Data Driven Approximation

Data-driven approximation focuses on learning functions from data to model complex systems and predict their behavior, often bypassing the need for explicit mathematical models. Current research emphasizes developing robust methods for handling high-dimensional data and heterogeneous data streams, employing techniques like sparse polynomial approximation, deep neural networks, and Koopman operator methods. These advancements are improving the accuracy and efficiency of approximating functions in diverse fields, including scientific computing, dynamical systems analysis, and decision-making under uncertainty. The resulting models find applications in areas such as predicting complex network dynamics, reconstructing surfaces from scattered data, and solving partially observable Markov decision processes.