Fetching the paper…
Reading the bibliography…
Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.
W. Kutta, “Beitrag zur naherungsweisen integration totaler differentialgleichungen,” Z. Math. Phys. , vol. 46, pp. 435–453, 1901
1901
Earlier work this paper cites.
R. Courant, K. Friedrichs, and H. Lewy, “On the partial difference equations of mathematical physics,” IBM journal of Research and Development , vol. 11, no. 2, pp. 215–234, 1967
1967
Earlier work this paper cites.
1967
Earlier work this paper cites.
H. B. Keller, Numerical solution of two point boundary value problems . SIAM, 1976
1976
Earlier work this paper cites.
O. Talagrand and P. Courtier, “Variational assimilation of meteorological observations with the adjoint vorticity equation. i: Theory,” Quarterly Journal of the Royal Meteorological Society , vol. 113, no. 478, pp. 1311–1328, 1987
1987
Earlier work this paper cites.
G. Berkooz, P. Holmes, and J. L. Lumley, “The proper orthogonal decomposition in the analysis of turbulent flows,” Annual review of fluid mechanics , vol. 25, no. 1, pp. 539–575, 1993
1993
Earlier work this paper cites.
J. T. Betts, “Survey of numerical methods for trajectory optimization,” Journal of guidance, control, and dynamics , vol. 21, no. 2, pp. 193–207, 1998
1998
Earlier work this paper cites.
N. Tishby, F. C. Pereira, and W. Bialek, “The information bottleneck method,” arXiv preprint physics/0004057 , 2000
2000
Earlier work this paper cites.
L. T. Biegler, O. Ghattas, M. Heinkenschloss, and B. v. Bloemen Waanders, “Large-scale pde-constrained optimization: an introduction,” in Large-Scale PDE-Constrained Optimization . Springer, 2003, pp. 3–13
2003
Earlier work this paper cites.
C.-W. Shu, “High-order finite difference and finite volume weno schemes and discontinuous galerkin methods for cfd,” International Journal of Computational Fluid Dynamics , vol. 17, no. 2, pp. 107–118, 2003
2003
Earlier work this paper cites.
R. Y. Rubinstein and D. P. Kroese, “The cross-entropy method: A unified approach to monte carlo simulation, randomized optimization and machine learning,” Information Science & Statistics, Springer Verlag, NY , 2004
2004
Earlier work this paper cites.
A. McNamara, A. Treuille, Z. Popović, and J. Stam, “Fluid control using the adjoint method,” ACM Transactions On Graphics (TOG) , vol. 23, no. 3, pp. 449–456, 2004
2004
Earlier work this paper cites.
J. Tromp, C. Tape, and Q. Liu, “Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels,” Geophysical Journal International , vol. 160, no. 1, pp. 195–216, 2005
2005
Earlier work this paper cites.
N. Sircombe, T. Arber, and R. Dendy, “Kinetic effects in laser-plasma coupling: Vlasov theory and computations,” in Journal de Physique IV (Proceedings) , vol. 133. EDP sciences, 2006, pp. 277–281
2006
Earlier work this paper cites.
D. E. Keyes, D. R. Reynolds, and C. S. Woodward, “Implicit solvers for large-scale nonlinear problems,” in Journal of Physics: Conference Series , vol. 46, no. 1. IOP Publishing, 2006, p. 060
2006
Earlier work this paper cites.
A. Treuille, A. Lewis, and Z. Popović, “Model reduction for real-time fluids,” ACM Transactions on Graphics (TOG) , vol. 25, no. 3, pp. 826–834, 2006
2006
Earlier work this paper cites.
M. Gupta and S. G. Narasimhan, “Legendre fluids: a unified framework for analytic reduced space modeling and rendering of participating media,” in Symposium on Computer Animation , 2007, pp. 17–25
2007
Earlier work this paper cites.
P. Lynch, “The origins of computer weather prediction and climate modeling,” Journal of computational physics , vol. 227, no. 7, pp. 3431–3444, 2008
2008
Earlier work this paper cites.
Y. Dubois and R. Teyssier, “Cosmological MHD simulation of a cooling flow cluster,” Astronomy & Astrophysics , vol. 482, no. 2, pp. L13–L16, 2008
2008
Earlier work this paper cites.
P. Chatelain, A. Curioni, M. Bergdorf, D. Rossinelli, W. Andreoni, and P. Koumoutsakos, “Billion vortex particle direct numerical simulations of aircraft wakes,” Computer Methods in Applied Mechanics and Engineering , vol. 197, no. 13-16, pp. 1296–1304, 2008
2008
Earlier work this paper cites.
