The Statistical Physics of Data Assimilation and Machine Learning

Description

Data assimilation is a hugely important mathematical technique, relevant in fields as diverse as geophysics, data science, and neuroscience. This modern book provides an authoritative treatment of the field as it relates to several scientific disciplines, with a particular emphasis on recent developments from machine learning and its role in the optimisation of data assimilation. Underlying theory from statistical physics, such as path integrals and Monte Carlo methods, are developed in the text as a basis for data assimilation, and the author then explores examples from current multidisciplinary research such as the modelling of shallow water systems, ocean dynamics, and neuronal dynamics in the avian brain. The theory of data assimilation and machine learning is introduced in an accessible and unified manner, and the book is suitable for undergraduate and graduate students from science and engineering without specialized experience of statistical physics. 00.0 01.0_pp_i_iv_Frontmatter 02.0_pp_v_viii_Contents 03.0_pp_ix_xviii_Preface 04.0_pp_1_4_A_Data_Assimilation_Reminder 05.0_pp_5_13_Remembrance_of_Things_Path 06.0_pp_14_25_SDA_Variational_Principles 07.0_pp_26_46_Using_Waveform_Information 08.0_pp_47_65_Annealing_in_the_Model_Precision_R_f 09.0_pp_66_94_Discrete_Time_Integration_in_Data_Assimilation_Variational_Principles_Lagrangian_and_Hamiltonian_For 10.0_pp_95_118_Monte_Carlo_Methods 11.0_pp_119_139_Machine_Learning_and_Its_Equivalence_to_Statistical_Data_Assimilation 12.0_pp_140_171_Two_Examples_of_the_Practical_Use_of_Data_Assimilation 13.0_pp_172_173_Unfinished_Business 14.0_pp_174_182_Bibliography 15.0_pp_183_188_Index