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Smoothed particle hydrodynamics (SPH) is omnipresent in modern engineering and scientific disciplines.
Über die partiellen differenzengleichungen der mathematischen physik
Courant, R., Friedrichs, K., and Lewy, H · 1928
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A two-dimensional interpolation function for irregularly-spaced data
Shepard, D · 1968
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An arbitrary lagrangian-eulerian computing method for all flow speeds
Hirt, C. W., Amsden, A. A., and Cook, J · 1974
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Smoothed particle hydrodynamics: theory and application to non-spherical stars
Gingold, R. A. and Monaghan, J. J · 1977
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A numerical approach to the testing of the fission hypothesis
Lucy, L. B · 1977
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Simulating free surface flows with sph
Monaghan, J. J · 1994
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Variational and momentum preservation aspects of smooth particle hydrodynamic formulations
Bonet, J. and Lok, T.-S · 1999
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Moving least-squares particle hydrodynamics ii: conservation and boundaries
Dilts, G. A · 2000
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Numerical simulation of interfacial flows by smoothed particle hydrodynamics
Colagrossi, A. and Landrini, M · 2003
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Smoothed particle hydrodynamics
Monaghan, J. J · 2005
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Regularization on discrete spaces
Zhou, D. and Schölkopf, B · 2005
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Modelling free surface flows with smoothed particle hydrodynamics
Sigalotti, L. D. G., Daza, J., and Donoso, A · 2006
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Numerical simulation of fluid–structure interaction by sph
Antoci, C., Gallati, M., and Sibilla, S · 2007
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Weakly compressible sph for free surface flows
Becker, M. and Teschner, M · 2007
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An incompressible multi-phase sph method
Hu, X. and Adams, N. A · 2007
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The graph neural network model
Scarselli, F., Gori, M., Tsoi, A. C., Hagenbuchner, M., and Monfardini, G · 2008
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Minimizing the dirichlet energy over a space of measure preserving maps
Taheri, A · 2009
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State-of-the-artofclassicalsphforfree-surfaceflows
Gomez-Gesteira, M., Rogers, B. D., Dalrymple, R. A., and Crespo, A. J · 2010
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Lebesgue and Sobolev Spaces with Variable Exponents , volume 1, chapter 13
Diening, L., Harjulehto, P., Hästö, P., and Ruzicka, M · 2011
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δ \delta -sph model for simulating violent impact flows
Marrone, S., Antuono, M., Colagrossi, A., Colicchio, G., Le Touzé, D., and Graziani, G · 2011
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A generalized wall boundary condition for smoothed particle hydrodynamics
Adami, S., Hu, X., and Adams, N. A · 2012
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Smoothed particle hydrodynamics and magnetohydrodynamics
Price, D. J · 2012
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A transport-velocity formulation for smoothed particle hydrodynamics
Adami, S., Hu, X., and Adams, N. A · 2013
Cited alongside, same era.
Towards consistence and convergence of conservative sph approximations
Litvinov, S., Hu, X., and Adams, N. A · 2015
Cited alongside, same era.
Convolutional neural networks for steady flow approximation
Guo, X., Li, W., and Iorio, F · 2016
Cited alongside, same era.
Smoothed particle hydrodynamics (sph) for free-surface flows: past, present and future
Violeau, D. and Rogers, B. D · 2016
Cited alongside, same era.
Neural message passing for quantum chemistry
Gilmer, J., Schoenholz, S. S., Riley, P. F., Vinyals, O., and Dahl, G. E · 2017
Cited alongside, same era.
Semi-supervised classification with graph convolutional networks
Kipf, T. N. and Welling, M · 2017
Cited alongside, same era.
Mace: Higher order equivariant message passing neural networks for fast and accurate force fields
Batatia, I., Kovacs, D. P., Simm, G., Ortner, C., and Csányi, G · 2022
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E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials
Batzner, S., Musaelian, A., Sun, L., Geiger, M., Mailoa, J. P., Kornbluth, M., Molinari, N., Smidt, T. E., and Kozinsky, B · 2022
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Composing partial differential equations with physics-aware neural networks
Karlbauer, M., Praditia, T., Otte, S., Oladyshkin, S., Nowak, W., and Butz, M. V · 2022
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Simulating liquids with graph networks
Klimesch, J., Holl, P., and Thuerey, N · 2022
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Graphcast: Learning skillful medium-range global weather forecasting
Lam, R., Sanchez-Gonzalez, A., Willson, M., Wirnsberger, P., Fortunato, M., Alet, F., Ravuri, S., Ewalds, T., Eaton-Rosen, Z., Hu, W., et al · 2022
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Relational inductive biases, deep learning, and graph networks
Battaglia, P. W., Hamrick, J. B., Bapst, V., Sanchez-Gonzalez, A., Zambaldi, V., Malinowski, M., Tacchetti, A., Raposo, D., Santoro, A., Faulkner, R., et al · 2018
Cited alongside, same era.
