Welcome to the Uncertainty Quantification Group at Duke University
Our research aims to propose regularization methodologies and stochastic methods for Scientific Machine Learning (ML) and Uncertainty Quantification (UQ) in Computational Mechanics and Materials Science. We address a wide array of applications, ranging from multiscale approaches (from the nanoscale to the macroscale) to inverse problems to challenging projects in biomedical engineering. We strive to tackle core questions through an interdisciplinary research approach combining mathematical models, advanced algorithms, and identification and validation tasks based on physical experiments.
The proposed frameworks find applications in a broad range of projects, such as:
- The multiscale and multiphysics modeling of heterogeneous materials and systems.
- The identification of linear or nonlinear material properties solving statistical inverse problems.
- The modeling of stochastic, linear and nonlinear constitutive models.
- The propagation of physics-based models of uncertainties through high-dimensional models.
- Uncertainty quantification on complex domains, such as 3D printed geometries or living tissues.
Financial support from Duke University, the National Science Foundation, the U.S. Naval Research Laboratory, and Sandia National Laboratories is gratefully acknowledged.