Fully-probabilistic Finite Element Modeling
The Finite Element Method (FEM) is a highly popular tool for numerical analysis of materials and structures. Yet, conventional FEM cannot naturally deal with uncertainties in material behavior, boundary conditions or numerical discretization. In this project, we aim at developing a fully-probabilistic variant of FEM in collaboration with Dr. Pierre Kerfriden (Mines ParisTech). The new method will enjoy full-field quantification of uncertainties related to mesh discretization and efficiently propagate uncertainties related to material behavior. Aside from providing richer solutions with epistemic regularization, it will also fit naturally into Bayesian data assimilation frameworks.
Responsible researcher: Anne Poot
Physics-informed machine learning for material modeling
Machine learning-based surrogate models are becoming a popular strategy for modeling complex, highly nonlinear and path-dependent material behavior. Although powerful in their flexibility, these techniques essentially discard decades of physics-based knowledge and engineering intuition that make up the foundation of highly-successful classical material models. With this PhD project, we aim at reconciling data-driven and physics-based material models into hybrid models with optimal flexibility and robustness.
Responsible researcher: Marina Maia
Efficient multiscale Bayesian inverse modeling
Calibration of material models classically relies on solving highly-nonlinear optimization problems in order to fit parameters of complex material models to noisy experimental observations. Bayesian inverse modeling can be used to regularize these problems and lead to parsimonious models with sound epistemic uncertainty information, but extending the formalism to very high-dimensional inference problems quickly becomes inefficient. This PhD project aims at developing efficient inverse modeling frameworks combining material behavior observations coming from both noisy experiments and misspecified lower-scale models in order to infer both structural as well as structure-property relations in complex materials.
Responsible researcher: Leon Riccius
Bayesian active learning frameworks for multiscale modeling
A popular approach for accelerating expensive multiscale simulations consists in training data-driven surrogate models offline with a representative dataset before deployment. For highly-nonlinear path-dependent materials, this strategy quickly becomes cumbersome. This PhD project will explore efficient ways to employ Bayesian active learning in order to bypass offline training altogether and build highly-tailored surrogate models for multiscale simulations.
Responsible researcher: Joep Storm
Bayesian inference for FEM models
Complex material models are computationally very expensive and take a long time to run. This PhD project aims to accelerate the computations by applying recent innovations in Markov Chain Monte Carlo (MCMC), such as Piecewise Deterministic Monte Carlo (PDMC) to Gaussian Process (GP) models and the statistical finite element method (SFEM).
Responsible researcher: Amirreza Memarzadeh