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
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The pricing of options and corporate liabilities
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Mastering the game of Go with deep neural networks and tree search
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Rasheed, A., San, O., & Kvamsdal, T. (2020) · IEEE Access · doi:10.1109/access.2020.2970143 · Cited by 1,952
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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
Li, W., & Hsu, C.-Y. (2022) · ISPRS International Journal of Geo-Information · doi:10.3390/ijgi11070385 · Cited by 147
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Gao, J., & Wang, D. (2024) · Nature Human Behaviour · doi:10.1038/s41562-024-02020-5 · Cited by 81
Digital Twin: Values, Challenges and Enablers
Rasheed, A., San, O., & Kvamsdal, T. (2019) · arXiv · doi:10.48550/arxiv.1910.01719 · Cited by 81
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks
Geist, M., Petersen, P., Raslan, M., Schneider, R., & Kutyniok, G. (2021) · Journal of Scientific Computing · doi:10.1007/s10915-021-01532-w · Cited by 57
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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Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
