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Discovering mathematical equations that govern physical and biological systems from observed data is a fundamental challenge in scientific research.
D. C. Liu and J. Nocedal, “On the limited memory bfgs method for large scale optimization,” Mathematical programming
1989
Earlier work this paper cites.
J. Sturis, K. S. Polonsky, E. Mosekilde, and E. Van Cauter, “Computer model for mechanisms underlying ultradian oscillations of insulin and glucose,” American Journal of Physiology-Endocrinology And Metabolism
1991
Earlier work this paper cites.
R. Rico-Martinez, J. Anderson, and I. Kevrekidis, “Continuous-time nonlinear signal processing: a neural network based approach for gray box identification,” in Proceedings of IEEE Workshop on Neural Networks for Signal Processing
1994
Earlier work this paper cites.
R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical Society: Series B (Methodological)
1996
Earlier work this paper cites.
D. L. Donoho, “Compressed sensing,” IEEE Transactions on information theory
2006
Earlier work this paper cites.
G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, “Extreme learning machine: theory and applications,” Neurocomputing
2006
Earlier work this paper cites.
M. Quach, N. Brunel, and F. d’Alché Buc, “Estimating parameters and hidden variables in non-linear state-space models based on odes for biological networks inference,” Bioinformatics
2007
Earlier work this paper cites.
CRC Press, 2011
B. Barnes and G. R. Fulford, Mathematical modelling with case studies: a differential equations approach using Maple and MATLAB · 2011
Earlier work this paper cites.
D. J. Albers, N. Elhadad, E. Tabak, A. Perotte, and G. Hripcsak, “Dynamical phenotyping: using temporal analysis of clinically collected physiologic data to stratify populations,” PloS one
2014
Earlier work this paper cites.
D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980
2014
Earlier work this paper cites.
T. Stephens, “gplearn: Genetic programming in python, with a scikitlearn inspired api. [online]. available: https://github.com/trevorstephens/gplearn,” 2015
2015
Earlier work this paper 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
2016
Earlier work this paper cites.
D. Mortari, “The theory of connections: Connecting points,” Mathematics
2017
Earlier work this paper cites.
D. Mortari, “Least-squares solution of linear differential equations,” Mathematics
2017
Earlier work this paper cites.
P. Andras, “Random projection neural network approximation,” in 2018 International Joint Conference on Neural Networks (IJCNN)
2018
Cited alongside, same era.
F. O. de França, “A greedy search tree heuristic for symbolic regression,” Information Sciences
2018
Cited alongside, same era.
J. Wandy, M. Niu, D. Giurghita, R. Daly, S. Rogers, and D. Husmeier, “Shinykgode: an interactive application for ode parameter inference using gradient matching,” Bioinformatics
2018
Cited alongside, same era.
C. Loos, S. Krause, and J. Hasenauer, “Hierarchical optimization for the efficient parametrization of ode models,” Bioinformatics
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
M. De Florio, E. Schiassi, A. D’Ambrosio, D. Mortari, and R. Furfaro, “Theory of functional connections applied to linear odes subject to integral constraints and linear ordinary integro-differential equations,” Mathematical and Computational Applications
2021
Later among the works it cites.
MIT press, 2022
I. Douven, The art of abduction · 2022
Later among the works it cites.
N. J. Christensen, S. Demharter, M. Machado, L. Pedersen, M. Salvatore, V. Stentoft-Hansen, and M. T. Iglesias, “Identifying interactions in omics data for clinical biomarker discovery using symbolic regression,” Bioinformatics
2022
Later among the works it cites.
M. De Florio, E. Schiassi, and R. Furfaro, “Physics-informed neural networks and functional interpolation for stiff chemical kinetics,” Chaos: An Interdisciplinary Journal of Nonlinear Science
2022
Later among the works it cites.
M. Virgolin and S. P. Pissis, “Symbolic regression is np-hard,” arXiv preprint arXiv:2207.01018
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2019
Cited alongside, same era.
R. J. Lovelett, J. L. Avalos, and I. G. Kevrekidis, “Partial observations and conservation laws: Gray-box modeling in biotechnology and optogenetics,” Industrial & Engineering Chemistry Research
2019
Cited alongside, same era.
S.-M. Udrescu and M. Tegmark, “Ai feynman: A physics-inspired method for symbolic regression,” Science Advances
2020
Cited alongside, same era.
A. Yazdani, L. Lu, M. Raissi, and G. E. Karniadakis, “Systems biology informed deep learning for inferring parameters and hidden dynamics,” PLoS computational biology
2020
Cited alongside, same era.
2021
Cited alongside, same era.
2021
Cited alongside, same era.
A. D. Jagtap and G. E. Karniadakis, “Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations.,” in AAAI spring symposium: MLPS
2021
Cited alongside, same era.
F. O. de Franca and M. Z. de Lima, “Interaction-transformation symbolic regression with extreme learning machine,” Neurocomputing
2021
Cited alongside, same era.
2022
Later among the works it cites.
E. Schiassi, M. De Florio, B. D. Ganapol, P. Picca, and R. Furfaro, “Physics-informed neural networks for the point kinetics equations for nuclear reactor dynamics,” Annals of Nuclear Energy
2022
Later among the works it cites.
Peer Reviewed
Z. Xiang, W. Peng, X. Liu, and W. Yao, “Self-adaptive loss balanced physics-informed neural networks,” Neurocomputing (Amsterdam) · 2022
Later among the works it cites.
A. D. Jagtap, Y. Shin, K. Kawaguchi, and G. E. Karniadakis, “Deep kronecker neural networks: A general framework for neural networks with adaptive activation functions,” Neurocomputing
2022
Later among the works it cites.
C. Cornelio, S. Dash, V. Austel, T. R. Josephson, J. Goncalves, K. L. Clarkson, N. Megiddo, B. El Khadir, and L. Horesh, “Combining data and theory for derivable scientific discovery with ai-descartes,” Nature Communications
2023
Closest in time.
2023
Closest in time.
F. P. Kemeth, S. Alonso, B. Echebarria, T. Moldenhawer, C. Beta, and I. G. Kevrekidis, “Black and gray box learning of amplitude equations: Application to phase field systems,” Physical Review E
2023
Closest in time.
M. Daneker, Z. Zhang, G. E. Karniadakis, and L. Lu, “Systems biology: Identifiability analysis and parameter identification via systems-biology-informed neural networks,” in Computational Modeling of Signaling Networks
2023
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2023
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L. D. McClenny and U. M. Braga-Neto, “Self-adaptive physics-informed neural networks,” Journal of Computational Physics
2023
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