• Developing Riemannian representations of model uncertainties

    Developing new models to account for model-form uncertainties, using Riemannian manifold description

  • Advancing New Tools for UQ on Brain Geometries

    Developing new stochastic tools for stochastic multiphysics simulations on patient-specific brain geometries (collaboration with Prof. L. Gomez at Purdue University)

  • Developing new tools for UQ on AM geometries

    Developing and validating a new stochastic modeling framework for uncertainty quantification on materials produced by additive manufacturing (funded by NSF)

  • Developing Domain-Constrained Representations for Stochastic Multiscale Methods

    Constructing new models accounting for microstructural complexity to advance high-fidelity stochastic multiscale methods

  • Combining Learning Techniques with Stochastic Modeling

    Combining probabilistic learning with stochastic modeling to enhance experimental and simulation datasets

Lab Group of Dr. Johann Guilleminot

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.

National Science Foundation