Fetching the paper…
Reading the bibliography…
One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks.
Unsupervised deep learning algorithm for pde-based forward and inverse problems
Bar, L. and Sochen, N. (2019) · 1904
Earlier work this paper cites.
Mixhop: Higher-order graph convolutional architectures via sparsified neighborhood mixing
Abu-El-Haija, S., Perozzi, B., Kapoor, A., Alipourfard, N., Lerman, K., Harutyunyan, H., Steeg, G. V., and Galstyan, A. (2019) · 1905
Earlier work this paper cites.
Semi-supervised classification on non-sparse graphs using low-rank graph convolutional networks
Alfke, D. and Stoll, M. (2019) · 1905
Earlier work this paper cites.
Gao, H. and Ji, S. (2019) · 1905
Earlier work this paper cites.
Lu, L., Jin, P., and Karniadakis, G. E. (2019) · 1910
Earlier work this paper cites.
Development of a generalized darcy equation
Tek, M. et al. (1957) · 1957
Earlier work this paper cites.
Korteweg-de vries equation and generalizations. iii. derivation of the korteweg-de vries equation and burgers equation
Su, C. H. and Gardner, C. S. (1969) · 1969
Earlier work this paper cites.
Zienkiewicz, O. C., Taylor, R. L., Nithiarasu, P., and Zhu, J. (1977) · 1977
Earlier work this paper cites.
A new version of the fast multipole method for the laplace equation in three dimensions
Greengard, L. and Rokhlin, V. (1997) · 1997
Earlier work this paper cites.
Hierarchical matrices
Börm, S., Grasedyck, L., and Hackbusch, W. (2003) · 2003
Earlier work this paper cites.
Dynamic multiscale graph neural networks for 3d skeleton-based human motion prediction
Li, M., Chen, S., Zhao, Y., Zhang, Y., Wang, Y., and Tian, Q. (2020a) · 2003
Earlier work this paper cites.
Neural operator: Graph kernel network for partial differential equations
Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A. (2020b) · 2003
Earlier work this paper cites.
Eikonet: Solving the eikonal equation with deep neural networks
Smith, J. D., Azizzadenesheli, K., and Ross, Z. E. (2020) · 2004
Earlier work this paper cites.
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
Ying, L., Biros, G., and Zorin, D. (2004) · 2004
Earlier work this paper cites.
Problems In Nonlinear Elasticity
Antman, S. S. (2005) · 2005
Earlier work this paper cites.
Model reduction and neural networks for parametric pde(s)
Bhattacharya, K., Kovachki, N. B., and Stuart, A. M. (2020) · 2005
Earlier work this paper cites.
Meshfreeflownet: A physics-constrained deep continuous space-time super-resolution framework
Jiang, C. M., Esmaeilzadeh, S., Azizzadenesheli, K., Kashinath, K., Mustafa, M., Tchelepi, H. A., Marcus, P., Anandkumar, A., et al. (2020) · 2005
Earlier work this paper cites.
The random feature model for input-output maps between banach spaces
Nelsen, N. H. and Stuart, A. M. (2020) · 2005
Cited alongside, same era.
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
Rozza, G., Huynh, D. B. P., and Patera, A. T. (2007) · 2007
Cited alongside, same era.
Boundary Element Methods
Sauter, S. A. and Schwab, C. (2010) · 2010
Cited alongside, same era.
Fundamentals of transport phenomena in porous media
Bear, J. and Corapcioglu, M. Y. (2012) · 2012
Cited alongside, same era.
Chapter 3: The Theoretical Foundation of Reduced Basis Methods
DeVore, R. A. (2014) · 2014
Cited alongside, same era.
Multiresolution matrix factorization
Kondor, R., Teneva, N., and Garg, V. (2014) · 2014
N-gcn: Multi-scale graph convolution for semi-supervised node classification
Abu-El-Haija, S., Kapoor, A., Perozzi, B., and Lee, J. (2018) · 2018
Later among the works it cites.
