DGM: A deep learning algorithm for solving partial differential equations
Abstrak
High-dimensional PDEs have been a longstanding computational challenge. We propose a deep learning algorithm similar in spirit to Galerkin methods, using a deep neural network instead of linear combinations of basis functions. The PDE is approximated with a deep neural network, which is trained on random batches of spatial points to satisfy the differential operator and boundary conditions. The algorithm is mesh-less, which is key since meshes become infeasible in higher dimensions. Instead of forming a mesh, sequences of spatial points are randomly sampled. We implement the approach for American options (a type of free-boundary PDE which is widely used in finance) in up to 100 dimensions. We call the algorithm a "Deep Galerkin Method (DGM)".
Topik & Kata Kunci
Penulis (2)
Justin A. Sirignano
K. Spiliopoulos
Akses Cepat
- Tahun Terbit
- 2017
- Bahasa
- en
- Total Sitasi
- 2404×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1016/j.jcp.2018.08.029
- Akses
- Open Access ✓