We survey in this article the connections between Machine Learning and Control Theory. Control Theory provide useful concepts and tools for Machine Learning. Conversely Machine Learning can be used to solve large control problems. In the first part of the paper, we develop the connections between reinforcement learning and Markov Decision Processes, which are discrete time control problems. In the second part, we review the concept of supervised learning and the relation with static optimization. Deep learning which extends supervised learning, can be viewed as a control problem. In the third part, we present the links between stochastic gradient descent and mean field theory. Conversely, in the fourth and fifth parts, we review machine learning approaches to stochastic control problems,and focus on the deterministic case, to explain, more easily, the numerical algorithms.
We propose in this paper a spectral method for the Boltzmann equation for gases with viscosity/friction. We describe the density of particles and compare the results in the case of gases with friction and rarefied gas. This is the first numerical result for the equation. We show numerically that under the presence of the viscosity, the solution dissipates to 0. The larger the viscosity is, the faster the solution converges to 0.
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