applied mathematics, including inverse problems, resulting in a major paradigm shift towards data-driven approaches. This volume, which is inspired by this cutting-edge area of research, brings together contributors from the inverse problem community and shows how to successfully combine model- and data-driven approaches to gain insight into practical and theoretical issues.

Hybrid Deep Learning How Combining Data Driven And Model Based Approaches Solves Inverse Problems In Computed Tomography And Beyond

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Author : Maximilian Schmidt
language : en
Publisher:
Release Date : 2022

Hybrid Deep Learning How Combining Data Driven And Model Based Approaches Solves Inverse Problems In Computed Tomography And Beyond written by Maximilian Schmidt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.

Artificial neural networks from the field of deep learning are increasingly becoming the state of the art in more and more applications. Their success is based on learning complex relationships in a system purely from data. For this, the data-driven networks often require hundreds of thousands of reference examples. They are contrasted by model-based approaches that use mathematical methods to describe the processes in a system. They work without large amounts of data but often cannot cover all the nuances of an application. In inverse problems, model-based approaches have been the standard so far. Here, the necessary amount of data to use purely data-driven deep learning is usually unavailable. In addition, requirements are placed on the model properties that cannot always be proven for classical neural networks. Hybrid deep learning models that combine data-driven and model-based approaches can solve these challenges. In recent years, their research has steadily gained importance. In this thesis, several hybrid deep learning approaches for solving inverse problems are presented and further developed. These include the deep image prior (DIP) and conditional invertible neural networks (CINN). The reconstruction problem in computed tomography (CT) serves as a central example to compare the models with each other, as well as to reveal their strengths and weaknesses. This is done in particular concerning the unique challenges in inverse problems, such as lack of data and ill-posedness. For this purpose, a realistic medical CT dataset is presented and used. The performed comparison for medical and industrial data clearly shows that the hybrid approaches are superior to the classical, model-based methods in many areas. Countless applications from inverse problems can thus already benefit from hybrid deep learning approaches.

Mathematical Modeling And Computational Predictions In Oncoimmunology

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Author : Vladimir A. Kuznetsov
language : en
Publisher: Frontiers Media SA
Release Date : 2024-06-06

Mathematical Modeling And Computational Predictions In Oncoimmunology written by Vladimir A. Kuznetsov and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-06 with Medical categories.

Cancer is a complex adaptive dynamic system that causes both local and systemic failures in the patient. Cancer is caused by a number of gain-of-function and loss-of-function events, that lead to cells proliferating without control by the host organism over time. In cancer, the immune system modulates cancer cell population heterogeneity and plays a crucial role in disease outcomes. The immune system itself also generates multiple clones of different cell types, with some clones proliferating quickly and maturing into effector cells. By creating regulatory signals and their networks, and generating effector cells and molecules, the immune system recognizes and kills abnormal cells. Anti-cancer immune mechanisms are realized as multi-layer, nonlinear cellular and molecular interactions. A number of factors determine the outcome of immune system-tumor interactions, including cancer-associated antigens, immune cells, and host organisms.

Digest

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Author :
language : en
Publisher:
Release Date : 1992

Digest written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Earth sciences categories.

Applied Data Analysis And Modeling For Energy Engineers And Scientists

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Author : T. Agami Reddy
language : en
Publisher: Springer Nature
Release Date : 2023-10-18

Applied Data Analysis And Modeling For Energy Engineers And Scientists written by T. Agami Reddy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-18 with Business & Economics categories.

Now in a thoroughly revised and expanded second edition, this classroom-tested text demonstrates and illustrates how to apply concepts and methods learned in disparate courses such as mathematical modeling, probability, statistics, experimental design, regression, optimization, parameter estimation, inverse modeling, risk analysis, decision-making, and sustainability assessment methods to energy processes and systems. It provides a formal structure that offers a broad and integrative perspective to enhance knowledge, skills, and confidence to work in applied data analysis and modeling problems. This new edition also reflects recent trends and advances in statistical modeling as applied to energy and building processes and systems. It includes numerous examples from recently published technical papers to nurture and stimulate a more research-focused mindset. How the traditional stochastic data modeling methods complement data analytic algorithmic approaches such as machine learning and data mining is also discussed. The important societal issue related to the sustainability of energy systems is presented, and a formal structure is proposed meant to classify the various assessment methods found in the literature. Applied Data Analysis and Modeling for Energy Engineers and Scientists is designed for senior-level undergraduate and graduate instruction in energy engineering and mathematical modeling, for continuing education professional courses, and as a self-study reference book for working professionals. In order for readers to have exposure and proficiency with performing hands-on analysis, the open-source Python and R programming languages have been adopted in the form of Jupyter notebooks and R markdown files, and numerous data sets and sample computer code reflective of real-world problems are available online.

Siam Journal On Scientific Computing

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Author :
language : en
Publisher:
Release Date : 2004

Siam Journal On Scientific Computing written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Electronic journals categories.

Dissertation Abstracts International

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Author :
language : en
Publisher:
Release Date : 2006

Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Dissertations, Academic categories.

Achievements And Trends In Material Forming

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Author : Gabriela Vincze
language : en
Publisher: Trans Tech Publications Ltd
Release Date : 2022-07-22

Achievements And Trends In Material Forming written by Gabriela Vincze and has been published by Trans Tech Publications Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-22 with Computers categories.

Peer-reviewed extended papers selected from the 25th International Conference on Material Forming (ESAFORM 2022) Peer-reviewed extended papers selected from the 25th International Conference on Material Forming (ESAFORM 2022), April 27-29, 2022, Portugal

A Sequential Monte Carlo Based Recursive Technique For Solving Nde Inverse Problems

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Author : Tariq Mairaj Rasool Khan
language : en
Publisher:
Release Date : 2009

A Sequential Monte Carlo Based Recursive Technique For Solving Nde Inverse Problems written by Tariq Mairaj Rasool Khan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Monte Carlo method categories.

Machine Learning Solutions For Inverse Problems Part A

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Author :
language : en
Publisher: Academic Press
Release Date : 2025-10-01

Machine Learning Solutions For Inverse Problems Part A written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-10-01 with Mathematics categories.

Machine Learning Solutions for Inverse Problems: Part A, Volume 26 in the Handbook of Numerical Analysis, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Data-Driven Approaches for Generalized Lasso Problems, Implicit Regularization of the Deep Inverse Prior via (Inertial) Gradient Flow, Generalized Hardness of Approximation, Hallucinations, and Trustworthiness in Machine Learning for Inverse Problems, Energy-Based Models for Inverse Imaging Problems, Regularization Theory of Stochastic Iterative Methods for Solving Inverse Problems, and more.Other sections cover Advances in Identifying Differential Equations from Noisy Data Observations, The Complete Electrode Model for Electrical Impedance Tomography: A Comparative Study of Deep Learning and Analytical Methods, Learned Iterative Schemes: Neural Network Architectures for Operator Learning, Jacobian-Free Backpropagation for Unfolded Schemes with Convergence Guarantees, and Operator Learning Meets Inverse Problems: A Probabilistic Perspective - Provides the authority and expertise of leading contributors from an international board of authors - Presents the latest release in the Handbook of Numerical Analysis series - Updated release includes the latest information on the Machine Learning Solutions for Inverse Problems