Constantinos Siettos works in the areas of Numerical Analysis and Machine Learning for the bridging of the scales, modelling, bifurcation analysis and control of complex and multiscale systems. The scientific keystones of the research integrate Numerical Analysis, Machine Learning and Manifold Learning, Data-Mining, Agent-based modelling, Bifurcation theory, Statistical Mechanics, Complex Networks and Control theory. There are three main directions in this effort:

(A) Development of "next generation" Equation-free numerical analysis methods that bypass the construction of surrogate Machine Learning models that impose bias in the analysis. The framework is based on manifold learning for dealing with the curse of dimensionality, thus discovering latent spaces where the emergent dynamics evolve. The aim is to bridge high-fidelity and detailed microscopic simulators with the emergent dynamics for the numerical bifurcation analysis and robust control of multiscale/complex/uncertain dynamical systems.

(B) Development of physics-informed machine learning and manifold learning algorithms for the numerical solution of both the inverse problem (the discovery of physical laws in the form of ODEs and PDEs from big data generated by detailed agent-based and high fidelity simulations) and the direct problem (the numerical solution of differential equations). A significant part is

(C) Modelling of complex multiscale and stochastic systems

Using state-of-the-art numerical simulation methods, and agent-based models, I strive to address emerging interdisciplinary challenging complex problems in Computational Epidemiology, Computational Neuroscience, Crowd and Social Dynamics, Economics and Finance, Environmental Modelling, in collaboration with strong and interested colleagues.

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