Fetching the paper…
Reading the bibliography…
In this study we put forth a modular approach for distilling hidden flow physics in discrete and sparse observations.
H. Bateman, “Some recent researches on the motion of fluids,” Monthly Weather Review 43
1915
Earlier work this paper cites.
T. Zhang, “Adaptive forward-backward greedy algorithm for sparse learning with linear models,” in Advances in Neural Information Processing Systems (Neural Information Processing Systems Foundation, Inc., 2009) pp. 1921–1928
1928
Earlier work this paper cites.
F. Rosenblatt, “The perceptron: a probabilistic model for information storage and organization in the brain.” Psychological Review 65
1958
Earlier work this paper cites.
J. Nagumo, S. Arimoto, and S. Yoshizawa, “An active pulse transmission line simulating nerve axon,” Proceedings of the IRE 50
1962
Earlier work this paper cites.
J. Perring and T. Skyrme, “A model unified field equation,” Nuclear Physics 31
1962
Earlier work this paper cites.
A. Scott, “Neuristor propagation on a tunnel diode loaded transmission line,” Proceedings of the IEEE 51
1963
Earlier work this paper cites.
J. Smagorinsky, “General circulation experiments with the primitive equations: I. the basic experiment,” Monthly Weather Review 91
1963
Earlier work this paper cites.
A. Arakawa, “Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. part i,” Journal of Computational Physics 1
1966
Earlier work this paper cites.
R. D. Ritchmyer and K. Norton, Difference methods for initial value problems (Jonh Wiley & Sons, New York, 1967)
1967
Earlier work this paper cites.
R. H. Kraichnan, “Inertial ranges in two-dimensional turbulence,” The Physics of Fluids 10
1967
Earlier work this paper cites.
A. Smith and T. Cebeci, “Numerical solution of the turbulent-boundary-layer equations,” Tech. Rep. DAC 33735 (DTIC, 1967)
1967
Earlier work this paper cites.
C. W. Hirt, “Heuristic stability theory for finite-difference equations,” Journal of Computational Physics 2
1968
Earlier work this paper cites.
C. E. Leith, “Diffusion approximation for two-dimensional turbulence,” The Physics of Fluids 11
1968
Earlier work this paper cites.
G. K. Batchelor, “Computation of the energy spectrum in homogeneous two-dimensional turbulence,” The Physics of Fluids 12
1969
Earlier work this paper cites.
A. Barone, F. Esposito, C. Magee, and A. Scott, “Theory and applications of the sine-gordon equation,” La Rivista del Nuovo Cimento (1971-1977) 1
1971
Earlier work this paper cites.
C. Leith, “Atmospheric predictability and two-dimensional turbulence,” Journal of the Atmospheric Sciences 28
1971
Earlier work this paper cites.
T. Kawahara, “Oscillatory solitary waves in dispersive media,” Journal of the Physical Society of Japan 33
1972
Earlier work this paper cites.
J. Isenberg and C. Gutfinger, “Heat transfer to a draining film,” International Journal of Heat and Mass Transfer 16
1973
Earlier work this paper cites.
T. Kawahara, N. Sugimoto, and T. Kakutani, “Nonlinear interaction between short and long capillary-gravity waves,” Journal of the Physical Society of Japan 39
1975
Earlier work this paper cites.
D. G. Aronson and H. F. Weinberger, “Multidimensional nonlinear diffusion arising in population genetics,” Advances in Mathematics 30
1978
Earlier work this paper cites.
A. Majda and S. Osher, “A systematic approach for correcting nonlinear instabilities,” Numerische Mathematik 30
1978
Earlier work this paper cites.
B. Baldwin and H. Lomax, “Thin-layer approximation and algebraic model for separated turbulentflows,” in 16th aerospace sciences meeting (AIAA Meeting Paper, 1978) p. 257
1978
Earlier work this paper cites.
G. L. Lamb Jr, Elements of soliton theory (Wiley-Interscience, New York, 1980)
1980
Earlier work this paper cites.
G. Klopfer and D. S. McRae, “Nonlinear truncation error analysis of finite difference schemes forthe euler equations,” AIAA Journal 21
1983
Earlier work this paper cites.
