Collaborative Research: Machine Learning methods for multi-disciplinary multi-scales problems

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This project addresses two of the most pressing challenges in modern scientific research: (a) modeling natural phenomena across a broad range of space and time scales, and (b) the application of data science to discover physically meaningful relationships from large datasets. It will leverage knowledge from related and disparate disciplines, connecting them through data science. Four specific problems will be studied: cloud formation and evolution, movement of particles through random media, frustrated magnetic systems, and the reconstruction of urban topography. These benchmark problems have been selected as they capture different disciplinary aspects of multi-scale challenges. State-of-the-art methods in machine learning (including Artificial Neural Networks) will be used to develop new mathematical representation for small-scale processes. If successful, this project will substantially increase the capability of scientific computing to address a wide variety of important problems from the natural and social sciences, and will be disseminated widely through a pair of workshops, multiple campus visits across the 5-institution consortium, high impact peer-reviewed publications and presentations and the training of a cadre of more than a dozen post-docs and students.This project will develop, implement and evaluate a new constrained optimization framework to discover and test physical phenomena at different resolutions and scales, including new machine learning algorithms aimed at discovering the stochastic differential equations underlying noisy data. This will be used to train physical parameterizations that account for the effects of small-scale processes in coarse resolution models. Core to this will be the design of a new framework to constrain artificial neural networks to deliver solutions that are interpretable and meaningful in the domain sciences and that can be directly associated with differential operators.This project is part of the National Science Foundation's Harnessing the Data Revolution (HDR) Big Idea activity, and is jointly supported by HDR and the Division of Mathematical Sciences within the NSF Directorate of Mathematical and Physical Sciences.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.