Mikil Radu Foss

Mentor: Prof. Andrew Lamperski | Read Paper

• Established rigorous theoretical guarantees for MINE by deriving quantitative error bounds of $O(m^{-1/2} + T^{-1/3})$ for KL divergence estimation using shallow neural networks.
• Synthesized advanced techniques from convex optimization and functional analysis to construct the main proof framework.

Mentors: Dr. Olena Burkovska & Dr. Konstantin Pieper

• Developing a custom sparsity-promoting algorithm to construct neural networks that approximate the memory kernel in the Generalized Langevin Equation.
• Achieved a 10x speedup in practice by developing an $O(N)$ SDE algorithmic improvement, replacing the previous $O(N^2)$ approach.
• Conducted and documented over 100 machine learning experiments to validate the theoretical framework.

Mentor: Prof. Vladimir Sverak

• Investigated the compressiveness of neural networks compared to traditional Fourier series, focusing on functions emerging as steady-state solutions to PDEs.
• Implemented numerical methods such as RK4, Spectral methods, and Godunov's scheme for PDE approximations.
• Utilized autoencoders and sparse autoencoders to measure and compare compressiveness.