The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations
Open accessAbstract
We study a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, which is based on an analogy between the BSDE and reinforcement learning with the gradient of the solution playing the role of the policy function, and the loss function given by the error between the prescribed terminal condition and the solution of the BSDE. The policy function is then approximated by a neural network, as is done in deep reinforcement learning. Numerical results using TensorFlow illustrate the efficiency and accuracy of the studied algorithm for several 100-dimensional nonlinear PDEs from physics and finance such as the Allen–Cahn equation, the Hamilton–Jacobi–Bellman equation, and a nonlinear pricing model for financial derivatives.
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Cites
ImageNet classification with deep convolutional neural networks
Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2017) · Communications of the ACM · doi:10.1145/3065386 · Cited by 112,155
LeCun, Y., Bengio, Y., & Hinton, G. (2015) · Nature · doi:10.1038/nature14539 · Cited by 84,126
Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
Ioffe, S., & Szegedy, C. (2015) · arXiv · doi:10.48550/arxiv.1502.03167 · Cited by 27,818
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
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
Wireless Network Intelligence at the Edge
Park, J., Samarakoon, S., Bennis, M., & Debbah, M. (2019) · Proceedings of the IEEE · doi:10.1109/jproc.2019.2941458 · Cited by 92
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
- E, W., Han, J., & Jentzen, A.
- Venue
- Communications in Mathematics and Statistics
- Published
- 2017-11-10
- Volume
- 5
- Issue
- 4
- Pages
- 349-380
- ISSN
- 2194-6701 (ISSN-L)
- 2194-671X
- OpenAlex
- W2625995436
- Cited by
- 822
- References
- 4
- FWCI
- 28.10
- Type
- journal article
- Language
- en
- Open access
- green
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