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Neural differential equations solving stochastic mean field games

Dummer, Sven (2021) Neural differential equations solving stochastic mean field games.

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Abstract:Mean field games (MFG) and mean field control are effective mathematical models for simulating and analysing interactions within large populations of agents. These models have applications for robust control in engineering and robotics, as well as in data science, economics and crowd motion. Recently, to overcome the curse of dimensionality for high-dimensional MFGs, deep learning techniques have been used effectively. Although stochastic MFGs have been well studied, the role of deep learning in stochastic Lagrangian frameworks is still unexplored. Hence, this thesis studies generative neural differential equations like neural ODEs and neural SDEs. To research their advantages, we study two dimensional particle motion examples. Simulations show that a neural SDE generator is more appropriate when information about the Lagrangian view of a stochastic MFG is desired. Moreover, a neural ODE generator can deal with costs in the MFG that cannot be dealt with via a standard neural network. Finally, we show that a neural SDE generator can even stabilize the training compared to standard neural network generators.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
Link to this item:http://purl.utwente.nl/essays/88503
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