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Description:
Simulations of complex systems are essential for applications ranging from weather forecasting to molecular systems and drug design. The veracity of the resulting predictions hinges on their capacity to capture the un- derlying system dynamics. Massively parallel simulations performed in High-Performance Computing (HPC) clusters capture these dynamics by resolving all spatio-temporal scales. The computational cost is often pro- hibitive for experimentation or optimization, while their findings might not allow for generalization. The design of dimensionality reduction methods and fast data-driven reduced-order models or surrogates have been matters of life-long research efforts. In the first part of this thesis, we focus on the design and training of data-driven recurrent neural networks for forecasting the spatio-temporal dynamics of high-dimensional and reduced-order complex systems. We propose architectural advances and training algorithms that alleviate the pitfalls of previously proposed methods, whose application was limited to lower-order systems. The designed algorithms extend the arsenal of predictive models for complex systems and spatio-temporal chaos. In the second part, we present a novel systematic framework that bridges large-scale simulations and reduced-order models to Learn the Effective Dynamics (LED) of complex systems. The framework forms algorithmic alloys between non-linear machine learning algorithms and the Equation- Free approach for modeling complex systems exhibiting spatio-temporal chaos. LED deploys autoencoders to map between fine- and coarse-grained representations and evolves the latent space dynamics using recurrent neural networks. The algorithm is validated on benchmark problems, and we find that it outperforms state-of-the-art reduced-order models in terms of predictability and large-scale simulations in terms of cost. LED is applicable to systems ranging from chemistry to fluid mechanics and reduces the computational effort by up to two orders of magnitude while maintaining ...