N. Kumar, “Unsteady flow against dispersion in finite porous media,” Journal of Hydrology 63
1983
Earlier work this paper cites.
V. Guvanasen and R. Volker, “Numerical solutions for solute transport in unconfined aquifers,” International Journal for Numerical Methods in Fluids 3
1983
Earlier work this paper cites.
J. K. Hunter and J. Scheurle, “Existence of perturbed solitary wave solutions to a model equation for water waves,” Physica D: Nonlinear Phenomena 32
1988
Earlier work this paper cites.
J. R. Koza, Genetic programming: on the programming of computers by means of natural selection , Vol. 1 (MIT Press, Cambridge, MA, USA, 1992)
1992
Earlier work this paper cites.
J. H. Holland, “Adaptation in natural and artificial systems. 1975,” Ann Arbor, MI: University of Michigan Press and (1992)
1992
Earlier work this paper cites.
C. Zhi-Xiong and G. Ben-Yu, “Analytic solutions of the nagumo equation,” IMA Journal of Applied Mathematics 48
1992
Earlier work this paper cites.
R. Tibshirani, “Regression shrinkage and selection via the LASSO,” Journal of the Royal Statistical Society: Series B 58
1996
Earlier work this paper cites.
M. Mitchell, An introduction to genetic algorithms (MIT press, 1998)
1998
Earlier work this paper cites.
U. Piomelli, “Large-eddy simulation: achievements and challenges,” Progress in Aerospace Sciences 35
1999
Earlier work this paper cites.
C. Meneveau and J. Katz, “Scale-invariance and turbulence models for large-eddy simulation,” Annual Review of Fluid Mechanics 32
2000
Earlier work this paper cites.
C. Ferreira, “Gene expression programming: a new adaptive algorithm for solving problems,” arXiv preprint cs/0102027 (2001)
2001
Earlier work this paper cites.
C. Ferreira, “Gene expression programming in problem solving,” in Soft Computing and Industry (Springer, 2002) pp. 635–653
2002
Earlier work this paper cites.
L. G. Margolin and W. J. Rider, “A rationale for implicit turbulence modelling,” International Journal for Numerical Methods in Fluids 39
2002
Earlier work this paper cites.
Sirendaoreji, “New exact travelling wave solutions for the Kawahara and modified Kawahara equations,” Chaos Solitons & Fractals 19
2004
Earlier work this paper cites.
N. Adams, S. Hickel, and S. Franz, “Implicit subgrid-scale modeling by adaptive deconvolution,” Journal of Computational Physics 200
2004
Earlier work this paper cites.
Y. Yang, C. Wang, and C. Soh, “Force identification of dynamic systems using genetic programming,” International Journal for Numerical Methods in Engineering 63
2005
Earlier work this paper cites.
H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67
2005
Earlier work this paper cites.
J. Kocijan, A. Girard, B. Banko, and R. Murray-Smith, “Dynamic systems identification with Gaussian processes,” Mathematical and Computer Modelling of Dynamical Systems 11
2005
Cited alongside, same era.
P. Meunier, S. Le Dizès, and T. Leweke, “Physics of vortex merging,” Comptes Rendus Physique 6
2005
Cited alongside, same era.
J. N. Reinaud and D. G. Dritschel, “The critical merger distance between two co-rotating quasi-geostrophic vortices,” Journal of Fluid Mechanics 522
2005
Cited alongside, same era.
C. Ferreira, Gene expression programming: mathematical modeling by an artificial intelligence , Vol. 21 (Springer, 2006)
2006
Cited alongside, same era.
E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences 59
C. Luo, Z. Hu, S.-L. Zhang, and Z. Jiang, “Adaptive space transformation: An invariant based method for predicting aerodynamic coefficients of hypersonic vehicles,” Engineering Applications of Artificial Intelligence 46
2015
Later among the works it cites.
S. L. Brunton and B. R. Noack, “Closed-loop turbulence control: progress and challenges,” Applied Mechanics Reviews 67
2015
Later among the works it cites.
N. Gautier, J.-L. Aider, T. Duriez, B. Noack, M. Segond, and M. Abel, “Closed-loop separation control using machine learning,” Journal of Fluid Mechanics 770
2015
Later among the works it cites.
