BOUJANDAR, Mlle Aicha (2019) *Implementation of some deep learning algorithms to solve partial differential equations* PRE - Research Project, ENSTA.

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## Abstract

Deep learning algorithms represent powerful tools to solve High dimensional non-linear equations (PDEs). Using deterministic methods, such as finite elements, turns to be impossible because of The "curse of dimensionality". Thus, we will present in this report some algorithms that solve these PDEs using deep learning. We will first set the analogy between PDEs and backward stochastic differential equations (BSDEs), then we will represent the algorithm presented in [5]. This algorithm will be implemented in two ways : with Tensorflow and from scratch, and we will compare our results with the ones in [5]. We will present and implement two other algorithms that were presented in [4] : Deep Backward Dynamic Programming 1 & 2 which, according to the authors of [4], avoid some problems faced in the first algorithm. Finally, we will present a powerful deep learning tool : Gausssian Processes, and we will propose an algorithm to solve PDEs using them, and in which, we can use the optimal calculation methods presented in [6].

Item Type: | Thesis (PRE - Research Project) |
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Uncontrolled Keywords: | Partial differential equations (PDEs), Backward stochastic differential equations (BSDEs), Neural networks, Primal-Dual algorithm, Deep backward dynamic programming, Gaussian processes |

Subjects: | Mathematics and Applications |

ID Code: | 7448 |

Deposited By: | Aicha Boujandar |

Deposited On: | 09 juin 2021 15:06 |

Dernière modification: | 09 juin 2021 15:06 |

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