Thomas Hogancamp

I enjoy combining mathematics and programming to create useful tools or gain research insights. Some of my projects can be found here.

Machine Learning and PDEs

Recent exciting results have shown that neural networks can be used to efficiently solve some nonlinear PDEs. A key idea is to create a loss function tailored to the given equations; terms representing the PDE and boundary conditions are included in addition to more problem specific quantities (for example, one might search for solutions with some type of symmetry and penalize non-symmetry). I am investigating applications of this technique to models inspired by my previous work on anti-plane shear.

Data Analysis

I am drawn to Data Science because it blends together several of my greatest passions: mathematicsl analysis, real-world problem solving, and exposition.