Dr. Mattheakis' research focus on designing artificial neural networks for implementation in applied physics and engineering. Moreover, he is interested in electronic properties of two-dimensional materials, wave propagation in random networks, and plasmonic metamaterials.

Predicting the state of complex, non-linear dynamical systems as a function of time is an important problem of great practical utility. Recent advances of machine learning methods have made possible significant applications in science, industry, and technology, with reliable prediction comprising one of the most promising areas of research. Artificial neural networks are a central technique in machine learning and can be used to predict the evolution of dynamical systems. We explore and present here the long-term forecasting capability of three different neural network architectures to predict the spatiotemporal evolution of two distinct complex dynamical phenomena: (i) the onset of branching singularities in electronic flow in two dimensional disordered materials focusing on graphene and (ii) the multi-clustered turbulent chimera states, that is collective, self-organized patterns of coexisting coherence and incoherence in coupled oscillator systems. These two phenomena represent opposite ends in complex spatiotemporal evolution with chimeras relating to dynamic self-organization and branching relating to the stochastic onset of singular motion. Generally, the underlying physical laws that are governing the time evolution of dynamical systems are expressed through differential equations. In addition to the previous data-driven forecasting, we present an unsupervised (data-free) neural network that solves the differential equations of motion. We focus on energy-conserving differential equations that are used in mathematical modeling in physical sciences. The proposed architecture is time invariant and guarantees the energy conservation through an embedded symplectic structure that is adopted by Hamitlonian formulation.