Fetching the paper…
Reading the bibliography…
We propose a novel machine learning algorithm for simulating radiative transfer.
On the distribution of points in a cube and the approximate evaluation of integrals
I. M. Sobol’ · 1967
Earlier work this paper cites.
Ray effects in discrete ordinates equations
K. D. Lathrop · 1968
Earlier work this paper cites.
Radiation transfer in an anisotropically scattering plane-parallel medium with space-dependent albedo ω \omega (x)
Y. Cengel, M. Özi, et al · 1985
Earlier work this paper cites.
Practical methods of optimization
R. Fletcher · 1987
Earlier work this paper cites.
Universal approximation bounds for superpositions of a sigmoidal function
A. R. Barron · 1993
Earlier work this paper cites.
Monte carlo and quasi-monte carlo methods
R. E. Caflisch · 1998
Earlier work this paper cites.
Artificial neural networks for solving ordinary and partial differential equations
I. E. Lagaris, A. Likas, and D. I. Fotiadis · 1998
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.
Radiative transfer with finite elements-i. basic method and tests
S. Richling, E. Meinköhn, N. Kryzhevoi, and G. Kanschat · 2001
Earlier work this paper cites.
Introduction to numerical analysis
J. Stoer and R. Bulirsch · 2002
Earlier work this paper cites.
Radiative heat transfer
M. F. Modest · 2003
Earlier work this paper cites.
Radiation hydrodynamics
J. I. Castor · 2004
Earlier work this paper cites.
Least-squares finite element formulations for one-dimensional radiative transfer
J. Pontaza and J. Reddy · 2005
Earlier work this paper cites.
Approximate models for radiative transfer
M. Frank · 2007
Earlier work this paper cites.
The prompt spectrum of a radiating sphere: Benchmark solutions for diffusion and transport
F. Graziani · 2008
Earlier work this paper cites.
Numerical methods in multi-dimensional radiative transfer
G. Kanschat and et. al · 2008
Earlier work this paper cites.
Elliptic pde formulation and boundary conditions of the spherical harmonics method of arbitrary order for general three-dimensional geometries
M. F. Modest and J. Yang · 2008
Cited alongside, same era.
Probing the initial conditions for star formation with monte carlo radiative transfer simulations
D. Stamatellos and A. P. Whitworth · 2008
Cited alongside, same era.
Enabling high fidelity neutron transport simulations on petascle architectures
D. Kaushik, M. Smith, A. Wollaber, B. Smith, A. Siegel, and W. S. Yang · 2009
Cited alongside, same era.
Sparse Finite Elements for Radiative Transfer
G. Widmer · 2009
Cited alongside, same era.
Sparse tensor spherical harmonics approximation in radiative transfer
K. Grella and C. Schwab · 2011
Cited alongside, same era.
Sparse tensor approximation for radiative transport
M. Raissi, A. Yazdani, and G. E. Karniadakis · 2018
Later among the works it cites.
Physics-informed neural networks for inverse problems in nano-optics and metamaterials
Y. Chen, L. Lu, G. E. Karniadakis, and L. D. Negro · 2019
Later among the works it cites.
Deepxde: A deep learning library for solving differential equations
L. Lu, X. Meng, Z. Mao, and G. E. Karniadakis · 2019
Later among the works it cites.
fpinns: Fractional physics-informed neural networks
G. Pang, L. Lu, and G. E. Karniadakis · 2019
Later among the works it cites.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
K. Grella · 2013
Cited alongside, same era.
Castro: A new compressible astrophysical solver. iii. multigroup radiation hydrodynamics
W. Zhang, L. Howell, A. Almgren, A. Burrows, J. . Dolence, and J. Bell · 2013
Cited alongside, same era.
Adam: A method for stochastic optimization
D. P. Kingma and J. Ba · 2015
Cited alongside, same era.
Deep learning
Y. LeCun, Y. Bengio, and G. Hinton · 2015
Cited alongside, same era.
Deep learning
I. Goodfellow, Y. Bengio, and A. Courville · 2016
Cited alongside, same era.
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
Cited alongside, same era.
Automatic differentiation in pytorch
A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer · 2017
Cited alongside, same era.
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2019
Later among the works it cites.
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
Closest in time.
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
A. D. Jagtap, K. Kawaguchi, and G. E. Karniadakis · 2020
Closest in time.
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
Closest in time.
Y. Liu, X. Meng, and G. E. Karniadakis · 2020
Closest in time.
K. . O. Lye, S. Mishra, P. Chandrasekhar, and D. Ray · 2020
Closest in time.
Deep learning observables in computational fluid dynamics
K. O. Lye, S. Mishra, and D. Ray · 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.
S. Mishra and R. Molinaro · 2020
Closest in time.
Estimates on the generalization error of physics informed neural networks (pinns) for approximating pdes
S. Mishra and R. Molinaro · 2020
Closest in time.
Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences
S. Mishra and T. K. Rusch · 2020
Closest in time.
Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks
K. Shukla, P. C. Di Leoni, J. Blackshire, D. Sparkman, and G. E. Karniadakis · 2020
Closest in time.