Abstract
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.
Keywords
Partial differential equationDeep learningComputer scienceApplied mathematicsMathematicsMathematical analysisArtificial intelligence
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Publication Info
- Year
- 2018
- Type
- article
- Volume
- 115
- Issue
- 34
- Pages
- 8505-8510
- Citations
- 1560
- Access
- Closed
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Cite This
Jiequn Han,
Arnulf Jentzen,
E Weinan
(2018).
Solving high-dimensional partial differential equations using deep learning.
Proceedings of the National Academy of Sciences
, 115
(34)
, 8505-8510.
https://doi.org/10.1073/pnas.1718942115
Identifiers
- DOI
- 10.1073/pnas.1718942115
- PMID
- 30082389
- PMCID
- PMC6112690
- arXiv
- 1707.02568