Inhalt

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   List of Abbreviations
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   List of Symbols and Notations
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   List of Figures
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   List of Tables
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   Introduction
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   Motivation
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  Objectives
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   O1: Develop the Multifidelity Machine Learning (MFML) Method
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   O2: Study Overall Cost of the ML Model Instead of Number of Training Samples Used
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   O3: Examine and Evaluate the Degrees of Freedom in MFML
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   O4: Benchmark Time-Cost of Multifidelity Methods
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   Roadmap
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   Structure
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   State of Art
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  A Primer of Fundamentals
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   Molecular Descriptors
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   The Regression Problem
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   Reproducing Kernel Hilbert Spaces
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   Gaussian Process Regression
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   Kernel Ridge Regression
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   Cholesky Decomposition
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   Machine Learning Model Evaluation Metrics
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   Multifidelity Models
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   Categorizing Low Fidelity Models
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  Combining Fidelities
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   Additive correction
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   Multiplicative correction
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   Comprehensive correction
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  Multifidelity Gaussian Processes
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   Simple Auto-regressive Model
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   Recursive Multifidelity Model
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   Multi-Task Gaussian Process Regression
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   Multifidelity Methods in Quantum Chemistry
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   Delta-Machine Learning Approach
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   Combination Technique Quantum Machine Learning
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   Hierarchical Machine Learning
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   Multi-Task Delta-Machine Learning
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   Revisiting the Objectives
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   Development of Technical Methods and Applications to Quantum Chemical Properties
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  Methodological Contributions
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   Multifidelity Machine Learning
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   Optimized Multifidelity Machine Learning
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   Multifidelity Delta-Machine Learning Method
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   Scaling Factors
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   Cross-Validation Scheme for Nested Multifidelity Data
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   Error Contours of MFML
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   The Gamma-Curve
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   Multifidelity Machine Learning for Molecular Excitation Energies
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   Calculating Excitation Energies of Arenes
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   Results
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   Multifidelity Structure Analysis
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   Multifidelity Results
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   Predictions in the Energy and Time Domains
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   Reduction of Computation Time for Generating Training Data
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   Conclusion
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   Optimized Multifidelity Machine Learning For Quantum Chemistry
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  Dataset
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   Atomization energies of QM7b
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   Excitation energies
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   Results
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   Atomization Energy Prediction on QM7b
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   Excitation Energy Prediction
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   Conclusion
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   QeMFi: Multifidelity Dataset of Quantum Chemical Properties of Molecules
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   Data Sampling and Quantum Chemistry Calculations
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   Data Records
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  Technical Validation
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   Conformation space coverage
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   Single molecule benchmarks
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   Cumulative use of the dataset
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   Usage Notes
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   Code availability
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   Conclusion
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   Assessing Non-Nested Configurations of Multifidelity Machine Learning
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   Non-Nested Multifidelity Data from QeMFi
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  Results
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   Preliminary data analysis
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   Ground state energies
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   Excitation energies
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   Conclusion
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   Benchmarking Data Efficiency in Delta-ML and Multifidelity Models
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   Dataset and Machine Learning Details
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  Results
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   Learning curves
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   Time-Cost assessment
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   Large Test Set Sizes
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   Conclusion
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   Investigating Data Hierarchies in Multifidelity Machine Learning
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  Methodological Refresher
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   Scaling factors
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   Error contours
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   Gamma-curve
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  Results
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   Learning curves
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   Time benefit analysis
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   Multifidelity error contours
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   Gamma-curves
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   Transferability Assessment
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   Conclusion
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   Complementary Applications and Conclusive Remarks
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  Multifidelity Machine Learning in Practical Applications
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   Molecular Energies of Monomers
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   Excitation Energy Transfer in Porphyrins
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  Conclusion
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   Summary
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   Outlook
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   Appendices and References
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  Appendix A - Supplementary Results
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  Additional Details and Analysis for Arenes
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   Generating training and evaluation data
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   ML details for the prediction of excitation energies
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   Supplementary results for MFML
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   Further discussion of DFTB-based anthracene
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   Scatter plots of the excitation energies
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   Impact of the use of several fidelities in MFML
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   Ordinary Least Squares
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  Supplementary Results for o-MFML
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   Comparison of difference in data and difference in model implementation of MFML
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   Generalization capabilities of the o-MFML for atomization energies
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   Coefficient analysis of o-MFML
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  Additional Results for Data Efficiency Assessment
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   Delta-ML for atomization energies of QM7b
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   Predicting QC_b for Delta-ML
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   Validation set and o-MFML learning curves
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   Training time of the models
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   Supplementary Results for Ground State Energies of Monomers
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  Supplementary Results for Excitation Energies of Porphyrin
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   Multifidelity data analysis
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   Full learning curves
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   Additional Gamma-curves
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   Appendix B - Selected Quantum Chemistry Details
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   Wave Function Theory
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   Density Functional Theory
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   Bibliography