The Computational Science and Engineering (CSE) Laboratory at the University of Notre Dame performs applied and fundamental work in the interface of Information Sciences and Scientific Computing addressing data-driven approaches to uncertainty quantification, predictive modeling, inverse design and control under uncertainty, inference, and decision making in complex scientific and engineering systems. Our approach is based on the integration of computational mathematics, computational statistics/machine learning and multiscale/ multiphysics modeling of physical/chemical and biological systems.
The main objective of our work is not to simply demonstrate the well understood role of data-science and machine learning to physical models but mainly to develop innovative mathematical and statistical approaches that address unique challenges in predictive modeling. The data-driven, multiscale/ multiphysics and high-dimensionality nature of the problems of interest gives rise to unifying themes that constitute our research. They include among others the following:
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Developing scalable Bayesian uncertainty quantification techniques for complex multiscale/multiphysics models.
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Information propagation and management across and within scales.
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Quantifying uncertainties about the structural form ("missing physics") of macroscopic models.
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Learning physical invariances through data-efficient machine learning.
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Non-parametric learning of macroscopic variables/features and their evolution from sparse high-dimensional multiphysics data.
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Predictive multiscale modeling in problems without scale separation or with a cascade of scales.
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Addressing multiscale/multiresolution/multiphysics inverse/control problems.
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Design of experiments (active learning) for efficient surrogate model development.
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Statistical and optimization approaches to rare-event modeling.
Our work relies heavily on computational mathematics and machine learning with strong emphasis on probabilistic modeling. Methodological areas in our recent work include the development of non-linear dimensionality reduction methods, sparse multi-output Gaussian process models, probabilistic graph-theoretic approaches to multiscale problems, and Bayesian deep learning algorithms using limited data. Key application areas include materials physics, geological and environmental sciences, and climate modeling.
