Collaborative Research: Randomized Feature Methods for Modeling and Dynamics: Theory and Algorithms

The objective of this research program is to develop consistent and theoretically validated machine learning algorithms for high-stakes decisions. The project will study randomized feature networks as a simpler but equally powerful alternative to fully-trainable neural networks for high-dimensional function approximation. The long-term goal is to develop methods that integrate machine learning and dynamical systems, a challenging new frontier in data science for scientific problems. This project also provides research training opportunities for undergraduate students, graduate students, and postdoctoral fellows. The main goal of this project is to develop new algorithms for data-driven function approximation, with the goal of using learning techniques for scientific modeling and dynamics. The focus is on the construction of randomized algorithms with complexity, accuracy, and/or stability guarantees. Rigorous algorithmic design and modeling is at the core of this scientific computing project, where we leverage advances in machine learning to augment simulations and extract better features for approximating dynamical systems. This project introduces a family of new algorithms based on randomized features with adaptive thresholding procedures to improve accuracy without overfitting. By incorporating various structural information, this has the potential to avoid the curse-of-dimensionality for several physical problems of interest. The main test problems focus on scientific models, high-dimensional systems, and high-dimensional dynamical systems. In addition, by understanding random feature models, we provide one avenue toward a better understanding of neural network models. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.