APPLICATIONS OF ARTIFICIAL NEURAL NETWORKS IN STATISTICAL MECHANICS AND NON-LINEAR DYNAMICS

Böttcher Lucas (Personal webpage)

This talk will outline how artificial neural networks (ANNs) can help to represent distributions and functions that are associated with different types of complex physical and biological systems. In the first part of my presentation, I will talk about the application of generative models in statistical and condensed matter physics. I will mainly focus on restricted Boltzmann machines (RBMs) and variational autoencoders (VAEs) as specific classes of neural networks that have been successfully applied in the context of physical featureextraction and representation learning. The second part of my presentation concerns the efficient control ofcomplex dynamical systems. In most real-world control problems, both control energy and cost constraints play a significant role. Although such optimal control problems can be formulated within the framework of variationalcalculus, their solution for complex systems is often analytically and computationally intractable. I will present a versatile control framework that uses neural ordinary differential equations to learn control signals that steer high-dimensional dynamical systems towards a desired target state within a specified time interval. Examples will illustrate that such control methods can solve a wide range of control and optimization problems, including those that are analytically intractable.