5 citations · 6 across the 5 of their papers we have counts for
5 papers
SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equations
Xuan Zhang, Jacob Helwig, Yuchao Lin +4
We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dy…
Minimum norm interpolation by perceptra: Explicit regularization and implicit bias
Jiyoung Park, Ian Pelakh, Stephan Wojtowytsch
We investigate how shallow ReLU networks interpolate between known regions. Our analysis shows that empirical risk minimizers converge to a minimum norm interpolant as the number o…
A qualitative difference between gradient flows of convex functions in finite- and infinite-dimensional Hilbert spaces
Jonathan W. Siegel, Stephan Wojtowytsch
We consider gradient flow/gradient descent and heavy ball/accelerated gradient descent optimization for convex objective functions. In the gradient flow case, we prove the followin…
Group Equivariant Fourier Neural Operators for Partial Differential Equations
Jacob Helwig, Xuan Zhang, Cong Fu +3
We consider solving partial differential equations (PDEs) with Fourier neural operators (FNOs), which operate in the frequency domain. Since the laws of physics do not depend on th…
Optimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality
Stephan Wojtowytsch
In this note, we study how neural networks with a single hidden layer and ReLU activation interpolate data drawn from a radially symmetric distribution with target labels 1 at the…