The statistical physics of data assimilation and machine learning:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
[2022]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvii, 187 Seiten Diagramme (teilweise farbig) |
| ISBN: | 9781316519639 |
Internformat
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| 245 | 1 | 0 | |a The statistical physics of data assimilation and machine learning |c Henry D. I. Abarbanel, University of California, San Diego |
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| 505 | 8 | |a 1. Prologue: linking 'The Future' with the present; 2. A data assimilation reminder; 3. Remembrance of things path; 4. SDA variational principles; Euler–Lagrange equations and Hamiltonian formulation; 5. Using waveform information; 6. Annealing in the model precision Rf; 7. Discrete time integration in data assimilation variational principles; Lagrangian and Hamiltonian formulations; 8. Monte Carlo methods; 9. Machine learning and its equivalence to statistical data assimilation; 10. Two examples of the practical use of data assimilation; 11. Unfinished business; Bibliography; Index | |
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Datensatz im Suchindex
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Contents Preface 1 2 3 4 A Data Assimilation Reminder 1.1 Recalling the Basic Idea of Statistical Data Assimilation 1.2 What Is in the Following Chapters? Remembrance of Things Path 2.1 Recursion Relation along the Path X 2.2 The ‘Action’ A(X) = -log[P(X|Y)] 2.3 Multiple Measurement Windows in Time 2.4 The Standard Model for SDA 2.5 The Standard Model Action for the Hodgkin-Huxley NaKL Model 2.6 Twin Experiments SDA Variational Principles 3.1 Estimating Expected Value Integrals 3.2 Laplace’s Method for Estimating Expected Value Integrals 3.3 The Euler-Lagrange Equations for the Standard Model: Continuous Time Using Waveform Information 4.1 Inconsistency in the Standard Model Action 4.2 Time Delay State Vectors and Data 4.3 “Old Nudging” for Proxy Vectors 4.4 L = 1 ; xi (t) Is Observed 4.5 Regularizing the Local Inverse of 3S/3x 4.6 Computing the Pseudoinverse with Singular Value Decomposition 4.7 Lorenz96 Model page ix 1 1 4 5 6 8 9 9 11 13 14 14 15 18 26 26 27 30 31 33 33 34 V
vi Contents 4.8 Synchronization Errors in Time 4.9 Rössler Hyperchaos 4.10 The Euler-Lagrange Equations for Measurement Terms in Proxy Vectors 4.11 Simplified Use of Waveforms 5 35 40 44 45 Annealing in the Model Precision Rf 5.1 Varying the Hyperparameter Rf 5.2 Lorenz96 Model with D = 5 5.3 Hodgkin-Huxley NaKL Neuron 5.4 Qualitative Commentary about Precision Annealing 47 49 53 58 63 6 Discrete Time Integration in Data Assimilation Variational Principles: Lagrangian and Hamiltonian Formulations 6.1 Symplecticity in Variational Data Assimilation 6.2 A Symplectic Annealing Method 6.3 Three Integration Methods 6.4 Numerical Twin Experiments 6.5 Summary of Symplectic Annealing Methods 7 Monte Carlo Methods 7.1 Metropolis-Hastings - Random Proposals 7.2 Precision Annealing MHR Sampling 7.3 Hamiltonian Monte Carlo Methods - Structured Proposals 7.4 Underappreciating HMC 7.5 Using PAHMC on Two Model Dynamics 7.6 HH NaKL Model 7.7 Lorenz96 Model; D = 20 7.8 Computational Considerations for PAHMR and PAHMC Procedures 8 Machine Learning and Its Equivalence to Statistical Data Assimilation 8.1 (A(X)) = (— log P(X|Y)); Action Is Information 8.2 General Discussion of ML 8.3 Using ML to Predict Subsequent Terms in a Time Series k(«)} 8.4 Action Levels for the Given Time Series {i (л)} 8.5 Errors in Training and Validation 8.6 “Twin Experiment” with a Multi-layer Perceptron 8.7 Continuous Layers: Deepest Learning 8.8 Comments on a Set of Curated Retinal Images 66 69 77 79 81 92 95 98 100 104 108 108 108 111 113 119 119 120 123 126 126 131 137 138
vii Contents 9 Two Examples of the Practical Use of Data Assimilation 9.1 Data Assimilation in Action 9.2 Experimental Data on Neurons in the Avian Brain 9.3 Shallow Water Equations; Lagrangian Drifters 9.4 Time-Delayed Nudging Used in the Shallow Water Equations 9.5 Twin Experiments 9.6 Nonlinear Shallow Water Equations 9.7 Results with Time Delay Nudging for the Shallow Water Equations 9.8 Summing It Up 140 140 141 149 155 159 160 161 171 10 Unfinished Business 172 Bibliography Index 174 183 |