M. Athanasopoulos, H. Ugail, and G. G. Castro, “Parametric design of aircraft geometry using partial differential equations,” Advances in Engineering Software , vol. 40, no. 7, pp. 479–486, 2009
2009
Earlier work this paper cites.
M. Wicke, M. Stanton, and A. Treuille, “Modular bases for fluid dynamics,” ACM Transactions on Graphics (TOG) , vol. 28, no. 3, pp. 1–8, 2009
2009
Earlier work this paper cites.
B. Long and E. Reinhard, “Real-time fluid simulation using discrete sine/cosine transforms,” in Proceedings of the 2009 symposium on Interactive 3D graphics and games , 2009, pp. 99–106
2009
Earlier work this paper cites.
D. S. Oliver and Y. Chen, “Recent progress on reservoir history matching: a review,” Computational Geosciences , vol. 15, no. 1, pp. 185–221, 2011
2011
Earlier work this paper cites.
T. De Witt, C. Lessig, and E. Fiume, “Fluid simulation using laplacian eigenfunctions,” ACM Transactions on Graphics (TOG) , vol. 31, no. 1, pp. 1–11, 2012
2012
Earlier work this paper cites.
D. Williamson, M. Goldstein, L. Allison, A. Blaker, P. Challenor, L. Jackson, and K. Yamazaki, “History matching for exploring and reducing climate model parameter space using observations and a large perturbed physics ensemble,” Climate dynamics , vol. 41, no. 7, pp. 1703–1729, 2013
2013
Cited alongside, same era.
T. Kim and J. Delaney, “Subspace fluid re-simulation,” ACM Transactions on Graphics (TOG) , vol. 32, no. 4, pp. 1–9, 2013
2013
Cited alongside, same era.
I. Vernon, M. Goldstein, and R. Bower, “Galaxy formation: Bayesian history matching for the observable universe,” Statistical science , pp. 81–90, 2014
2014
Cited alongside, same era.
B. Liu, G. Mason, J. Hodgson, Y. Tong, and M. Desbrun, “Model-reduced variational fluid simulation,” ACM Transactions on Graphics (TOG) , vol. 34, no. 6, pp. 1–12, 2015
2015
Cited alongside, same era.
A. Sanchez, D. Kochkov, J. A. Smith, M. Brenner, P. Battaglia, and T. J. Pfaff, “Learning latent field dynamics of PDEs,” Advances in Neural Information Processing Systems , 2020
2020
Later among the works it cites.
R. C. Julian, E. Heiden, Z. He, H. Zhang, S. Schaal, J. J. Lim, G. S. Sukhatme, and K. Hausman, “Scaling simulation-to-real transfer by learning a latent space of robot skills,” The International Journal of Robotics Research , vol. 39, no. 10-11, pp. 1259–1278, 2020
2020
Later among the works it cites.
A. X. Lee, A. Nagabandi, P. Abbeel, and S. Levine, “Stochastic latent actor-critic: Deep reinforcement learning with a latent variable model,” Advances in Neural Information Processing Systems , vol. 33, pp. 741–752, 2020
2020
Later among the works it cites.
R. Wang, K. Kashinath, M. Mustafa, A. Albert, and R. Yu, “Towards physics-informed deep learning for turbulent flow prediction,” in Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining , 2020, pp. 1457–1466
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2015
Cited alongside, same era.
O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” in International Conference on Medical image computing and computer-assisted intervention . Springer, 2015, pp. 234–241
2015
Cited alongside, same era.
T. Lelievre and G. Stoltz, “Partial differential equations and stochastic methods in molecular dynamics,” Acta Numerica , vol. 25, pp. 681–880, 2016
2016
Cited alongside, same era.
Ö. Çiçek, A. Abdulkadir, S. S. Lienkamp, T. Brox, and O. Ronneberger, “3d u-net: learning dense volumetric segmentation from sparse annotation,” in International conference on medical image computing and computer-assisted intervention . Springer, 2016, pp. 424–432
2016
Cited alongside, same era.
K. T. Butler, J. M. Frost, J. M. Skelton, K. L. Svane, and A. Walsh, “Computational materials design of crystalline solids,” Chemical Society Reviews , vol. 45, no. 22, pp. 6138–6146, 2016
2016
Cited alongside, same era.
2016
Cited alongside, same era.
K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition , 2016, pp. 770–778
2016
Cited alongside, same era.
N. Watters, D. Zoran, T. Weber, P. Battaglia, R. Pascanu, and A. Tacchetti, “Visual interaction networks: Learning a physics simulator from video,” Advances in neural information processing systems , vol. 30, 2017
2017
Cited alongside, same era.
2020
Later among the works it cites.
