Fetching the paper…
Reading the bibliography…
Physics informed neural networks approximate solutions of PDEs by minimizing pointwise residuals.
Théorie de l’addition des variables aléatoires
P. Lévy and P. Lévy · 1954
Earlier work this paper cites.
Neural-network-based approximations for solving partial differential equations
M. Dissanayake and N. Phan-Thien · 1994
Earlier work this paper cites.
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
T. Chen and H. Chen · 1995
Earlier work this paper cites.
Neural-network methods for bound- ary value problems with irregular boundaries
I. E. Lagaris, A. Likas, and P. G. D · 2000
Earlier work this paper cites.
Artificial neural networks for solving ordinary and partial differential equations
I. E. Lagaris, A. Likas, and D. I. Fotiadis · 2000
Earlier work this paper cites.
Stochastic differential equations
B. Øksendal · 2003
Earlier work this paper cites.
Numerical Methods for Elliptic and Parabolic Boundary Value Problems
R. Hiptmair and C. Schwab · 2008
Earlier work this paper cites.
Introduction to stochastic calculus with applications
F. C. Klebaner · 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.
Numerical Analysis of Stochastic Ordinary Differential Equations
A. Barth, A. Jentzen, A. Lang, and C. Schwab · 2018
Earlier work this paper cites.
P. Grohs, F. Hornung, A. Jentzen, and P. Von Wurstemberger · 2018
Earlier work this paper cites.
Hidden physics models: Machine learning of nonlinear partial differential equations
M. Raissi and G. E. Karniadakis · 2018
Earlier work this paper cites.
M. Raissi, A. Yazdani, and G. E. Karniadakis · 2018
Earlier work this paper cites.
L. Lu, P. Jin, and G. E. Karniadakis · 2019
Earlier work this paper cites.
fPINNs: Fractional physics-informed neural networks
G. Pang, L. Lu, and G. E. Karniadakis · 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.
Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in uq
C. Schwab and J. Zech · 2019
Cited alongside, same era.
Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of black–scholes partial differential equations
J. Berner, P. Grohs, and A. Jentzen · 2020
Cited alongside, same era.
Error bounds for approximations with deep ReLU neural networks in W s , p {W}^{s,p} norms
I. Gühring, G. Kutyniok, and P. Petersen · 2020
Error estimates of residual minimization using neural networks for linear equations
Y. Shin, Z. Zhang, and G. E. Karniadakis · 2020
Later among the works it cites.
Physics informed neural networks (PINNs) for approximating nonlinear dispersive PDEs
G. Bai, U. Koley, S. Mishra, and R. Molinaro · 2021
Closest in time.
On the approximation of functions by tanh neural networks, 2021
T. De Ryck, S. Lanthaler, and S. Mishra · 2021
Closest in time.
Approximation rates for neural networks with encodable weights in smoothness spaces
I. Gühring and M. Raslan · 2021
Closest in time.
A theoretical analysis of deep neural networks and parametric pdes
G. Kutyniok, P. Petersen, M. Raslan, and R. Schneider · 2021
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Space-time deep neural network approximations for high-dimensional partial differential equations
F. Hornung, A. Jentzen, and D. Salimova · 2020
Cited alongside, same era.
Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations
A. D. Jagtap and G. E. Karniadakis · 2020
Cited alongside, same era.
Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
A. D. Jagtap, E. Kharazmi, and G. E. Karniadakis · 2020
Cited alongside, same era.
Fourier neural operator for parametric partial differential equations, 2020
Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar · 2020
Cited alongside, same era.
Deep learning observables in computational fluid dynamics
K. O. Lye, S. Mishra, and D. Ray · 2020
Cited alongside, same era.
Physics-informed neural networks for high-speed flows
Z. Mao, A. D. Jagtap, and G. E. Karniadakis · 2020
Cited alongside, same era.
S. Mishra and R. Molinaro · 2020
Cited alongside, same era.
Error estimates for DeepOnets: A deep learning framework in infinite dimensions, 2021
S. Lanthaler, S. Mishra, and G. E. Karniadakis · 2021
Closest in time.
DeepXDE: A deep learning library for solving differential equations
L. Lu, X. Meng, Z. Mao, and G. E. Karniadakis · 2021
Closest in time.
Iterative surrogate model optimization (ISMO): An active learning algorithm for pde constrained optimization with deep neural networks
K. O. Lye, S. Mishra, D. Ray, and P. Chandrashekar · 2021
Closest in time.
Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for pdes
S. Mishra and R. Molinaro · 2021
Closest in time.
Physics informed neural networks for simulating radiative transfer
S. Mishra and R. Molinaro · 2021
Closest in time.
Physics informed neural networks for option pricing
S. Mishra, R. Molinaro, and R. Tanios · 2021
Closest in time.
Physics informed neural networks in computational finance: high-dimensional forward and inverse option pricing
R. Tanios · 2021
Closest in time.
B-PINNs: Bayesian physics-informed neural networks for forward and inverse pde problems with noisy data
L. Yang, X. Meng, and G. E. Karniadakis · 2021
Closest in time.