| Description |
1 online resource (473 pages) |
| Series |
Lecture Notes in Physics Ser. ; v. 968 |
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Lecture notes in physics ; 968.
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| Contents |
Intro -- Contents -- 1 Introduction -- References -- Part I Fundamentals -- Preface -- References -- 2 Introduction to Material Modeling -- 2.1 Introduction -- 2.2 Structure-Property Relationship -- 2.2.1 Atomic Structure -- 2.2.2 Molecular and Material Properties -- 2.3 Quantum Mechanics -- 2.4 Statistical Mechanics -- Glossary -- References -- 3 Kernel Methods for Quantum Chemistry -- 3.1 Introduction -- 3.2 Representations of Physical Systems -- 3.3 Implicit Feature Mapping: The Kernel Trick -- 3.4 Kernel Methods -- 3.4.1 Kernel Ridge Regression -- 3.4.2 Kernel Principal Component Analysis |
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3.5 Relevant Dimension Estimation -- 3.6 Conclusion -- References -- 4 Introduction to Neural Networks -- 4.1 Introduction -- 4.2 Neural Network Basics -- 4.2.1 The Forward Pass -- 4.2.2 The Backward Pass -- 4.2.3 Optimizing Neural Networks -- 4.3 Efficient Training of Neural Networks -- 4.3.1 Hessian-Based Analysis of the Error Function -- 4.3.2 Normalizing the Input Data -- 4.3.3 Choosing the Activation Function -- 4.3.4 Initialization and Network Size -- 4.3.5 Learning Rate, Momentum, and Mini-Batches -- 4.4 Improving Neural Network Generalization -- 4.4.1 Model Regularization |
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4.4.2 Invariant Input Representations -- 4.4.3 Structured Neural Networks -- 4.4.4 Smoothness of the Prediction Function -- 4.5 Model Selection, Evaluation, and Understanding -- 4.5.1 Model Selection and Evaluation -- 4.5.2 Understanding Neural Network Predictions -- 4.5.3 Layer-Wise Relevance Propagation -- 4.5.4 What Did the Neural Network Actually Learn? -- 4.6 Conclusion -- References -- Part II Incorporating Prior Knowledge: Invariances, Symmetries, Conservation Laws -- Preface -- References -- 5 Building Nonparametric n-Body Force Fields Using Gaussian Process Regression -- 5.1 Introduction |
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5.2 Nonparametric n-body Force Field Construction -- 5.2.1 Gaussian Process Regression -- 5.2.2 Local Energy from Global Energies and Forces -- 5.2.3 Incorporating Prior Information in the Kernel -- 5.2.3.1 Function Smoothness -- 5.2.3.2 Physical Symmetries -- 5.2.3.3 Interaction Order -- 5.2.4 Smooth, Symmetric Kernels of Finite Order n -- 5.2.5 Choosing the Optimal Kernel Order -- 5.2.6 Kernels for Multiple Chemical Species -- 5.2.7 Summary -- 5.3 Practical Considerations -- 5.3.1 Applying Model Selection to Nickel Systems -- 5.3.2 Speeding Up Predictions by Building MFFs -- 5.4 Conclusions |
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References -- 6 Machine-Learning of Atomic-Scale Properties Based on Physical Principles -- 6.1 Introduction -- 6.2 Kernel Fitting -- 6.2.1 Selection of a Representative Set -- 6.2.2 Linear Combination of Kernels -- 6.2.3 Derivatives -- 6.2.4 Learning from Linear Functionals -- 6.2.5 Learning Multiple Models Simultaneously -- 6.3 Density-Based Representations and Kernels -- 6.3.1 A Dirac Notation for Structural Representations -- 6.3.2 Smooth Overlap of Atomic Positions -- 6.3.3 Body-Order Potentials -- 6.3.4 Kernel Operators and Feature Optimization |
| Summary |
Designing molecules and materials with desired properties is an important prerequisite for advancing technology in our modern societies. This requires both the ability to calculate accurate microscopic properties, such as energies, forces and electrostatic multipoles of specific configurations, as well as efficient sampling of potential energy surfaces to obtain corresponding macroscopic properties. Tools that can provide this are accurate first-principles calculations rooted in quantum mechanics, and statistical mechanics, respectively. Unfortunately, they come at a high computational cost that prohibits calculations for large systems and long time-scales, thus presenting a severe bottleneck both for searching the vast chemical compound space and the stupendously many dynamical configurations that a molecule can assume. To overcome this challenge, recently there have been increased efforts to accelerate quantum simulations with machine learning (ML). This emerging interdisciplinary community encompasses chemists, material scientists, physicists, mathematicians and computer scientists, joining forces to contribute to the exciting hot topic of progressing machine learning and AI for molecules and materials. The book that has emerged from a series of workshops provides a snapshot of this rapidly developing field. It contains tutorial material explaining the relevant foundations needed in chemistry, physics as well as machine learning to give an easy starting point for interested readers. In addition, a number of research papers defining the current state-of-the-art are included. The book has five parts (Fundamentals, Incorporating Prior Knowledge, Deep Learning of Atomistic Representations, Atomistic Simulations and Discovery and Design), each prefaced by editorial commentary that puts the respective parts into a broader scientific context |
| Bibliography |
Includes bibliographical references |
| Notes |
Print version record |
| Subject |
Machine learning.
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Quantum theory.
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Quantum Theory
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Machine Learning
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Mathematical physics.
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Machine learning.
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Quantum & theoretical chemistry.
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Quantum physics (quantum mechanics & quantum field theory)
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Science -- Mathematical Physics.
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Computers -- Intelligence (AI) & Semantics.
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Science -- Chemistry -- Physical & Theoretical.
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Science -- Quantum Theory.
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Machine learning
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Quantum theory
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| Form |
Electronic book
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| Author |
Schütt, Kristof T
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Chmiela, Stefan
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Von Lilienfeld, O. Anatole
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Tkatchenko, Alexandre
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Tsuda, Koji
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Müller, Klaus-Robert.
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| ISBN |
9783030402457 |
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3030402452 |
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9783030402464 |
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3030402460 |
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