# STAR-seminars: Nacira Agram

The webinars will take place on Zoom and a link to the virtual room will be sent out to all those who registered at the registration page.

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**Speaker:** Nacira Agram - Linnaeus University

**Title: Deep learning and stochastic mean-field control for a neural network model**

**Abstract: **We study a membrane voltage potential model by means of stochastic control of mean-field stochastic differential equations and by machine learning techniques. The mean-field stochastic control problem is a new type, involving the expected value of a combination of the state X(t) and the running control u(t) at time t. Moreover, the control is two-dimensional, involving both the initial value z of the state and the running control u(t).

We prove a necessary condition for optimality and a verification theorem of a control (u; z) for such a general stochastic mean-field problem. The results are then applied to study a particular case of a neural network problem, where the system has a drift given by E[u(t)X(t)] and the problem is to arrive at a terminal state value X(T) which is close in terms of variance to a given terminal value F under minimal costs, measured by z^2 and the integral of u^2(t).

This problem is too complicated to handle by mathematical methods alone. We solve it using deep learning techniques.

The talk is based on joint work with A. Bakdi and B. Øksendal at University of Oslo.

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This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to renewable energy markets and production. This series brings together the major research themes of the projects STORM, SCROLLER, and SPATUS.