My research lies in the areas of Numerical Analysis, SciML schemes, and Scientific Computing for the bridging of the scales, modelling, bifurcation analysis and control of complex and multiscale dynamical systems. The scientific keystones of the research integrate Numerical Analysis, Machine Learning and Manifold Learning, Data-Mining, Complex Systems, Nonlinear Systems, Bifurcation theory, and Control theory. All in all, I am trying to tackle the "curse of dimensionality" by developing explainable SciML schemes with the aid of niche numerical analysis.  There are three main directions in this effort:

(A) Development of explainable and physics-informed SciML schemes, with the aid of numerical analysis, to deal with the "curse of dimensionality" in complex and multiscale systems. My interests focus on the solution of both the inverse problem (the discovery of physical laws in the form of ODEs and PDEs operators from big data generated by high fidelity dynamical models) and the forward problem (the numerical solution of differential equations). 

(B) Development of methods leveraging manifold learning and the equation-free approach for dimensionality reduction, i.e. discover latent spaces where the emrgent dynamics of complex systems evolve. The aim is to bridge the scales of multiscale/complex/stochastic dynamical systems to facilitate their rigorous numerical analysis.

(C) Modelling of complex multiscale and stochastic systems and Applications in Sciences

Using the developed methodologies, I strive to address emerging interdisciplinary challenging complex problems with applications 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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