Fetching the paper…
Reading the bibliography…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs).
A mathematical model illustrating the theory of turbulence
Burgers, J. M · 1948
Earlier work this paper cites.
Free energy of a nonuniform system. i. interfacial free energy
Cahn, J. W. & Hilliard, J. E · 1958
Earlier work this paper cites.
Gravity segregation of miscible fluids in linear models
Gardner, G., Downie, J. & Kendall, H · 1962
Earlier work this paper cites.
Finite bandwidth, finite amplitude convection
Newell, A. C. & Whitehead, J. A · 1969
Earlier work this paper cites.
A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening
Allen, S. M. & Cahn, J. W · 1979
Earlier work this paper cites.
Symbolic regression via genetic programming
Augusto, D. A. & Barbosa, H. J · 2000
Earlier work this paper cites.
Distilling free-form natural laws from experimental data
Schmidt, M. & Lipson, H · 2009
Earlier work this paper cites.
Numerical approximations of allen-cahn and cahn-hilliard equations
Shen, J. & Yang, X · 2010
Earlier work this paper cites.
Asymptotic first exit times of the chafee-infante equation with small heavy-tailed lévy noise
Debussche, A., Högele, M. & Imkeller, P · 2011
Earlier work this paper cites.
Semantically-based crossover in genetic programming: application to real-valued symbolic regression
Uy, N. Q., Hoai, N. X., O’Neill, M., McKay, R. I. & Galván-López, E · 2011
Earlier work this paper cites.
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Brunton, S. L., Proctor, J. L. & Kutz, J. N · 2016
Earlier work this paper cites.
Extrapolation and learning equations
Martius, G. & Lampert, C. H · 2016
Earlier work this paper cites.
Data-driven discovery of partial differential equations
Rudy, S. H., Brunton, S. L., Proctor, J. L. & Kutz, J. N · 2017
Earlier work this paper cites.
Statistical genetic programming for symbolic regression
Haeri, M. A., Ebadzadeh, M. M. & Folino, G · 2017
Earlier work this paper cites.
Thermodynamic stability of driven open systems and control of phase separation by electro-autocatalysis
Bazant, M. Z · 2017
Cited alongside, same era.
Pde-net: Learning pdes from data
Long, Z., Lu, Y., Ma, X. & Dong, B · 2018
Cited alongside, same era.
Learning equations for extrapolation and control
Sahoo, S., Lampert, C. & Martius, G · 2018
Cited alongside, same era.
Exact solutions to (2+1)-dimensional chaffee–infante equation
Mao, Y · 2018
Cited alongside, same era.
Complex wave solutions to mathematical biology models i: Newell–whitehead–segel and zeldovich equations
Korkmaz, A · 2018
Cited alongside, same era.
Automatic differentiation in machine learning: a survey
Baydin, A. G., Pearlmutter, B. A., Radul, A. A. & Siskind, J. M · 2018
Cited alongside, same era.
Advancing mathematics by guiding human intuition with ai
Davies, A. et al · 2021
Later among the works it cites.
Sindy-bvp: Sparse identification of nonlinear dynamics for boundary value problems
Shea, D. E., Brunton, S. L. & Kutz, J. N · 2021
Later among the works it cites.
Weak sindy for partial differential equations
Messenger, D. A. & Bortz, D. M · 2021
Later among the works it cites.
Physics-informed learning of governing equations from scarce data
Chen, Z., Liu, Y. & Sun, H · 2021
Later among the works it cites.
Rl-gep: Symbolic regression via gene expression programming and reinforcement learning
Zhang, H. & Zhou, A · 2021
Later among the works it cites.
Symbolic regression via neural-guided genetic programming population seeding
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Pde-net 2.0: Learning pdes from data with a numeric-symbolic hybrid deep network
Long, Z., Lu, Y. & Dong, B · 2019
Cited alongside, same era.
Data-driven discovery of formulas by symbolic regression
Sun, S., Ouyang, R., Zhang, B. & Zhang, T.-Y · 2019
Cited alongside, same era.
Genetic programming performance prediction and its application for symbolic regression problems
Astarabadi, S. S. M. & Ebadzadeh, M. M · 2019
Cited alongside, same era.
Sindy-pi: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics
Kaheman, K., Kutz, J. N. & Brunton, S. L · 2020
Cited alongside, same era.
Dlga-pde: Discovery of pdes with incomplete candidate library via combination of deep learning and genetic algorithm
Xu, H., Chang, H. & Zhang, D · 2020
Cited alongside, same era.
Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients
Petersen, B. K. et al · 2020
Cited alongside, same era.
Mundhenk, T. N. et al · 2021
Later among the works it cites.
Dl-pde: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data
Xu, H., Chang, H. & Zhang, D · 2021
Later among the works it cites.
Partial differential equations discovery with epde framework: application for real and synthetic data
Maslyaev, M., Hvatov, A. & Kalyuzhnaya, A. V · 2021
Later among the works it cites.
Learning emergent partial differential equations in a learned emergent space
Kemeth, F. P. et al · 2022
Closest in time.
Ensemble-sindy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control
Fasel, U., Kutz, J. N., Brunton, B. W. & Brunton, S. L · 2022
Closest in time.
Symbolic genetic algorithm for discovering open-form partial differential equations (sga-pde)
Chen, Y., Luo, Y., Liu, Q., Xu, H. & Zhang, D · 2022
Closest in time.
Integration of knowledge and data in machine learning
Chen, Y. & Zhang, D · 2022
Closest in time.
Autoke: An automatic knowledge embedding framework for scientific machine learning
Du, M., Chen, Y. & Zhang, D · 2022
Closest in time.
Symbolic physics learner: Discovering governing equations via monte carlo tree search
Sun, F., Liu, Y., Wang, J.-X. & Sun, H · 2023
Closest in time.