2015
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2006
Cited alongside, same era.
T. Ozis and S. Ozer, “A simple similarity-transformation-iterative scheme applied to Korteweg–de Vries equation,” Applied Mathematics and Computation 173
2006
Cited alongside, same era.
P. Sagaut, Large eddy simulation for incompressible flows: an introduction (Springer Science & Business Media, 2006)
2006
Cited alongside, same era.
J. Bongard and H. Lipson, “Automated reverse engineering of nonlinear dynamical systems,” Proceedings of the National Academy of Sciences 104
2007
Cited alongside, same era.
M. F. Brameier and W. Banzhaf, Linear genetic programming (Springe-Verlag, New York, 2007)
2007
Cited alongside, same era.
R. G. Baraniuk, “Compressive sensing,” IEEE Signal Processing Magazine 24
2007
Cited alongside, same era.
C. Hirsch, Numerical computation of internal and external flows: The fundamentals of computational fluid dynamics (Elsevier, Burlington, MA, 2007)
2007
Cited alongside, same era.
E. J. Candes, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity by reweighted ℓ \ell 1 minimization,” Journal of Fourier Analysis and Applications 14
2008
Cited alongside, same era.
R. Tibshirani, M. Wainwright, and T. Hastie, Statistical learning with sparsity: the LASSO and generalizations (Chapman and Hall/CRC, Florida, USA, 2015)
2015
Later among the works it cites.
A. Karpathy and L. Fei-Fei, “Deep visual-semantic alignments for generating image descriptions,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2015) pp. 3128–3137
2015
Later among the works it cites.
A. Debien, K. A. Von Krbek, N. Mazellier, T. Duriez, L. Cordier, B. R. Noack, M. W. Abel, and A. Kourta, “Closed-loop separation control over a sharp edge ramp using genetic programming,” Experiments in Fluids 57
2016
Later among the works it cites.
M. Quade, M. Abel, K. Shafi, R. K. Niven, and B. R. Noack, “Prediction of dynamical systems by symbolic regression,” Physical Review E 94
2016
Later among the works it cites.
J. Weatheritt and R. Sandberg, “A novel evolutionary algorithm applied to algebraic modifications of the rans stress–strain relationship,” Journal of Computational Physics 325
2016
Later among the works it cites.
S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Discovering governing equations from data by sparse identification of nonlinear dynamical systems,” Proceedings of the National Academy of Sciences 113
2016
Later among the works it cites.
N. M. Mangan, S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Inferring biological networks by sparse identification of nonlinear dynamics,” IEEE Transactions on Molecular, Biological and Multi-Scale Communications 2
2016
Later among the works it cites.
R. S. Faradonbeh and M. Monjezi, “Prediction and minimization of blast-induced ground vibration using two robust meta-heuristic algorithms,” Engineering with Computers 33
2017
Later among the works it cites.
R. S. Faradonbeh, A. Salimi, M. Monjezi, A. Ebrahimabadi, and C. Moormann, “Roadheader performance prediction using genetic programming (GP) and gene expression programming (GEP) techniques,” Environmental Earth Sciences 76
2017
Later among the works it cites.
F. S. Hoseinian, R. S. Faradonbeh, A. Abdollahzadeh, B. Rezai, and S. Soltani-Mohammadi, “Semi-autogenous mill power model development using gene expression programming,” Powder Technology 308
2017
Later among the works it cites.
J. Weatheritt and R. D. Sandberg, “Hybrid reynolds-averaged/large-eddy simulation methodology from symbolic regression: formulation and application,” AIAA Journal , 5577 – 5584 (2017)
2017
Later among the works it cites.
S. H. Rudy, S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Data-driven discovery of partial differential equations,” Science Advances 3
2017
Later among the works it cites.
H. Schaeffer, “Learning partial differential equations via data discovery and sparse optimization,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473
2017
Later among the works it cites.
G. Tran and R. Ward, “Exact recovery of chaotic systems from highly corrupted data,” Multiscale Modeling & Simulation 15
2017
Later among the works it cites.
N. M. Mangan, J. N. Kutz, S. L. Brunton, and J. L. Proctor, “Model selection for dynamical systems via sparse regression and information criteria,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473
2017
Later among the works it cites.
