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Partial differential equation parameter estimation is a mathematical and computational process used to estimate the unknown parameters in a partial differential equation model from observational data.
J. H. Halton, “On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals,” Numerische Mathematik , vol. 2, pp. 84–90, 1960
1960
Earlier work this paper cites.
I. M. Sobol, “On the distribution of points in a cube and the approximate evaluation of integrals,” USSR Computational Mathematics and Mathematical Physics , vol. 7, no. 4, pp. 86–112, 1967
1967
Earlier work this paper cites.
R. Tibshirani, “Regression shrinkage and selection via the Lasso,” J. Roy. Statist. Soc.: Series B (Methodological) , vol. 58, no. 1, pp. 267–288, 1996
1996
Earlier work this paper cites.
W.-S. L. Tien-Tsin Wong and P.-A. Heng, “Sampling with hammersley and halton points,” Journal of Graphics Tools , vol. 2, no. 2, pp. 9–24, 1997
1997
Earlier work this paper cites.
K. Kunisch and S. Volkwein, “Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics,” SIAM J. Numer. Anal. , vol. 40, no. 2, pp. 492–515, 2002
2002
Earlier work this paper cites.
X. Feng and A. Prohl, “Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows,” Numerische Mathematik , vol. 94, pp. 33–65, 2003
2003
Earlier work this paper cites.
T. Öziş, E. Aksan, and A. Özdeş, “A finite element approach for solution of Burger’s equation,” Applied Mathematics and Computation , vol. 139, no. 2-3, pp. 417–428, 2003
2003
Earlier work this paper cites.
M. Barrault, Y. Maday, N. C. Nguyen, and A. T. Patera, “An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations,” Comptes Rendus Mathematique , vol. 339, no. 9, pp. 667–672, 2004
2004
Earlier work this paper cites.
F. De Barros, W. Mills, and R. Cotta, “Integral transform solution of a two-dimensional model for contaminant dispersion in rivers and channels with spatially variable coefficients,” Environmental Modelling & Software , vol. 21, no. 5, pp. 699–709, 2006
2006
Earlier work this paper cites.
S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l 1 l_{1} -regularized least squares,” IEEE Journal of Selected Topics in Signal Processing , vol. 1, no. 4, pp. 606–617, 2007
2007
Earlier work this paper cites.
D. Arthur and S. Vassilvitskii, “ K-means++
2007
Earlier work this paper cites.
S. Joshi and S. Boyd, “Sensor selection via convex optimization,” IEEE Transactions on Signal Processing , vol. 57, no. 2, pp. 451–462, 2008
2008
Earlier work this paper cites.
S. Lau, R. Eichardt, L. Di Rienzo, and J. Haueisen, “Tabu search optimization of magnetic sensor systems for magnetocardiography,” IEEE Transactions on Magnetics , vol. 44, no. 6, pp. 1442–1445, 2008
2008
Earlier work this paper cites.
T. Hastie, R. Tibshirani, J. H. Friedman, and J. H. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction . Springer, 2009, vol. 2
2009
Earlier work this paper cites.
S. Chaturantabut and D. C. Sorensen, “Nonlinear model reduction via discrete empirical interpolation,” SIAM Journal on Scientific Computing , vol. 32, no. 5, pp. 2737–2764, 2010
2010
Earlier work this paper cites.
J. Friedman, T. Hastie, and R. Tibshirani, “Regularization paths for generalized linear models via coordinate descent,” Journal of Statistical Software , vol. 33, no. 1, p. 1, 2010
2010
Earlier work this paper cites.
E. Haber, Computational Methods in Geophysical Electromagnetics . SIAM, 2014
2014
Earlier work this paper cites.
J. Ranieri, A. Chebira, and M. Vetterli, “Near-optimal sensor placement for linear inverse problems,” IEEE Transactions on signal processing , vol. 62, no. 5, pp. 1135–1146, 2014
2014
Earlier work this paper cites.
M. Gavish and D. L. Donoho, “The optimal hard threshold for singular values is 4 3 \frac{4}{\sqrt{3}} ,” IEEE Transactions on Information Theory , vol. 60, no. 8, pp. 5040–5053, 2014
2014
Cited alongside, same era.
D. Kingma and J. Ba, “Adam: A method for stochastic optimization,” in International Conference on Learning Representations (ICLR) , San Diega, CA, USA, 2015
2015
Cited alongside, same era.
Z. Drmac and S. Gugercin, “A new selection operator for the discrete empirical interpolation method—improved a priori error bound and extensions,” SIAM Journal on Scientific Computing , vol. 38, no. 2, pp. A631–A648, 2016
2016
Cited alongside, same era.
Z. Zhang, X. Yang, and G. Lin, “POD-based constrained sensor placement and field reconstruction from noisy wind measurements: A perturbation study,” Mathematics , vol. 4, no. 2, p. 26, 2016
2016
Cited alongside, same era.
A. M. Tartakovsky, C. O. Marrero, P. Perdikaris, G. D. Tartakovsky, and D. Barajas-Solano, “Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems,” Water Resources Research , vol. 56, no. 5, p. e2019WR026731, 2020
2020
Later among the works it cites.
