Generative Mapping and Control of Stationary Points in Complex Dynamical Systems

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Complex dynamical systems, from protein folding to brain dynamics, from complex networks to galaxies, present structures that are key to predicting and controlling their evolution. Among these structures, equilibrium points, periodic and libration solutions and resonances are of paramount importance to understand and control the evolution of these systems.Identifying these structures is fundamental to ensure the resilience of national infrastructures, manufacture effective medication, understand and cure disease, study the evolution of climate on Earth, preserve our ability to access space. Just to name some key applications.However, the identification of these structures in complex high dimensional system is a daunting task with a computational complexity that grows exponentially with the number of dimensions. In this project we propose to use recent advances in generative machine learning to develop a new paradigm to automatically discover these structures and lay down the foundations of Generative Dynamics. The new paradigm, called MAX-net, has the potential to break the curse of dimensionality affecting many problems in scientific computing and provide a game changing enabling technology in all fields of engineering and science.