Machine Learning approximations for Some Parabolic Partial Differential Equations

Machine Learning approximations for Some Parabolic Partial Differential Equations

Idris Kharroubi – GJM, Volume 6, Issue 1 (2021), 1-26.

These lecture notes are devoted to machine learning based algorithms for the approximation of solutions to some second order parabolic partial differential equations (PDE for short). We present a new kind of probabilistic approximation for these PDEs which is based on Neural network approximations. This is referred to as Machine learning approximation methods. The paper is divided into three parts. A first part presents approximation results for feedforward neural networks. A second part studies probabilistic representations of solutions to parabolic PDEs in terms of backward stochastic differential equations (BSDEs for short). Finally, a third part deals with the neural network approximations of those BSDEs.

Categories: Issue1

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Received: August 18, 2020
Accepted: Mars 08, 2021
Published online: May 22, 2021

Authors:

Idris Kharroubi
Laboratoire de Probabilités, Statistique et Modélisation,
Sorbonne Université, Université de Paris,
CNRS, UMR 8001, France.

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