Fetching the paper…
Reading the bibliography…
We use explicit representation formulas to show that solutions to certain partial differential equations lie in Barron spaces or multilayer spaces if the PDE data lie in such function spaces.
Short proofs of three theorems on harmonic functions
H. Boas and R. Boas · 1988
Earlier work this paper cites.
Universal approximation bounds for superpositions of a sigmoidal function
A. R. Barron · 1993
Earlier work this paper cites.
Sparse grids in a nutshell
J. Garcke · 2012
Earlier work this paper cites.
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
W. E, J. Han, and A. Jentzen · 2017
Earlier work this paper cites.
Error bounds for approximations with deep ReLU networks
D. Yarotsky · 2017
Earlier work this paper cites.
Deep relaxation: partial differential equations for optimizing deep neural networks
P. Chaudhari, A. Oberman, S. Osher, S. Soatto, and G. Carlier · 2018
Earlier work this paper cites.
The deep ritz method: a deep learning-based numerical algorithm for solving variational problems
W. E and B. Yu · 2018
Earlier work this paper cites.
P. Grohs, F. Hornung, A. Jentzen, and P. Von Wurstemberger · 2018
Earlier work this paper cites.
Solving high-dimensional partial differential equations using deep learning
J. Han, A. Jentzen, and W. E · 2018
Earlier work this paper cites.
A. Jentzen, D. Salimova, and T. Welti · 2018
Earlier work this paper cites.
Dgm: A deep learning algorithm for solving partial differential equations
J. Sirignano and K. Spiliopoulos · 2018
Cited alongside, same era.
DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics
H. Wang, L. Zhang, J. Han, and W. E · 2018
Cited alongside, same era.
Barron spaces and the compositional function spaces for neural network models
W. E, C. Ma, and L. Wu · 2019
Cited alongside, same era.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2019
Cited alongside, same era.
Model reduction and neural networks for parametric pdes
K. Bhattacharya, B. Hosseini, N. B. Kovachki, and A. M. Stuart · 2020
On the Banach spaces associated with multi-layer ReLU networks of infinite width
W. E and S. Wojtowytsch · 2020
Closest in time.
Representation formulas and pointwise properties for Barron functions
W. E and S. Wojtowytsch · 2020
Closest in time.
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
M. Hutzenthaler, A. Jentzen, T. Kruse, and T. A. Nguyen · 2020
Closest in time.
Space-time deep neural network approximations for high-dimensional partial differential equations
F. Hornung, A. Jentzen, and D. Salimova · 2020
Closest in time.
Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4d flow MRI data using physics-informed neural networks
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
J. Chen, R. Du, and K. Wu · 2020
Cited alongside, same era.
A. Caragea, P. Petersen, and F. Voigtlaender · 2020
Cited alongside, same era.
Overcoming the curse of dimensionality for some hamilton–jacobi partial differential equations via neural network architectures
J. Darbon, G. P. Langlois, and T. Meng · 2020
Cited alongside, same era.
Towards a mathematical understanding of neural network-based machine learning: what we know and what we don’t
W. E, C. Ma, S. Wojtowytsch, and L. Wu · 2020
Cited alongside, same era.
G. Kissas, Y. Yang, E. Hwuang, W. R. Witschey, J. A. Detre, and P. Perdikaris · 2020
Closest in time.
Complexity measures for neural networks with general activation functions using path-based norms
Z. Li, C. Ma, and L. Wu · 2020
Closest in time.
Physics-informed neural networks for high-speed flows
Z. Mao, A. D. Jagtap, and G. E. Karniadakis · 2020
Closest in time.
Neupde: Neural network based ordinary and partial differential equations for modeling time-dependent data
Y. Sun, L. Zhang, and H. Schaeffer · 2020
Closest in time.
Kolmogorov width decay and poor approximators in machine learning: Shallow neural networks, random feature models and neural tangent kernels
W. E and S. Wojtowytsch · 2021
Closest in time.