Rebecca Gjini

Stratocumulus clouds are low level clouds with cloud decks that cover immense stretches of subtropical oceans and provide a net cooling effect on the planet. Stratocumulus clouds are an important area of study because clouds and aerosols are one of the largest sources of uncertainty when calculating Earth’s energy budget. My research explores the use of mathematics, computation, and inverse modeling to better understand stratocumulus clouds. Specifically, I work with two very different stratocumulus cloud models and connect the two using feature-based inversion. The first model is known as a large-eddy simulation (LES), a computationally expensive, 3D and time simulation that describes the state of the atmosphere. The second model is a phenomenological model based on predator-prey dynamics. In this scenario, the rain is the predator of clouds. To learn more about how I utilize inverse modeling to compare these two stratocumulus models, check out my recent SIAM News article below.

Check out my research:

Stratocumulus Clouds and Predator-prey Dynamics

Ensemble Kalman Inversion (EKI) is a derivative-free optimization method used to solve nonlinear least squares problems. The algorithm is designed to solve for the minimizer of a cost function over multiple iterations. EKI relies on an ensemble to approximate the derivatives needed to iterate through an optimization problem. The derivative approximations are calculated from the ensemble itself using covariance matrices. During each iteration, the ensemble members are updated using the derivative approximation and eventually the ensemble will collapse onto the minimizer of the cost function.

Also known as algorithmic differentiation (AD), AD is a tool that is used to compute function derivatives in a methodological way. When a human programmer codes a function and its associated derivative, typically the derivative needs to be coded by hand. AD allows programmers to code up their original function and use the AD computer algorithm to solve for the derivative function. I implemented AD within a python package called PyDDA (Pythonic Direct Data Assimilation) during my internship at the Argonne National Laboratory. PyDDA uses data from multiple weather radars to get 3D wind field velocities based on the 3D variational technique. I implemented AD within all the gradient functions of the package used to perform the cost function minimization. For more information on PyDDA and how AD is used within the package check out the PyDDA documentation and github.

Check out PyDDA:

PyDDA documentation PyDDA github

Inverse problems are important scientific and mathematical problems because the solutions help us understand physical processes that are difficult to observe. The opposite of a forward problem, inverse problems are used to determine the factors that cause a set of observations to occur. One method of solving inverse problems is to use a Bayesian approach. The idea behind Bayesian inversion is to better understand model parameters (and their associated model output) in relation to data. In my research, I specifically use feature-based Bayesian inversion and Markov-chain Monte Carlo (MCMC) to numerically solve an inverse problem. For more information on feature-based inversion and its applications to various numerical problems, below is a paper written by my advisor.

Check out this journal article:

Feature-based data assimilation in geophysics

The scattering transform is a mathematical model of Convolutional Neural Networks (CNNs) allowing the use of predefined wavelet filters. Motivated by classification tasks, I worked on applying the scattering transform to graph structured data during an REU at Michigan State University with several other students. The scattering transform produces a sequence of coefficients at each layer of the network which can be used to classify different classes of graph data. During the REU, I, along with my research group, helped implement the scattering transform to improve upon results from previous studies, classify different models of random graphs, and explore the use of principal component analysis applied to the scattering coefficients. For more information on this work, below is a link to a virtual poster presentation my research group and I presented at an undergraduate conference.

Check out our presentation:

Graph Scattering Transform