Fetching the paper…
Reading the bibliography…
Enforcing sparse structure within learning has led to significant advances in the field of data-driven discovery of dynamical systems.
1901
Earlier work this paper cites.
1908
Earlier work this paper cites.
E. N. Lorenz, Deterministic nonperiodic flow, Journal of the Atmospheric Sciences 20 (2) (1963) 130–141
1963
Earlier work this paper cites.
L. Petzold, Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations, SIAM Journal on Scientific and Statistical Computing 4 (1) (1983) 136–148
1983
Earlier work this paper cites.
A. C. Hindmarsh, Odepack, a systematized collection of ode solvers, Scientific Computing (1983) 55–64
1983
Earlier work this paper cites.
B. G. Brown, R. W. Katz, A. H. Murphy, Time series models to simulate and forecast wind speed and wind power, Journal of Climate and Applied Meteorology 23 (8) (1984) 1184–1195
1984
Earlier work this paper cites.
F. Santosa, W. W. Symes, Linear inversion of band-limited reflection seismograms, SIAM Journal on Scientific and Statistical Computing 7 (4) (1986) 1307–1330
1986
Earlier work this paper cites.
J. M. Ball, J. Carr, O. Penrose, The becker-döring cluster equations: basic properties and asymptotic behaviour of solutions, Communications in Mathematical Physics 104 (4) (1986) 657–692
1986
Earlier work this paper cites.
P. Shaman, R. A. Stine, The bias of autoregressive coefficient estimators, Journal of the American Statistical Association 83 (403) (1988) 842–848
1988
Earlier work this paper cites.
J. M. Ball, J. Carr, The discrete coagulation-fragmentation equations: existence, uniqueness, and density conservation, Journal of Statistical Physics 61 (1-2) (1990) 203–234
1990
Earlier work this paper cites.
P. J. Brockwell, R. A. Davis, S. E. Fienberg, Time series: theory and methods: theory and methods, Springer Science & Business Media, 1991
1991
Earlier work this paper cites.
L. I. Rudin, S. Osher, E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena 60 (1-4) (1992) 259–268
1992
Earlier work this paper cites.
R. Tibshirani, Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society: Series B (Methodological) 58 (1) (1996) 267–288
1996
Earlier work this paper cites.
R. Martin, C. Openshaw, Autoregressive modelling in vector spaces: An application to narrow-bandwidth spectral estimation, Signal processing 50 (3) (1996) 189–194
1996
Earlier work this paper cites.
E. N. Lorenz, Predictability: A problem partly solved, in: Proc. Seminar on Predictability, Vol. 1, 1996
1996
Earlier work this paper cites.
A. Neumaier, T. Schneider, Estimation of parameters and eigenmodes of multivariate autoregressive models, ACM Trans. Math. Softw. 27 (2001) 27–57
2001
Earlier work this paper cites.
T. Schneider, A. Neumaier, Algorithm 808: ARfit — A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models, ACM Trans. Math. Softw. 27 (2001) 58–65
2001
Earlier work this paper cites.
Y. Chen, D. Oliver, Ensemble randomized maximum likelihood method as an iterative ensemble smoother, Mathematical Geosciences 44 (1) (2002) 1–26
2002
Earlier work this paper cites.
J. C. Mattingly, A. M. Stuart, D. J. Higham, Ergodicity for sdes and approximations: locally lipschitz vector fields and degenerate noise, Stochastic processes and their applications 101 (2) (2002) 185–232
2002
Earlier work this paper cites.
S. M. Cox, P. C. Matthews, Exponential time differencing for stiff systems, Journal of Computational Physics 176 (2) (2002) 430–455
2002
Earlier work this paper cites.
E. Kalnay, Atmospheric Modeling, Data Assimilation and Predictability, Cambridge University Press, 2003
2003
Cited alongside, same era.
2004
Cited alongside, same era.
I. Fatkullin, E. Vanden-Eijnden, A computational strategy for multiscale systems with applications to lorenz 96 model, Journal of Computational Physics 200 (2) (2004) 605–638
2004
Cited alongside, same era.
2005
Cited alongside, same era.
D. L. Donoho, Compressed sensing, IEEE Transactions on Information Theory 52 (4) (2006) 1289–1306
2006
M. A. Iglesias, K. J. Law, A. M. Stuart, Ensemble Kalman methods for inverse problems, Inverse Problems 29 (4) (2013) 045001
2013
Later among the works it cites.
A. Emerick, A. Reynolds, Investigation of the sampling performance of ensemble-based methods with a simple reservoir model, Computational Geosciences 17 (2) (2013) 325–350
2013
Later among the works it cites.
I. Gibson, D. W. Rosen, B. Stucker, et al., Additive manufacturing technologies, Vol. 17, Springer, 2014
2014
Later among the works it cites.
