Numerical Methods for Prediction and Discovery with Big Data
Abstract
The major objective of the project is to develop a mathematical and numerical framework for scientific prediction and discovery in the realm of big data. Our goal is to develop a set of mathematical and numerical tools that are applicable to big data and subsequently take advantage of the potential and opportunities offered by big data. More specifically, we aim at developing numerical algorithms to discover the physical and mathematical laws behind observational data and create reliable predictive models for the unknown systems. During the course of the project, the PI and his team made tremendous progresses on data driven discovery and prediction. Moreover, modern machine learning (ML) tools such as deep neural network (DNN) were adopted during the project and enabled us to develop highly flexible and powerful algorithms for data driven modeling. The most notable outcomes of the project include the following. - A novel framework of flow map learning (FML) for unknown dynamical systems. This establishes a rigorous mathematical foundation of data driven modeling of dynamical systems. Learning in the form of flow map enables us to design rigorous and flexible numerical predictive tools. - Learning parametric systems. The FML is extended to unknown dynamical systems with parametric dependence. The resulting learning algorithm is able to model the parameter dependence of the system and create an effective model for UQ analysis. - Learning non-autonomous systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 25, 2022
- Accession Number
- AD1190028
Entities
People
- Dongbin Xiu
Organizations
- Ohio State University