Relational inductive biases, deep learning, and graph networks
Battaglia, P. W., Hamrick, J. B., Bapst, V., Sanchez-Gonzalez, A., Zambaldi, V. F., Malinowski, M., Tacchetti, A., Raposo, D., Santoro, A., Faulkner, R., Gülçehre, Ç., Song, H. F., Ballard, A. J., Gilmer, J., Dahl, G. E., Vaswani, A., Allen, K. R., Nash, C., Langston, V., Dyer, C., Heess, N., Wierstra, D., Kohli, P., Botvinick, M., Vinyals, O., Li, Y., and Pascanu, R. (2018) · 2018
Later among the works it cites.
The deep ritz method: A deep learning-based numerical algorithm for solving variational problems
E, W. and Yu, B. (2018) · 2018
Later among the works it cites.
Learning particle dynamics for manipulating rigid bodies, deformable objects, and fluids
Li, Y., Wu, J., Tedrake, R., Tenenbaum, J. B., and Torralba, A. (2018) · 2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Approximation of high-dimensional parametric pdes
Cohen, A. and DeVore, R. (2015) · 2015
Cited alongside, same era.
Reduced basis methods for partial differential equations: an introduction
Quarteroni, A., Manzoni, A., and Negri, F. (2015) · 2015
Cited alongside, same era.
U-net: Convolutional networks for biomedical image segmentation
Ronneberger, O., Fischer, P., and Brox, T. (2015) · 2015
Cited alongside, same era.
Convolutional neural networks for steady flow approximation
Guo, X., Li, W., and Iorio, F. (2016) · 2016
Cited alongside, same era.
Semi-supervised classification with graph convolutional networks
Kipf, T. N. and Welling, M. (2016) · 2016
Cited alongside, same era.
Solving ill-posed inverse problems using iterative deep neural networks
Adler, J. and Oktem, O. (2017) · 2017
Cited alongside, same era.
Mrowca, D., Zhuang, C., Wang, E., Haber, N., Fei-Fei, L., Tenenbaum, J. B., and Yamins, D. L. K. (2018) · 2018
Later among the works it cites.
Janossy pooling: Learning deep permutation-invariant functions for variable-size inputs
Murphy, R. L., Srinivasan, B., Rao, V., and Ribeiro, B. (2018) · 2018
Later among the works it cites.
Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification
Zhu, Y. and Zabaras, N. (2018) · 2018
Later among the works it cites.
Graph element networks: adaptive, structured computation and memory
Alet, F., Jeewajee, A. K., Villalonga, M. B., Rodriguez, A., Lozano-Perez, T., and Kaelbling, L. (2019) · 2019
Later among the works it cites.
Prediction of aerodynamic flow fields using convolutional neural networks
Bhatnagar, S., Afshar, Y., Pan, S., Duraisamy, K., and Kaushik, S. (2019) · 2019
Later among the works it cites.
Gauge equivariant convolutional networks and the icosahedral cnn
Cohen, T. S., Weiler, M., Kicanaoglu, B., and Welling, M. (2019) · 2019
Later among the works it cites.
Fast graph representation learning with PyTorch Geometric
Fey, M. and Lenssen, J. E. (2019) · 2019
Later among the works it cites.
Mgnet: A unified framework of multigrid and convolutional neural network
He, J. and Xu, J. (2019) · 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
Raissi, M., Perdikaris, P., and Karniadakis, G. E. (2019) · 2019
Later among the works it cites.
Gauge equivariant mesh cnns: Anisotropic convolutions on geometric graphs
de Haan, P., Weiler, M., Cohen, T., and Welling, M. (2020) · 2020
Closest in time.
Lagrangian fluid simulation with continuous convolutions
Ummenhofer, B., Prantl, L., Thürey, N., and Koltun, V. (2020) · 2020
Closest in time.
A comprehensive survey on graph neural networks
Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., and Philip, S. Y. (2020) · 2020
Closest in time.