I was born and raised in south Jersey. For my undergraduate, I attended Rensselaer Polytechnic Institute in Troy, NY for Physics and Applied Mathematics. Upon graduating, I moved to Los Angeles in the summer of 2016 to pursue a PhD in applied mathematics at UCLA. Currently, I am beginning my third year of the program, and I have passed all three of my qualifying exams.
In addition to being a graduate student and teaching assistant, I also do private tutoring for high school level, undergraduate, and intro graduate level mathematics. For more information, contact me! Also, check out 2 year old Balto below!
My primary interests are in embodied intelligence, cheap control in reinforcement learning, and analyzing theoretical properties of neural networks. In addition, I've been exploring the representational capacity of sparsely connected Restricted Boltzmann Machines and related probabilistic graphical models. Currently, I'm working on a paper discussing the representational capacity of stochastic feedforward networks.
In the recent past, I have been interested in model-order reduction methods, high performance computing, and modeling stochastic phenomena. I have a relatively large amount of background in numerical PDEs and physical simulations.
At Rensselaer, I primarily did research on the evolution of thin film morphology. Here we were interested in developing a model of nanosurface growth under high ambient pressure, which has previously been found to result in time invariant surface roughness, a novel property for thin films to display. This model was then tested and verified by Monte Carlo simulations. Publications and results have been listed in my curriculum vitae found below. Other projects I worked on were computationally determining the universality class scaling coefficients for the stochastic KPZ growth equation in (2+1) dimensions, studying scaling coefficients for diffusion limited aggregation, and the accurate computation of resistivity in trapezoidal shaped nanowires.
Other projects I have worked on briefly include mathematically modeling neuron networks, and applying empirical dynamical modeling techniques to plasma thruster simulations. The former was a project I continued in the RPI mathematics department, where I implemented the leaky integrate-and-fire model on complex networks with intention of applying it to modeling spike time dependent plasticity. Although this project stopped to prioritize the above research, I still think there are many interesting topics to be explored in mathematical neuroscience. The latter was my research during the summer of 2017 at Edwards Air Force Research Lab. This research was a proof of concept study to show that methods in compressed sensing and optimization can be used to determine low dimensional models of dynamical systems directly from noisy time series measurements. One notable technique utilized here was SINDy, the sparse identification of nonlinear dynamics (see Steven L. Brunton et al. 2016).
For the summer of 2018, I continued at the Air Force Research Lab. At the time, there was interest in discovering low dimensional trajectory manifolds within high dimensional noisy experimental data. I decided to try several nonlinear dimensional reduction strategies for this task and decided that autoencoders were most appropriate for their needs. Below, there is an example of a 3D manifold found within high dimensional experimental data. An interesting direction forward may be to use SINDy (see above) to identify the equations that give rise to the encoded manifold, as they would hopefully be telling of the underlying physics interactions.