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Neural operators, serving as physics surrogate models, have recently gained increased interest.
Mechanism of the production of small eddies from large ones
Taylor, G. I. and Green, A. E · 1937
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Local structure of turbulence in an incompressible fluid at very high reynolds numbers
Kolmoqorov, A · 1941
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A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high reynolds number
Kolmogorov, A. N · 1962
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General circulation experiments with the primitive equations: I. the basic experiment
Smagorinsky, J · 1963
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A reynolds stress model of turbulence and its application to thin shear flows
Hanjalic, K. and Brian, L · 1972
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A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows
Patankar, S. V. and Spalding, B. D · 1972
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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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A discrete numerical model for granular assemblies
Cundall, P. A. and Strack, O. D · 1979
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Shock simulation by the particle method sph
Monaghan, J. J. and Gingold, R. A · 1983
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Flip: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions
Brackbill, J. U. and Ruppel, H. M · 1986
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Solution of the implicitly discretized fluid flow equations by operator-splitting
Issa, R · 1986
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Smoothed particle hydrodynamics
Monaghan, J. J · 1992
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A particle method for history-dependent materials
Sulsky, D., Chen, Z., and Schreyer, H. L · 1994
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Modeling low reynolds number incompressible flows using sph
Morris, J., Fox, P., and Zhu, Y · 1997
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Direct numerical simulation: a tool in turbulence research
Moin, P. and Mahesh, K · 1998
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A tensorial approach to computational continuum mechanics using object-oriented techniques
Weller, H. G., Tabor, G., Jasak, H., and Fureby, C · 1998
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An introduction to turbulent flow
Mathieu, J. and Scott, J · 2000
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Turbulent flows
Pope, S. B · 2001
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Navier-Stokes equations: theory and numerical analysis , volume 343
Temam, R · 2001
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Numerical simulation of interfacial flows by smoothed particle hydrodynamics
Colagrossi, A. and Maurizio, L · 2003
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Neural operator: Graph kernel network for partial differential equations
Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2003
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Smoothed particle hydrodynamics
Monaghan, J. J · 2005
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Smoothed particle hydrodynamics on gpus
Harada, T., Koshizuka, S., and Kawaguchi, Y · 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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Formulation of the k-omega turbulence model revisited
Wilcox, D · 2008
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Fourier neural operator for parametric partial differential equations
Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., and Anandkumar, A · 2010
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Rectified linear units improve restricted boltzmann machines
Nair, V. and Hinton, G. E · 2010
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Gpus, a new tool of acceleration in cfd: efficiency and reliability on smoothed particle hydrodynamics methods
Crespo, A., Dominguez, J. M., Barreiro, A., Gomez-Gasteira, M., and D, R. B · 2011
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Introduction to partial differential equations
Olver, P. J · 2014
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Shapenet: An information-rich 3d model repository
Chang, A. X., Funkhouser, T. A., Guibas, L. J., Hanrahan, P., Huang, Q., Li, Z., Savarese, S., Savva, M., Song, S., Su, H., Xiao, J., Yi, L., and Yu, F · 2015
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Adam: A method for stochastic optimization
Kingma, D. P. and Ba, J · 2015
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U-net: Convolutional networks for biomedical image segmentation
Ronneberger, O., Fischer, P., and Brox, T · 2015
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Ba, L. J., Kiros, J. R., and Hinton, G. E · 2016
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Numerical Approximation of Partial Differential Equations
Bartels, S · 2016
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Interaction networks for learning about objects, relations and physics
Battaglia, P., Pascanu, R., Lai, M., Jimenez Rezende, D., et al · 2016
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Convolutional neural networks for steady flow approximation
Guo, X., Li, W., and Iorio, F · 2016
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Gaussian error linear units (gelus)
Hendrycks, D. and Gimpel, K · 2016
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Neural message passing for quantum chemistry
Gilmer, J., Schoenholz, S. S., Riley, P. F., Vinyals, O., and Dahl, G. E · 2017
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Semi-supervised classification with graph convolutional networks
Kipf, T. N. and Welling, M · 2017
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SGDR: stochastic gradient descent with warm restarts
Loshchilov, I. and Hutter, F · 2017
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Attention is all you need
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., and Polosukhin, I · 2017
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Relational inductive biases, deep learning, and graph networks
Graphcast: Learning skillful medium-range global weather forecasting
Lam, R., Sanchez-Gonzalez, A., Willson, M., Wirnsberger, P., Fortunato, M., Pritzel, A., Ravuri, S., Ewalds, T., Alet, F., Eaton-Rosen, Z., et al · 2022
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Transformer for partial differential equations’ operator learning
Li, Z., Meidani, K., and Farimani, A. B · 2022
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High-resolution image synthesis with latent diffusion models
Rombach, R., Blattmann, A., Lorenz, D., Esser, P., and Ommer, B · 2022
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Nomad: Nonlinear manifold decoders for operator learning
