Research
Data-Driven Equation Â鶹ÊÓƵy
Within the field of inverse problems, data-driven equation discovery seeks to leverage available data from physical systems to uncover governing equations. Often, these governing equations are written as ordinary differential equations, or, more commonly in mechanics, as partial differential equations. Our lab investigates both interpretable partial differential equation discovery for material characterization, and neural network based discovery.
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Uncertainty Quantification
Uncertainty quantification (UQ) is a field of study that focuses on understanding and modeling uncertainties in computational models and real-world systems. It is a disciplinary domain among computational mathematics, statistics, and engineering. Our group has been working on this field with following extensions:
- UQ with reduce-order modeling;
- Randomized algorithms;
- Multi-fidelity UQ;
- Generative machine learning on UQ problems.
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