Research

Here is a short list of projects I’ve been involved with in the past or am currently working on. Note that complete publication history (with detailed citations) is located in my CV. Overall, much of my work is currently directed towards solving PDE-constrained optimization problems, especially with regards to solving nonsmooth and nonconvex problems. In the past, I’ve also worked on uncertainty quantification for biological models.

2022
1. Adaptive Randomized Sketching for Dynamic Nonsmooth Optimization; to appear in Proceedings of the International Model Analysis Conference XLI.
2. A Proximal Trust-Region Method for Nonsmooth Optimization with Inexact Function and Gradient Evaluations.
3. A Levenberg-Marquardt Method for Nonsmooth Regularized Least Squares (submitted to SIAM Journal on Scientific Computing).
4. Tsunami Early Warning from Global Navigation Satellite System Data using Convolutional Neural Networks in Geophysical Review Letters.
2021
1. A Proximal Quasi-Newton Trust-Region Method for Nonsmooth Regularized Optimization, with the ArXiv version here.
2. Comparison of Machine Learning Approaches for TsunamiForecasting from Sparse Observation. The EarchArXiv version can be found here.
2019
1. Basis Pursuit Denoise with Nonsmooth Constraints. The IEEE Transactions on Signal Processing version can be found here.
2. Relaxation algorithms for matrix completion, with applications to seismic travel-time data interpolation. The Inverse Problems version can be found here.
2016
1. Validation of a Mathematical Model for Green Algae (Raphidocelis subcapitata) Growth and Implications for a Coupled DynamicalSystem with Daphnia Magna.
2. Parameter Estimation Using Unidentified Individual Data in Individual Based Models
2015
2014
1. Uncertainty quantification for a model of HIV-1 patient response to antiretroviral therapy interruptions.
2. The Effects of Parameterization on Inverse Problems
2013
1. Mathematical Modeling of HCV Viral Kinetics
Work-in-Progress
1. Combining Reduced Order Models with Implicit Sampling (presented at SIAM CSE, February 2019 by Matthew Zahr)
2. FWI with SMART
3. Fast Solutions to PDE constrained optimization
4. Nonsmooth Trust Region methods
5. Exact Relaxation - trying to find the correct hyperparameters for our work in BPDN and other relaxation algorithms.

Here is an unordered bibliography of work I’ve submitted/published/reported/talked. A more complete/detailed version is located in my CV.

2021 2
2020 1
2018 2
2017 1

2021

Comparison of Machine Learning Approaches for Tsunami Forecasting from Sparse Observations

1 minute read

We present several different methods for predicting tsunami wave height from GeoClaw runs.

A Proximal Quasi-Newton Trust-Region Method for Nonsmooth Regularized Optimization

1 minute read

We present a trust-region algorithm that computes the descent direction with a proximal gradient-like step.

2020

Moreau-Yoshida Regularization and First Order Methods with Firedrake

11 minute read

A run-through of regularization and first order methods for solving the obstacle problem in Firedrake.

2018

Basis Pursuit Denoise with Nonsmooth Constraints

1 minute read

We tried to solve the classic basis-pursuit denoise problem where we enforced sparsity in the solution and the observed data.

Relaxation algorithms for matrix completion, with applications to seismic travel-time data interpolation

less than 1 minute read

We developed a fast, amenable low-rank interpolation technique for travel time tomography data.

2017

CSE 546 Machine Learning Final Project - Identifying Genre by Album Cover

6 minute read

In this project, we attempted to develop an algorithm that will classify an album’s musical genre/style based on the cover art. We pursued a color analysis w...