S. Krumscheid, M. Pradas, G. Pavliotis, S. Kalliadasis, Data-driven coarse graining in action: Modeling and prediction of complex systems, Physical Review E 92 (4) (2015) 042139
2015
Later among the works it cites.
S. Kalliadasis, S. Krumscheid, G. A. Pavliotis, A new framework for extracting coarse-grained models from time series with multiscale structure, Journal of Computational Physics 296 (2015) 314–328
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
E. J. Candes, J. K. Romberg, 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 (8) (2006) 1207–1223
2006
Cited alongside, same era.
A. Seifert, K. D. Beheng, A two-moment cloud microphysics parameterization for mixed-phase clouds. part 1: Model description, Meteorol. Atmos. Phys. 92 (2006) 45–66
2006
Cited alongside, same era.
X. Mao, Stochastic Differential Equations and Applications, Elsevier, 2007
2007
Cited alongside, same era.
E. J. Candes, M. B. Wakin, S. P. Boyd, Enhancing sparsity by reweighted ℓ 1 \ell_{1} minimization, Journal of Fourier Analysis and Applications 14 (5-6) (2008) 877–905
2008
Cited alongside, same era.
A. M. Bruckstein, D. L. Donoho, M. Elad, From sparse solutions of systems of equations to sparse modeling of signals and images, SIAM Review 51 (1) (2009) 34–81
2009
Cited alongside, same era.
F. Kwasniok, G. Lohmann, Deriving dynamical models from paleoclimatic records: Application to glacial millennial-scale climate variability, Physical Review E 80 (6) (2009) 066104
2009
Cited alongside, same era.
T. Goldstein, S. Osher, The split bregman method for l1-regularized problems, SIAM journal on imaging sciences 2 (2) (2009) 323–343
2009
Cited alongside, same era.
2015
Later among the works it cites.
I. Goodfellow, Y. Bengio, A. Courville, Deep learning, MIT press, 2016
2016
Later among the works it cites.
S. L. Brunton, J. L. Proctor, J. N. Kutz, Discovering governing equations from data by sparse identification of nonlinear dynamical systems, Proceedings of the National Academy of Sciences 113 (15) (2016) 3932–3937
2016
Later among the works it cites.
M. A. Iglesias, A regularizing iterative ensemble Kalman method for pde-constrained inverse problems, Inverse Problems 32 (2) (2016) 025002
2016
Later among the works it cites.
S. H. Rudy, S. L. Brunton, J. L. Proctor, J. N. Kutz, Data-driven discovery of partial differential equations, Science Advances 3 (4) (2017) e1602614
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 (2197) (2017) 20160446
2017
Later among the works it cites.
G. Tran, R. Ward, Exact recovery of chaotic systems from highly corrupted data, Multiscale Modeling & Simulation 15 (3) (2017) 1108–1129
2017
Later among the works it cites.
C. Schillings, A. M. Stuart, Analysis of the ensemble Kalman filter for inverse problems, SIAM Journal on Numerical Analysis 55 (3) (2017) 1264–1290
2017
Later among the works it cites.
H. Schaeffer, G. Tran, R. Ward, Extracting sparse high-dimensional dynamics from limited data, SIAM Journal on Applied Mathematics 78 (6) (2018) 3279–3295
2018
Later among the works it cites.
L. Boninsegna, F. Nüske, C. Clementi, Sparse learning of stochastic dynamical equations, The Journal of Chemical Physics 148 (24) (2018) 241723
2018
Later among the works it cites.
A. Javanmard, A. Montanari, et al., Debiasing the lasso: Optimal sample size for gaussian designs, The Annals of Statistics 46 (6A) (2018) 2593–2622
2018
Later among the works it cites.
J. Wu, J.-X. Wang, S. C. Shadden, Adding constraints to Bayesian Inverse Problems, in: Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 33, 2019, pp. 1666–1673
2019
Later among the works it cites.
S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, C. Schütte, Data-driven approximation of the Koopman generator: Model reduction, system identification, and control, Physica D: Nonlinear Phenomena 406 (2020) 132416
2020
Closest in time.
X. Zhang, C. Michelén-Ströfer, H. Xiao, Regularized ensemble kalman methods for inverse problems, Journal of Computational Physics (2020) 109517
2020
Closest in time.
C. A. M. Ströfer, X.-L. Zhang, H. Xiao, O. Coutier-Delgosha, Enforcing boundary conditions on physical fields in bayesian inversion, Computer Methods in Applied Mechanics and Engineering 367 (2020) 113097
2020
Closest in time.
A. Garbuno-Inigo, F. Hoffmann, W. Li, A. M. Stuart, Interacting Langevin diffusions: Gradient structure and ensemble Kalman sampler, SIAM Journal on Applied Dynamical Systems 19 (1) (2020) 412–441
2020
Closest in time.