Seidman, J., Kissas, G., Perdikaris, P., and Pappas, G. J · 2022
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Learned simulators for turbulence
Stachenfeld, K., Fielding, D. B., Kochkov, D., Cranmer, M., Pfaff, T., Godwin, J., Cui, C., Ho, S., Battaglia, P., and Sanchez-Gonzalez, A · 2022
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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
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Bert: Pre-training of deep bidirectional transformers for language understanding
Devlin, J., Chang, M.-W., Lee, K., and Toutanova, K · 2018
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Deep learning for universal linear embeddings of nonlinear dynamics
Lusch, B., Kutz, J. N., and Brunton, S. L · 2018
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Deep dynamical modeling and control of unsteady fluid flows
Morton, J., Jameson, A., Kochenderfer, M. J., and Witherden, F · 2018
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Film: Visual reasoning with a general conditioning layer
Perez, E., Strub, F., de Vries, H., Dumoulin, V., and Courville, A. C · 2018
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Lectures on Navier-Stokes equations , volume 192
Tsai, T.-P · 2018
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Learning three-dimensional flow for interactive aerodynamic design
Umetani, N. and Bickel, B · 2018
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Pdebench: An extensive benchmark for scientific machine learning
Takamoto, M., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pflüger, D., and Niepert, M · 2022
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Enhancing computational fluid dynamics with machine learning
Vinuesa, R. and Brunton, S. L · 2022
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Deep learning for day forecasts from sparse observations
Andrychowicz, M., Espeholt, L., Li, D., Merchant, S., Merose, A., Zyda, F., Agrawal, S., and Kalchbrenner, N · 2023
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Symbolic discovery of optimization algorithms
Chen, X., Liang, C., Huang, D., Real, E., Wang, K., Liu, Y., Pham, H., Dong, X., Luong, T., Hsieh, C., Lu, Y., and Le, Q. V · 2023
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Gnot: A general neural operator transformer for operator learning
Hao, Z., Wang, Z., Su, H., Ying, C., Dong, Y., Liu, S., Cheng, Z., Song, J., and Zhu, J · 2023
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Turbulent flow simulation using autoregressive conditional diffusion models
Kohl, G., Chen, L.-W., and Thuerey, N · 2023
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The nonlocal neural operator: Universal approximation
Lanthaler, S., Li, Z., and Stuart, A. M · 2023
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Geometry-informed neural operator for large-scale 3d pdes
Li, Z., Kovachki, N. B., Choy, C., Li, B., Kossaifi, J., Otta, S. P., Nabian, M. A., Stadler, M., Hundt, C., Azizzadenesheli, K., et al · 2023
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Generative diffusion for 3d turbulent flows
Lienen, M., Hansen-Palmus, J., Lüdke, D., and Günnemann, S · 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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Multiple physics pretraining for physical surrogate models
McCabe, M., Blancard, B. R.-S., Parker, L. H., Ohana, R., Cranmer, M., Bietti, A., Eickenberg, M., Golkar, S., Krawezik, G., Lanusse, F., et al · 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: A foundation model for weather and climate
Nguyen, T., Brandstetter, J., Kapoor, A., Gupta, J. K., and Grover, A · 2023
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Scalable diffusion models with transformers
Peebles, W. and Xie, S · 2023
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A unifying framework for operator learning via neural fields, Dec 2023
Perdikaris, P · 2023
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Convolutional neural operators
Raonić, B., Molinaro, R., Rohner, T., Mishra, S., and de Bezenac, E · 2023
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Lagrangebench: A lagrangian fluid mechanics benchmarking suite
Toshev, A. P., Galletti, G., Fritz, F., Adami, S., and Adams, N. A · 2023
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Factorized fourier neural operators
Tran, A., Mathews, A. P., Xie, L., and Ong, C. S · 2023
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Convnext V2: co-designing and scaling convnets with masked autoencoders
Woo, S., Debnath, S., Hu, R., Chen, X., Liu, Z., Kweon, I. S., and Xie, S · 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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Artificial intelligence for science in quantum, atomistic, and continuum systems
Zhang, X., Wang, L., Helwig, J., Luo, Y., Fu, C., Xie, Y., Liu, M., Lin, Y., Xu, Z., Yan, K., et al · 2023
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Hamlet: Graph transformer neural operator for partial differential equations
Bryutkin, A., Huang, J., Deng, Z., Yang, G., Schönlieb, C.-B., and Aviles-Rivero, A · 2024
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Continuum attention for neural operators
Calvello, E., Kovachki, N. B., Levine, M. E., and Stuart, A. M · 2024
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Carey, N., Zanisi, L., Pamela, S., Gopakumar, V., Omotani, J., Buchanan, J., and Brandstetter, J · 2024
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DPOT: auto-regressive denoising operator transformer for large-scale PDE pre-training
Hao, Z., Su, C., Liu, S., Berner, J., Ying, C., Su, H., Anandkumar, A., Song, J., and Zhu, J · 2024
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Latent neural PDE solver: a reduced-order modelling framework for partial differential equations
Li, Z., Patil, S., Ogoke, F., Shu, D., Zhen, W., Schneier, M., Jr., J. R. B., and Farimani, A. B · 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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Neural sph: Improved neural modeling of lagrangian fluid dynamics
Toshev, A. P., Erbesdobler, J. A., Adams, N. A., and Brandstetter, J · 2024
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Bridging operator learning and conditioned neural fields: A unifying perspective
Wang, S., Seidman, J. H., Sankaran, S., Wang, H., Pappas, G. J., and Perdikaris, P · 2024
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Transolver: A fast transformer solver for pdes on general geometries
Wu, H., Luo, H., Wang, H., Wang, J., and Long, M · 2024
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Equivariant graph neural operator for modeling 3d dynamics
Xu, M., Han, J., Lou, A., Kossaifi, J., Ramanathan, A., Azizzadenesheli, K., Leskovec, J., Ermon, S., and Anandkumar, A · 2024
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