C. Chen, C. Luo, and Z. Jiang, “Elite bases regression: a real-time algorithm for symbolic regression,” in 2017 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD) (IEEE, 2017) pp. 529–535
2017
Later among the works it cites.
A. E. Sallab, M. Abdou, E. Perot, and S. Yogamani, “Deep reinforcement learning framework for autonomous driving,” Electronic Imaging 2017
2017
Later among the works it cites.
B. Dong, Q. Jiang, and Z. Shen, “Image restoration: Wavelet frame shrinkage, nonlinear evolution PDEs, and beyond,” Multiscale Modeling & Simulation 15
2017
Later among the works it cites.
M. Schoepplein, J. Weatheritt, R. Sandberg, M. Talei, and M. Klein, “Application of an evolutionary algorithm to les modelling of turbulent transport in premixed flames,” Journal of Computational Physics 374
2018
Later among the works it cites.
H. Schaeffer, G. Tran, and R. Ward, “Extracting sparse high-dimensional dynamics from limited data,” SIAM Journal on Applied Mathematics 78
2018
Later among the works it cites.
J.-C. Loiseau, B. R. Noack, and S. L. Brunton, “Sparse reduced-order modelling: sensor-based dynamics to full-state estimation,” Journal of Fluid Mechanics 844
2018
Later among the works it cites.
M. Schmelzer, R. Dwight, and P. Cinnella, “Data-driven deterministic symbolic regression of nonlinear stress-strain relation for rans turbulence modelling,” in 2018 Fluid Dynamics Conference (AIAA Aviation Forum, 2018) p. 2900
2018
Later among the works it cites.
P. Zheng, T. Askham, S. L. Brunton, J. N. Kutz, and A. Y. Aravkin, “A unified framework for sparse relaxed regularized regression: SR3,” IEEE Access 7
2018
Later among the works it cites.
M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Numerical gaussian processes for time-dependent and nonlinear partial differential equations,” SIAM Journal on Scientific Computing 40
2018
Later among the works it cites.
M. Raissi and G. E. Karniadakis, “Hidden physics models: Machine learning of nonlinear partial differential equations,” Journal of Computational Physics 357
2018
Later among the works it cites.
Z. Wang, D. Xiao, F. Fang, R. Govindan, C. C. Pain, and Y. Guo, “Model identification of reduced order fluid dynamics systems using deep learning,” International Journal for Numerical Methods in Fluids 86
2018
Later among the works it cites.
Z. Long, Y. Lu, X. Ma, and B. Dong, “PDE-net: Learning PDEs from data,” in Proceedings of the 35th International Conference on Machine Learning , Proceedings of Machine Learning Research, Vol. 80, edited by J. Dy and A. Krause (PMLR, Stockholmsmässan, Stockholm Sweden, 2018) pp. 3208–3216
2018
Later among the works it cites.
R. Maulik, O. San, A. Rasheed, and P. Vedula, “Data-driven deconvolution for large eddy simulations of kraichnan turbulence,” Physics of Fluids 30
2018
Later among the works it cites.
S. Thaler, L. Paehler, and N. A. Adams, “Sparse identification of truncation errors,” Journal of Computational Physics 397
2019
Closest in time.
H. Vaddireddy and O. San, “Equation discovery using fast function extraction: a deterministic symbolic regression approach,” Fluids 4
2019
Closest in time.
2019
Closest in time.
M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” Journal of Computational Physics 378
2019
Closest in time.
Z. Long, Y. Lu, and B. Dong, “PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network,” Journal of Computational Physics 399
2019
Closest in time.
G. Shuhua, “geppy: a gene expression programming framework in python,” https://github.com/ShuhuaGao/geppy (2019)
2019
Closest in time.
S. Dhingra, R. B. Madda, A. H. Gandomi, R. Patan, and M. Daneshmand, “Internet of things mobile-air pollution monitoring system (IoT-Mobair),” IEEE Internet of Things Journal 6
2019
Closest in time.
S. Pawar and O. San, “CFD Julia: A learning module structuring an introductory course on computational fluid dynamics,” Fluids 4
2019
Closest in time.