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Learning stochastic dynamical systems with neural networks mimicking the Euler-Maruyama scheme

Noura Dridi 1, 2 Lucas Drumetz 1, 2 Ronan Fablet 1, 2 
2 Lab-STICC_OSE - Equipe Observations Signal & Environnement
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance : UMR6285
Abstract : Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random unknown factors. However, this makes learning SDEs much more challenging than ordinary differential equations (ODEs). In this paper, we propose a data driven approach where parameters of the SDE are represented by a neural network with a built-in SDE integration scheme. The loss function is based on a maximum likelihood criterion, under order one Markov Gaussian assumptions. The algorithm is applied to the geometric brownian motion and a stochastic version of the Lorenz-63 model. The latter is particularly hard to handle due to the presence of a stochastic component that depends on the state. The algorithm performance is attested using different simulations results. Besides, comparisons are performed with the reference gradient matching method used for non linear drift estimation, and a neural networks-based method, that does not consider the stochastic term.
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Submitted on : Friday, June 18, 2021 - 6:39:28 PM
Last modification on : Friday, August 5, 2022 - 2:54:52 PM
Long-term archiving on: : Sunday, September 19, 2021 - 7:07:14 PM


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Noura Dridi, Lucas Drumetz, Ronan Fablet. Learning stochastic dynamical systems with neural networks mimicking the Euler-Maruyama scheme. EUSIPCO 2021: 29th European Signal Processing Conference, Aug 2021, Dublin, Ireland. ⟨10.23919/EUSIPCO54536.2021.9616068⟩. ⟨hal-03265004⟩



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