Fetching the paper…
Reading the bibliography…
Neural networks are a central technique in machine learning.
Noether E., Invariante Variationsprobleme, Nachr. d. König. Gesellsch. d. Wiss. zu Göttingen, Math. Phys. Klasse 2
1918
Earlier work this paper cites.
Hénon, M., Heiles, C.: The applicability of the third integral of motion: Some numerical experiments. The Astronomical Journal. 69
1964
Earlier work this paper cites.
Hornik, K.: Approximation capabilities of multilayer feedforward networks. Neural networks, 4
1991
Earlier work this paper cites.
Lagaris, I. E., Likas, A., Fotiadis, D. I.: Artificial Neural Networks for Solving Ordinary and pdes. IEEE Transactions on Neural Networks, 9
1998
Earlier work this paper cites.
Ling, J., Jones, R., Templeton, J: Machine learning strategies for systems with invariance properties. Journal of Computational Physics, 318
2016
Earlier work this paper cites.
Ling, J., Kurzawski, A., Templeton, J.: Reynolds averaged turbulence modeling using deep neural networks with embedded invariance. Journal of Fluid Mechanics, 807
2016
Earlier work this paper cites.
Carleo, G., Troyer, M.: Solving the quantum many-body problem with artificial neural networks. Science, 355
2017
Earlier work this paper cites.
Lu, Z., Pathak, J., Hunt, B., Girvan, M., Brockett, R., Ott, E.: Reservoir observers: Model-free inference of unmeasured variables in chaotic systems. Chaos, 27
2017
Earlier work this paper cites.
Raissi, M., Perdikaris, P., Karniadakis, G. E.: Inferring solutions of differential equations using noisy multi-fidelity data. J. of Comp. Physics, 335
2017
Cited alongside, same era.
Raissi, M., Perdikaris, P. Karniadakis, G.: Machine learning of linear differential equations using Gaussian processes. J. of Comp. Physics 348
2017
Cited alongside, same era.
Kutz, N., Rudy, S., Alla, A., Brunton, S.: Data-Driven discovery of governing physical laws and their parametric dependencies in engineering, physics and biology. IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 1–5 (2017)
2017
Cited alongside, same era.
Haber E., Ruthotto, L.: Stable architectures for deep neural networks. Inverse Problems. 34
2017
Cited alongside, same era.
Vlachas, P. R., Byeon, W., Wan, Z. Y., Sapsis, T. P., Koumoutsakos, P.: Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks. Proceedings Royal Society A, 474
2018
Later among the works it cites.
2018
Later among the works it cites.
Chen, R. T. Q., Rubanova, Y., Bettencourt, J., Duvenaud, D.: Neural Ordinary Differential Equations. 32nd Conference on Neural Information Processing Systems (NIPS 2018), 6572–6583 (2018)
2018
Later among the works it cites.
Sirignano J., Spiliopoulos, K.: DGM: A deep learning algorithm for solving partial differential equations. Journal of Computational Physics, 375
2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2018
Cited alongside, same era.
Zhang, P., Shen, H., Zhai, H.: Machine Learning Topological Invariants with Neural Networks. Physical Review Letters, 120
2018
Cited alongside, same era.
2018
Cited alongside, same era.
Magill, M., Qureshi, F., Haan, H.: Neural Networks Trained to Solve Differential Equations Learn General Representations. 32nd Conference on Neural Information Processing Systems (NIPS 2018), 4075–4085 (2018)
2018
Later among the works it cites.
Neofotistos, G., Mattheakis, M., Barmparis, G. D., Hizanidis, J., Tsironis, G. P., Kaxiras, E.: Machine learning with observers predicts complex spatiotemporal behavior. Front. Phys. - Quantum Computing. 7
2019
Closest in time.
Raissi, M., Perdikaris, P., Karniadakis, G. E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. of Comp. Physics 378
2019
Closest in time.