Preface Chapter 1 Overview of Statistical Learning Methods 1.1 A brief introduction of statistical learning 1.2 Linear model 1.2.1 Linear regression model 1.2.2 Regularized linear regression 1.2.3 Reproducing kernel model References Chapter 2 Online Kernel Learning of Nonlinear Spatiotemporal Systems 2.1 Motivation of this chapter 2.2 Discretization and lattice dynamic systems 2.3 MIMO partially linear model 2.4 The PM-RLS-SVM for MIMO partially linear systems 2.5 Numerical simulations and some discussions 2.6 Summary References Chapter 3 Learning of Partially Known Nonlinear Stochastic Spatiotemporal Dynamical Systems 3.1 Motivation of this chapter 3.2 Reproducing kernel methods for partially linear models 3.3 The extended partially linear model for SPDE 3.4 Extended partially ridge regression 3.5 Simulations and comparison 3.6 Summary References Chapter 4 Learning of Nonlinear Stochastic Spatiotemporal Dynamical Systems 4.1 Motivation of this chapter 4.2 Stochastic evolution equation and approximation error of FEM 4.3 Learning framework and the kernel learning method 4.4 Learning with irregular observation data 4.5 Simulations and comparison 4.6 Summary References Chapter 5 Learning of Nonlinear Spatiotemporal Dynamical Systems with Non-Uniform Observations 5.1 Motivation of this chapter 5.2 Discretization and non-uniform sampling problem 5.3 A multi-step learning method with non-uniform sampling data 5.4 Inverse meshless collocation model and learning algorithm 5.5 Numerical example 5.6 Summary References Chapter 6 Online Learning of Nonlinear Stochastic Spatiotemporal System with Multiplicative Noise 6.1 Motivation of this chapter 6.2 Discretization and heterogeneous partially linear model 6.3 Error dynamical system of PLM 6.4 Robust optimal control algorithm for error dynamical system 6.5 Numerical examples 6.6 Summary References Chapter 7 Robust Online Learning Method Based on Dynamical Linear Quadratic Regulator 7.1 Motivation of this chapter
7.2 Benchmark online learning methods 7.3 Online learning framework 7.4 Robust online learning method based on LQR 7.5 The online learning in kernel spaces 7.6 Numerical examples 7.7 Summary References Chapter 8 Approximate Controllability of Nonlinear Stochastic Partial Di.erential Systems 8.1 Motivation of this chapter 8.2 Basic concepts and preliminaries 8.3 The controllability results 8.4 Illustrative example 8.5 Summary References
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