The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
Solving high-dimensional partial differential equations using deep learning
Open accessAbstract
Significance: Partial differential equations (PDEs) are among the most ubiquitous tools used in modeling problems in nature. However, solving high-dimensional PDEs has been notoriously difficult due to the “curse of dimensionality.” This paper introduces a practical algorithm for solving nonlinear PDEs in very high (hundreds and potentially thousands of) dimensions. Numerical results suggest that the proposed algorithm is quite effective for a wide variety of problems, in terms of both accuracy and speed. We believe that this opens up a host of possibilities in economics, finance, operational research, and physics, by considering all participating agents, assets, resources, or particles together at the same time, instead of making ad hoc assumptions on their interrelationships.
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Cites
LeCun, Y., Bengio, Y., & Hinton, G. (2015) · Nature · doi:10.1038/nature14539 · Cited by 84,126
The pricing of options and corporate liabilities
Black, F., & Scholes, M. (1973) · Journal of Political Economy · doi:10.1086/260062 · Cited by 29,074
Mastering the game of Go with deep neural networks and tree search
Silver, D., Huang, A., Maddison, C. J., Guez, A., Sifre, L., van den Driessche, G., Schrittwieser, J., Antonoglou, I., Panneershelvam, V., Lanctot, M., et al. (2016) · Nature · doi:10.1038/nature16961 · Cited by 15,612
Bellman, R. E. (2010) · doi:10.1515/9781400835386 · Cited by 14,588
Hinton, G., Deng, L., Yu, D., Dahl, G., Mohamed, A.-R., Jaitly, N., Senior, A., Vanhoucke, V., Nguyen, P., Sainath, T., et al. (2012) · IEEE Signal Processing Magazine · doi:10.1109/msp.2012.2205597 · Cited by 10,260
Cited by
Physics-informed machine learning
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00314-5 · Cited by 8,718
Digital twin: values, challenges and enablers from a modeling perspective
Rasheed, A., San, O., & Kvamsdal, T. (2020) · IEEE Access · doi:10.1109/access.2020.2970143 · Cited by 1,952
Photonics for artificial intelligence and neuromorphic computing
Shastri, B. J., Tait, A. N., Ferreira de Lima, T., Pernice, W. H. P., Bhaskaran, H., Wright, C. D., & Prucnal, P. R. (2021) · Nature Photonics · doi:10.1038/s41566-020-00754-y · Cited by 1,756
Universal Differential Equations for Scientific Machine Learning
Rackauckas, C., Ma, Y., Martensen, J., Warner, C., Zubov, K., Supekar, R., Skinner, D., Ramadhan, A., & Edelman, A. (2020) · doi:10.21203/rs.3.rs-55125/v1 · Cited by 643
Weak adversarial networks for high-dimensional partial differential equations
Zang, Y., Bao, G., Ye, X., & Zhou, H. (2020) · Journal of Computational Physics · doi:10.1016/j.jcp.2020.109409 · Cited by 444
Metadata
- Authors
- Han, J., Jentzen, A., & E, W.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 2018-08-06
- Volume
- 115
- Issue
- 34
- Pages
- 8505-8510
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W2803629276
- Cited by
- 1,722
- References
- 5
- FWCI
- 62.31
- Type
- journal article
- Language
- en
- Open access
- green
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