JAX: composable transformations of Python+NumPy programs, 2018
Bradbury, J., Frostig, R., Hawkins, P., Johnson, M. J., Leary, C., Maclaurin, D., Necula, G., Paszke, A., VanderPlas, J., Wanderman-Milne, S., and Zhang, Q · 2018
Cited alongside, same era.
Multi-resolution delta-plus-sph with tensile instability control: Towards high reynolds number flows
Sun, P., Colagrossi, A., Marrone, S., Antuono, M., and Zhang, A · 2018
Cited alongside, same era.
3d steerable cnns: Learning rotationally equivariant features in volumetric data
Weiler, M., Geiger, M., Welling, M., Boomsma, W., and Cohen, T. S · 2018
Cited alongside, same era.
A note on over-smoothing for graph neural networks
Cai, C. and Wang, Y · 2020
Cited alongside, same era.
Fourier neural operator for parametric partial differential equations
Li, Z., Kovachki, N. B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., Anandkumar, A., et al · 2020
Cited alongside, same era.
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Graph neural network-accelerated lagrangian fluid simulation
Li, Z. and Farimani, A. B · 2022
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Learning the dynamics of physical systems from sparse observations with finite element networks
Lienen, M. and Günnemann, S · 2022
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Forecasting global weather with graph neural networks
Pathak, J., Subramanian, S., Harrington, P., Raja, S., Chattopadhyay, A., Mardani, M., Kurth, T., Hall, D., Li, Z., Azizzadenesheli, K., Hassanzadeh, P., Kashinath, K., and Anandkumar, A · 2022
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Machine learning for partial differential equations (mar
Brunton, S. L. and Kutz, J. N · 2023
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Understanding convolution on graphs via energies
Di Giovanni, F., Rowbottom, J., Chamberlain, B. P., Markovich, T., and Bronstein, M. M · 2023
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Towards multi-spatiotemporal-scale generalized pde modeling
Gupta, J. K. and Brandstetter, J · 2023
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Towards sph simulations of cavitating flows with an eosb cavitation model
Lyu, H.-G., Sun, P.-N., Colagrossi, A., and Zhang, A.-M · 2023
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Boundary graph neural networks for 3d simulations
Mayr, A., Lehner, S., Mayrhofer, A., Kloss, C., Hochreiter, S., and Brandstetter, J · 2023
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Scaling deep learning for materials discovery
Merchant, A., Batzner, S., Schoenholz, S. S., Aykol, M., Cheon, G., and Cubuk, E. D · 2023
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Climax: a25 foundation model for weather and climate
Nguyen, T., Brandstetter, J., Kapoor, A., Gupta, J. K., and Grover, A · 2023
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Mattergen: a generative model for inorganic materials design
Zeni, C., Pinsler, R., Zügner, D., Fowler, A., Horton, M., Fu, X., Shysheya, S., Crabbé, J., Sun, L., Smith, J., et al · 2023
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Universal physics transformers
Alkin, B., Fürst, A., Schmid, S., Gruber, L., Holzleitner, M., and Brandstetter, J · 2024
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Aurora: A foundation model of the atmosphere
Bodnar, C., Bruinsma, W. P., Lucic, A., Stanley, M., Brandstetter, J., Garvan, P., Riechert, M., Weyn, J., Dong, H., Vaughan, A., et al · 2024
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Fan, Y., Li, X., Zhang, S., Hu, X., and Adams, N. A · 2024
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Pde-refiner: Achieving accurate long rollouts with neural pde solvers
Lippe, P., Veeling, B., Perdikaris, P., Turner, R., and Brandstetter, J · 2024
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Lagrangebench datasets, January 2024
Toshev, A. P. and Adams, N. A · 2024
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Symmetric basis convolutions for learning lagrangian fluid mechanics
Winchenbach, R. and Thuerey, N · 2024
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