Deep splitting method for parabolic PDEs
In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational graph for each of the subproblems is comparatively small,...
| Main Authors: | , , , , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/153744 |
| _version_ | 1811690936577556480 |
|---|---|
| author | Beck, Christian Becker, Sebastian Cheridito, Patrick Jentzen, Arnulf Neufeld, Ariel |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Beck, Christian Becker, Sebastian Cheridito, Patrick Jentzen, Arnulf Neufeld, Ariel |
| author_sort | Beck, Christian |
| collection | NTU |
| description | In this paper we introduce a numerical method for nonlinear parabolic PDEs
that combines operator splitting with deep learning. It divides the PDE
approximation problem into a sequence of separate learning problems. Since the
computational graph for each of the subproblems is comparatively small, the
approach can handle extremely high-dimensional PDEs. We test the method on
different examples from physics, stochastic control and mathematical finance.
In all cases, it yields very good results in up to 10,000 dimensions with short
run times. |
| first_indexed | 2024-10-01T06:11:55Z |
| format | Journal Article |
| id | ntu-10356/153744 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:11:55Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1537442023-02-28T19:57:49Z Deep splitting method for parabolic PDEs Beck, Christian Becker, Sebastian Cheridito, Patrick Jentzen, Arnulf Neufeld, Ariel School of Physical and Mathematical Sciences Science::Mathematics Nonlinear Partial Differential Equations Splitting-Up Method In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational graph for each of the subproblems is comparatively small, the approach can handle extremely high-dimensional PDEs. We test the method on different examples from physics, stochastic control and mathematical finance. In all cases, it yields very good results in up to 10,000 dimensions with short run times. Nanyang Technological University Published version This work was supported by Swiss National Science Foundation grant 200020 175699 ``Higher order numerical approximation methods for stochastic partial differential equations,"" by the Deutsche Forschungsgemeinschaft under Germany's Excellence Strategy EXC 2044-390685587, Mathematics M\"unster: Dynamics - Geometry - Structure, and by Nanyang Assistant Professorship grant ``Machine Learning based Algorithms in Finance and Insurance." 2022-01-20T07:25:30Z 2022-01-20T07:25:30Z 2021 Journal Article Beck, C., Becker, S., Cheridito, P., Jentzen, A. & Neufeld, A. (2021). Deep splitting method for parabolic PDEs. SIAM Journal On Scientific Computing, 43(5), A3135-A3154. https://dx.doi.org/10.1137/19M1297919 1064-8275 https://hdl.handle.net/10356/153744 10.1137/19M1297919 2-s2.0-85115265695 5 43 A3135 A3154 en SIAM Journal on Scientific Computing © 2021 Society for Industrial and Applied Mathematics. All rights reserved. This paper was published in SIAM Journal on Scientific Computing and is made available with permission of Society for Industrial and Applied Mathematics. application/pdf |
| spellingShingle | Science::Mathematics Nonlinear Partial Differential Equations Splitting-Up Method Beck, Christian Becker, Sebastian Cheridito, Patrick Jentzen, Arnulf Neufeld, Ariel Deep splitting method for parabolic PDEs |
| title | Deep splitting method for parabolic PDEs |
| title_full | Deep splitting method for parabolic PDEs |
| title_fullStr | Deep splitting method for parabolic PDEs |
| title_full_unstemmed | Deep splitting method for parabolic PDEs |
| title_short | Deep splitting method for parabolic PDEs |
| title_sort | deep splitting method for parabolic pdes |
| topic | Science::Mathematics Nonlinear Partial Differential Equations Splitting-Up Method |
| url | https://hdl.handle.net/10356/153744 |
| work_keys_str_mv | AT beckchristian deepsplittingmethodforparabolicpdes AT beckersebastian deepsplittingmethodforparabolicpdes AT cheriditopatrick deepsplittingmethodforparabolicpdes AT jentzenarnulf deepsplittingmethodforparabolicpdes AT neufeldariel deepsplittingmethodforparabolicpdes |