École Nationale Supérieure de
Techniques Avancées

Résumé

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].