V. Sitzmann, J. N. P. Martel, A. W. Bergman, D. B. Lindell, and G. Wetzstein, “Implicit neural representations with periodic activation functions,” in Proceedings of the 34th International Conference on Neural Information Processing Systems , ser. NIPS’20. Red Hook, NY, USA: Curran Associates Inc., 2020
2020
Later among the works it cites.
M. Zeneli, A. Nikolopoulos, S. Karellas, and N. Nikolopoulos, “Numerical methods for solid-liquid phase-change problems,” in Ultra-high Temperature Thermal Energy Storage, Transfer and Conversion . Elsevier, 2021, pp. 165–199
2021
Later among the works it cites.
J. Blechschmidt and O. G. Ernst, “Three ways to solve partial differential equations with neural networks – a review,” GAMM-Mitteilungen , vol. 44, no. 2, p. e202100006, 2021
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S. H. Rudy, S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Data-driven discovery of partial differential equations,” Science Advances , vol. 3, no. 4, p. e1602614, 2017
2017
Cited alongside, same era.
Q. Ye, “Accurate inverses for computing eigenvalues of extremely ill-conditioned matrices and differential operators,” Mathematics of Computation , vol. 87, no. 309, pp. 237–259, 2018
2018
Cited alongside, same era.
K. Manohar, B. W. Brunton, J. N. Kutz, and S. L. Brunton, “Data-driven sparse sensor placement for reconstruction: Demonstrating the benefits of exploiting known patterns,” IEEE Control Systems Magazine , vol. 38, no. 3, pp. 63–86, 2018
2018
Cited alongside, same era.
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 , vol. 378, pp. 686–707, 2019
2019
Cited alongside, same era.
G. Pang, L. Lu, and G. E. Karniadakis, “fPINNs: Fractional physics-informed neural networks,” SIAM Journal on Scientific Computing , vol. 41, no. 4, pp. A2603–A2626, 2019
2019
Cited alongside, same era.
D. Zhang, L. Lu, L. Guo, and G. E. Karniadakis, “Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems,” Journal of Computational Physics , vol. 397, p. 108850, 2019
2019
Cited alongside, same era.
M. A. Nabian and H. Meidani, “A deep learning solution approach for high-dimensional random differential equations,” Probabilistic Engineering Mechanics , vol. 57, pp. 14–25, 2019
2019
Cited alongside, same era.
S. W. Fung and L. Ruthotto, “A multiscale method for model order reduction in PDE parameter estimation,” Journal of Computational and Applied Mathematics , vol. 350, pp. 19–34, 2019
2019
Cited alongside, same era.
2021
Later among the works it cites.
L. Lu, X. Meng, Z. Mao, and G. E. Karniadakis, “Deepxde: A deep learning library for solving differential equations,” SIAM Review , vol. 63, no. 1, pp. 208–228, 2021
2021
Later among the works it cites.
2021
Later among the works it cites.
2021
Later among the works it cites.
G.-J. Both, S. Choudhury, P. Sens, and R. Kusters, “Deepmod: Deep learning for model discovery in noisy data,” Journal of Computational Physics , vol. 428, p. 109985, 2021
2021
Later among the works it cites.
C. L. Wight and J. Zhao, “Solving Allen-Cahn and Cahn-Hilliard equations using the adaptive physics informed neural networks,” Communications in Computational Physics , vol. 29, no. 3, pp. 930–954, 2021
2021
Later among the works it cites.
B. Bai, H. Ci, H. Lei, and Y. Cui, “A local integral-generalized finite difference method with mesh-meshless duality and its application,” Engineering Analysis with Boundary Elements , vol. 139, pp. 14–31, 2022
2022
Later among the works it cites.
N. Wandel, M. Weinmann, M. Neidlin, and R. Klein, “Spline-pinn: Approaching pdes without data using fast, physics-informed hermite-spline cnns,” in Proceedings of the AAAI Conference on Artificial Intelligence , vol. 36, no. 8, 2022, pp. 8529–8538
2022
Later among the works it cites.
S. Mowlavi and S. Nabi, “Optimal control of PDEs using physics-informed neural networks,” Journal of Computational Physics , vol. 473, p. 111731, 2023
2023
Later among the works it cites.
C. Wu, M. Zhu, Q. Tan, Y. Kartha, and L. Lu, “A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks,” Computer Methods in Applied Mechanics and Engineering , vol. 403, p. 115671, 2023
2023
Later among the works it cites.
A. Moslemi, “Sparse representation learning using l1- 2 compressed sensing and rank-revealing qr factorization,” Engineering Applications of Artificial Intelligence , vol. 125, p. 106663, 2023
2023
Later among the works it cites.
K. Eshkofti and S. M. Hosseini, “A gradient-enhanced physics-informed neural network (gPINN) scheme for the coupled non-fickian/non-fourierian diffusion-thermoelasticity analysis: A novel gpinn structure,” Engineering Applications of Artificial Intelligence , vol. 126, p. 106908, 2023
2023
Later among the works it cites.
2023
Later among the works it cites.
P. Goyal and P. Benner, “Neural ordinary differential equations with irregular and noisy data,” Roy. Soc. Open Sci. , vol. 10, no. 7, p. 221475, 2023
2023
Later among the works it cites.
S. Manavi, E. Fattahi, and T. Becker, “A trial solution for imposing boundary conditions of partial differential equations in physics-informed neural networks,” Engineering Applications of Artificial Intelligence , vol. 127, p. 107236, 2024
2024
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