The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Neural‐network‐based approximations for solving partial differential equations
Abstract
A numerical method, based on neural‐network‐based functions, for solving partial differential equations is reported in the paper. Using a ‘universal approximator’ based on a neural network and point collocation, the numerical problem of solving the partial differential equation is transformed to an unconstrained minimization problem. The method is extremely easy to implement and is suitable for obtaining an approximate solution in a short period of time. The technique is illustrated with the aid of two numerical examples.
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Citations
Cites
Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., & White, H. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90020-8 · Cited by 21,728
Cited by
Machine Learning for Fluid Mechanics
Brunton, S. L., Noack, B. R., & Koumoutsakos, P. (2020) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-010719-060214 · Cited by 3,063
fPINNs: Fractional Physics-Informed Neural Networks
Pang, G., Lu, L., & Karniadakis, G. E. (2019) · SIAM Journal on Scientific Computing · doi:10.1137/18m1229845 · Cited by 1,105
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
Perspectives on the integration between first-principles and data-driven modeling
Bradley, W., Kim, J., Kilwein, Z., Blakely, L., Eydenberg, M., Jalvin, J., Laird, C., & Boukouvala, F. (2022) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2022.107898 · Cited by 231
Metadata
- Authors
- Dissanayake, M. W. M. G., & Phan‐Thien, N.
- Venue
- Communications in Numerical Methods in Engineering
- Publisher
- Wiley
- Published
- 1994-03
- Volume
- 10
- Issue
- 3
- Pages
- 195-201
- ISSN
- 1069-8299 (ISSN-L)
- 1099-0887
- OpenAlex
- W1970454553
- Cited by
- 622
- References
- 1
- FWCI
- 0.29
- Type
- journal article
- Language
- en
- Open access
- closed
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- Dissanayake, M. W. M. G., & Phan‐Thien, N. (1994). Neural‐network‐based approximations for solving partial differential equations. Communications in Numerical Methods in Engineering. https://doi.org/10.1002/cnm.1640100303
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