2020
Later among the works it cites.
Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, A. Stuart, K. Bhattacharya, and A. Anandkumar, “Multipole graph neural operator for parametric partial differential equations,” Advances in Neural Information Processing Systems , vol. 33, pp. 6755–6766, 2020
2020
Later among the works it cites.
K. Lee and K. T. Carlberg, “Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders,” Journal of Computational Physics , vol. 404, p. 108973, 2020
2020
Later among the works it cites.
S. Wiewel, B. Kim, V. C. Azevedo, B. Solenthaler, and N. Thuerey, “Latent space subdivision: stable and controllable time predictions for fluid flow,” in Computer Graphics Forum , vol. 39, no. 8. Wiley Online Library, 2020, pp. 15–25
2020
Later among the works it cites.
T. Wu and I. Fischer, “Phase transitions for the information bottleneck in representation learning,” in International Conference on Learning Representations , 2020. [Online]. Available: https://openreview.net/forum?id=HJloElBYvB
2020
Later among the works it cites.
P. Holl, N. Thuerey, and V. Koltun, “Learning to control pdes with differentiable physics,” in International Conference on Learning Representations , 2020. [Online]. Available: https://openreview.net/forum?id=HyeSin4FPB
2020
Later among the works it cites.
F. Carpanese, “Development of free-boundary equilibrium and transport solvers for simulation and real-time interpretation of tokamak experiments,” EPFL, Tech. Rep., 2021
2021
Later among the works it cites.
Z. Li, N. B. Kovachki, K. Azizzadenesheli, B. liu, K. Bhattacharya, A. Stuart, and A. Anandkumar, “Fourier neural operator for parametric partial differential equations,” in International Conference on Learning Representations , 2021. [Online]. Available: https://openreview.net/forum?id=c8P9NQVtmnO
2021
Later among the works it cites.
D. Kochkov, J. A. Smith, A. Alieva, Q. Wang, M. P. Brenner, and S. Hoyer, “Machine learning–accelerated computational fluid dynamics,” Proceedings of the National Academy of Sciences , vol. 118, no. 21, 2021
2021
Later among the works it cites.
S.-M. Udrescu and M. Tegmark, “Symbolic pregression: discovering physical laws from distorted video,” Physical Review E , vol. 103, no. 4, p. 043307, 2021
2021
Later among the works it cites.
T. Pfaff, M. Fortunato, A. Sanchez-Gonzalez, and P. W. Battaglia, “Learning mesh-based simulation with graph networks,” in International Conference on Learning Representations , 2021
2021
Later among the works it cites.
Y. Khoo, J. Lu, and L. Ying, “Solving parametric pde problems with artificial neural networks,” European Journal of Applied Mathematics , vol. 32, no. 3, pp. 421–435, 2021
2021
Later among the works it cites.
L. Lu, P. Jin, G. Pang, Z. Zhang, and G. Karniadakis, “Learning nonlinear operators via deeponet based on the universal approximation theorem of operators. nature mach. intell. 3 (3), 218–229 (2021).”
2021
Later among the works it cites.
J. Brandstetter, D. E. Worrall, and M. Welling, “Message passing neural PDE solvers,” in International Conference on Learning Representations , 2022. [Online]. Available: https://openreview.net/forum?id=vSix3HPYKSU
2022
Closest in time.
T. Wu, Q. Wang, Y. Zhang, R. Ying, K. Cao, R. Sosic, R. Jalali, H. Hamam, M. Maucec, and J. Leskovec, “Learning large-scale subsurface simulations with a hybrid graph network simulator,” in Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining , 2022, pp. 4184–4194
2022
Closest in time.
Z. Li and A. B. Farimani, “Graph neural network-accelerated lagrangian fluid simulation,” Computers & Graphics , vol. 103, pp. 201–211, 2022
2022
Closest in time.
2022
Closest in time.
P. R. Vlachas, G. Arampatzis, C. Uhler, and P. Koumoutsakos, “Multiscale simulations of complex systems by learning their effective dynamics,” Nature Machine Intelligence , vol. 4, no. 4, pp. 359–366, 2022
2022
Closest in time.
A. Zylstra, O. Hurricane, D. Callahan, A. Kritcher, J. Ralph, H. Robey, J. Ross, C. Young, K. Baker, D. Casey et al. , “Burning plasma achieved in inertial fusion,” Nature , vol. 601, no. 7894, pp. 542–548, 2022
2022
Closest in time.
Q. Zhao, D. B. Lindell, and G. Wetzstein, “Learning to solve pde-constrained inverse problems with graph networks,” International Conference on Machine Learning , 2022
2022
Closest in time.