PrerequisiteCalculus, Mathematics StatisticsAbstractSparse Identification of Nonlinear Dynamics (SINDy) is a machine learning method proposed by Steven L. Brunton group to identify the form of differential equations. SINDy method has been widely used in various fields, such as real-time prediction of aeroelastic model in aerospace field, inference of gene control network in biochemistry field. ...
Description: We will introduce the problems and methods on eigenfunctions of the Laplacian.Contents: Review of the Laplacian and the d'Alembertian, the Hadamard parametrix, the sharp Weyl formula, stationary phase and microlocal analysis, improved spectral asymptotics and periodic geodesics, classical and quantum ergodicity.Prerequisite:Real analysis, functional analysisReference:C.D. Sogge, ...