50 citations · 193 across the 27 of their papers we have counts for
7 papers · 1 filter
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…
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…
Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation
Josiah Park, Stephan Wojtowytsch
In this article, we prove approximation theorems in classes of deep and shallow neural networks with analytic activation functions by elementary arguments. We prove for both real a…
Stochastic gradient descent with noise of machine learning type. Part II: Continuous time analysis
Stephan Wojtowytsch
The representation of functions by artificial neural networks depends on a large number of parameters in a non-linear fashion. Suitable parameters of these are found by minimizing…
On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers
Weinan E, Stephan Wojtowytsch
A recent numerical study observed that neural network classifiers enjoy a large degree of symmetry in the penultimate layer. Namely, if where is a linear map…
Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't
Weinan E, Chao Ma, Stephan Wojtowytsch +1
The purpose of this article is to review the achievements made in the last few years towards the understanding of the reasons behind the success and subtleties of neural network-ba…
Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective
Stephan Wojtowytsch, Weinan E
We prove that the gradient descent training of a two-layer neural network on empirical or population risk may not decrease population risk at an order faster than un…