arXiv subjects

Thambirajah Ravichandran

Publications and source records attributed to Thambirajah Ravichandran.

2 recordsLinked to original sources

arXiv2021

Stochastic Parameterization using Compressed Sensing: Application to the Lorenz-96 Atmospheric Model

Growing set of optimization and regression techniques, based upon sparse representations of signals, to build models from data sets has received widespread attention recently with the advent of compressed sensing. This paper deals with the parameterization of the Lorenz-96 model with two time-scales that mimics mid-latitude atmospheric dynamics with microscopic convective processes. Compressed sensing is used to build models (vector fields) to emulate the behavior of the fine-scale process, so that explicit simulations become an online benchmark for parameterization. We apply compressed sensing, where the sparse recovery is achieved by constructing a sensing/dictionary matrix from ergodic samples generated by the Lorenz-96 atmospheric model, to parameterize the unresolved variables in terms of resolved variables. Stochastic parameterization is achieved by auto-regressive modelling of noise. We utilize the ensemble Kalman filter for data assimilation, where observations (direct measurements) are assimilated in the low-dimensional stochastic parameterized model to provide predictions. Finally, we compare the predictions of compressed sensing and Wilk's polynomial regression to demonstrate the potential effectiveness of the proposed methodology.

math.DS↗

arXiv2021

Compressed Compressor

In this paper, we present a data-driven reduced order model of viscous Moore-Greitzer (MG) partial differential equation (PDE) by threading together ideas from principal component analysis (PCA) and autoencoder neural networks to sparse regression and compressed sensing. Numerical simulation of the infinite dimensional viscous MG system is reduced into low dimensional data using PCA and autoencoder neural networks based reduced order modelling (ROM) approaches. Based on the observation that MG equations close to bifurcations have a sparse representation (normal form) with respect to high-dimensional polynomial spaces, we use the Sparse Identification of Dynamical Systems (SINDy) algorithm which uses a collection of all monomials as sampling matrix and the LASSO algorithm to recover a system of sparse two ordinary differential equations (ODEs) with cubic nonlinearities. The discovered governing equations can be used to fully recover the original system dynamics up to 98.9% accuracy. When dimensional reduction is performed along the dataset's principal components, the resulting low dimensional differential equations will be consistent and have some resemblance to the normal form structure. Additionally, a new nonlinear behaviour is exhibited in viscous MG equations during rotating stall instability past the Hopf bifurcation point.

math.DS↗