Emerging Machine Learning Methods Integrated with Dynamics
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Direct Solution Methods for Ax=b: Gaussian Elimination
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LU Decomposition for Solving Ax=b
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Jacobi Iterative Scheme for Solving Ax=b
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Eigenvector and Eigenvalue Decomposition of Matrix A
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Principal Components Analysis from Singular Value Decomposition
About Nonlinear Model Reduction
Our goal in this set of lectures is to highlight the key elements of producing a reduced order model in a nonlinear dynamical system. The dynamical system produced is typically extremely high dimensional and nonlinear, thus necessitating the model reduction framework. Not only are appropriate coordinates required for the dimensionality reduction (POD modes), but a Galerkin projection must be computed and the nonlinear inner products efficiently evaluated. All these aspects of the reduction will be highlighted in the following set of lectures.