Data-Driven Modeling for experimental data

Data-driven modeling is a computational approach where mathematical models are derived primarily from data rather than from predefined physical laws. It leverages advanced algorithms to identify patterns and relationships in complex datasets, providing insights into dynamic systems. Notable techniques in this field include Dynamic Mode Decomposition (DMD), which analyzes time-series data to extract dominant dynamic modes of a system, and SINDy (Sparse Identification of Nonlinear Dynamics), which identifies the governing equations of nonlinear systems by sparsely selecting relevant terms from data. Additionally, Physics-Informed Neural Networks (PINNs) combine neural networks with physical laws, such as partial differential equations, to solve complex problems while ensuring model consistency with known physics. These methods are powerful tools for discovering hidden dynamics in systems across a wide range of applications. Our work focuses on the efficient development of algorithms and applications to control problems and Turing patterns. 

Components: Alessandro Alla