My research lies in the areas of Numerical Analysis, Scientific Machine Learning and Scientific Computing for the bridging of the scales, modelling, bifurcation analysis and control of complex large scale 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. 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 numerical analysis. The framework is based on manifold learning/ data mining for dealing with the curse of dimensionality, thus discovering latent spaces where the emergent dynamics evolve. The aim is to bridge the scales of multiscale/complex/stochastic dynamical systems for their rigorous numerical analysis.

(B) Development of (physics-informed) machine learning and manifold learning algorithms to deal with the "curse of dimensionality" for the numerical 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). 

(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 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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