Sparse Modeling and Machine Learning for Nonlinear Partial Differential Equations
Technical Report,15 Apr 2017,14 Apr 2020
Carnegie Mellon University Pittsburgh United States
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The main goal of the grant was to construct new approaches and algorithms for learning dynamical systems from data. The objective of this research was to develop and analyze new approaches for discovering the underlying governing equations that model a given dataset. We assumed that the data was generated by some unknown dynamic process, typically satisfying a time-dependent differential equation. The technical strategies were based on sparse optimization with limited samplingand structured networks. This work involved sparsity-promoting optimization based on the l1 penalty, which was used to regularize the recovery process. The results include several new algorithmic and theoretical developments.
- Statistics and Probability