3 papers
math.NA2026
The double descent and Runge phenomena in overparametrized polynomial interpolation
Jason Wein, Stephan Wojtowytsch
The Runge phenomenon in polynomial interpolation is often considered a classical analogue of the double descent phenomenon in machine learning. In this note, we explore overparamet…
math.AP2026
Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method
Stephan Wojtowytsch
We prove that harmonic functions with Dirichlet boundary data in Barron space, a function class tailored to wide ReLU networks with a single hidden layer and suitably bounded weigh…
math.AP2024
Solving the Poisson Equation with Dirichlet data by shallow ReLU-networks: A regularity and approximation perspective
Malhar Vaishampayan, Stephan Wojtowytsch
For several classes of neural PDE solvers (Deep Ritz, PINNs, DeepONets), the ability to approximate the solution or solution operator to a partial differential equation (PDE) hinge…