Model order reduction for complex systems

The discretization of a partial differential equation leads to a large-scale system of differential equations, making its approximation computationally expensive. Model order reduction aims to simplify complex mathematical models by constructing low-dimensional surrogate models that accurately represent the system's behavior. The method relies on orthogonal projection onto low-dimensional manifolds, which are built from snapshots of the system's dynamics. This technique is particularly useful in many-query scenarios, where the same problem needs to be solved for different parameter configurations, significantly increasing computational cost. Our work focuses on real-world applications, such as fluid and structure simulations, control, and Turing patterns. We also explore the construction of appropriate nonlinear manifolds to improve the accuracy of surrogate models. Key methods include Proper Orthogonal Decomposition, Reduced Basis, Empirical Interpolation Methods and Neural Networks. 

Components: Alessandro Alla and Davide Torlo