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| contents | 1. Prologue: linking 'The Future' with the present; 2. A data assimilation reminder; 3. Remembrance of things path; 4. SDA variational principles; Euler–Lagrange equations and Hamiltonian formulation; 5. Using waveform information; 6. Annealing in the model precision Rf; 7. Discrete time integration in data assimilation variational principles; Lagrangian and Hamiltonian formulations; 8. Monte Carlo methods; 9. Machine learning and its equivalence to statistical data assimilation; 10. Two examples of the practical use of data assimilation; 11. Unfinished business; Bibliography; Index |
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| spelling | Abarbanel, H. D. I. 1943- Verfasser (DE-588)171943899 aut The statistical physics of data assimilation and machine learning Henry D. I. Abarbanel, University of California, San Diego Cambridge Cambridge University Press [2022] © 2022 xvii, 187 Seiten Diagramme (teilweise farbig) txt rdacontent n rdamedia nc rdacarrier 1. Prologue: linking 'The Future' with the present; 2. A data assimilation reminder; 3. Remembrance of things path; 4. SDA variational principles; Euler–Lagrange equations and Hamiltonian formulation; 5. Using waveform information; 6. Annealing in the model precision Rf; 7. Discrete time integration in data assimilation variational principles; Lagrangian and Hamiltonian formulations; 8. Monte Carlo methods; 9. Machine learning and its equivalence to statistical data assimilation; 10. Two examples of the practical use of data assimilation; 11. Unfinished business; Bibliography; Index bicssc Statistische Physik (DE-588)4057000-9 gnd rswk-swf Datenassimilation (DE-588)4803260-8 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf Discrete-time systems Maschinelles Lernen (DE-588)4193754-5 s Datenassimilation (DE-588)4803260-8 s Statistische Physik (DE-588)4057000-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-009024846 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033193691&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abarbanel, H. D. I. 1943- The statistical physics of data assimilation and machine learning 1. Prologue: linking 'The Future' with the present; 2. A data assimilation reminder; 3. Remembrance of things path; 4. SDA variational principles; Euler–Lagrange equations and Hamiltonian formulation; 5. Using waveform information; 6. Annealing in the model precision Rf; 7. Discrete time integration in data assimilation variational principles; Lagrangian and Hamiltonian formulations; 8. Monte Carlo methods; 9. Machine learning and its equivalence to statistical data assimilation; 10. Two examples of the practical use of data assimilation; 11. Unfinished business; Bibliography; Index bicssc Statistische Physik (DE-588)4057000-9 gnd Datenassimilation (DE-588)4803260-8 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| subject_GND | (DE-588)4057000-9 (DE-588)4803260-8 (DE-588)4193754-5 |
| title | The statistical physics of data assimilation and machine learning |
| title_auth | The statistical physics of data assimilation and machine learning |
| title_exact_search | The statistical physics of data assimilation and machine learning |
| title_exact_search_txtP | The statistical physics of data assimilation and machine learning |
| title_full | The statistical physics of data assimilation and machine learning Henry D. I. Abarbanel, University of California, San Diego |
| title_fullStr | The statistical physics of data assimilation and machine learning Henry D. I. Abarbanel, University of California, San Diego |
| title_full_unstemmed | The statistical physics of data assimilation and machine learning Henry D. I. Abarbanel, University of California, San Diego |
| title_short | The statistical physics of data assimilation and machine learning |
| title_sort | the statistical physics of data assimilation and machine learning |
| topic | bicssc Statistische Physik (DE-588)4057000-9 gnd Datenassimilation (DE-588)4803260-8 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| topic_facet | bicssc Statistische Physik Datenassimilation Maschinelles Lernen |
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