Gerrit Welper

Dr. Gerrit Welper is Assistant Professor of Mathematics at the University of Central Florida's College of Sciences, specializing in approximation theory and neural network optimization. His research bridges computational mathematics and machine learning, particularly analyzing gradient descent dynamics in neural networks and developing efficient reduced-order models for transport equations.

Recent work establishes approximation guarantees for gradient-flow trained shallow networks, develops neural representations of entropy solutions, and creates transformed snapshot interpolation techniques for parametric systems. He has advanced adaptive Petrov-Galerkin methods for hyperbolic PDEs and developed rigorous performance bounds for reduced-order models.

Dr. Welper's publications demonstrate increasing focus on physics-informed machine learning architectures and their mathematical foundations, with recent innovations in sparse backpropagation and low-rank neural representations.