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About Solving High-Dimensional Partial Differential Equations Using Deep Learning
This document presents a deep learning approach for solving high-dimensional partial differential equations (PDEs). It reformulates PDEs as backward stochastic differential equations (BSDEs) and approximates the gradient of the solution using neural networks, similar to deep reinforcement learning. Numerical results on nonlinear Black-Scholes, Hamilton-Jacobi-Bellman, and Allen-Cahn equations show the method is effective in high dimensions in terms of accuracy and cost. This opens new applications by considering all interacting variables simultaneously instead of making assumptions about their relationships.
Detailed Information
| Author: | ['James Mattos'] |
|---|---|
| Publication Year: | 2019 |
| Pages: | 14 |
| Language: | English |
| Format: | |
| Price: | FREE |
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