The focus of my research has been the development of probabilistic models and numerical procedures for the the analysis of systems in engineering mechanics in which uncertainties play an important role. Particular subjects include:

a) Advanced stochastic simulation

The intense interest in the analysis of large and complex systems in solid mechanics has led to the development of elaborate deterministic solvers (e.g. Finite Element codes) which can accurately account for a wide range of physical processes and phenomena. They lack however stochastic components which can deal with the various sources of uncertainties such as random fluctuations in the materials properties or loads. We investigate the use of deterministic solvers as black boxes in the context of stochastic simulation. As each of these runs can be computationally expensive, the challenge is to maximize information extraction and provide accurate estimates with the minimum possible number of runs in order to perform uncertainty quantification and response prediction in such systems. Furthermore we are currently investigating methods for optimizing mechanical components in the presence of uncertainties with respect to a large number of design variables.

b) Random Heterogeneous Materials

These are encountered in a wide range of engineering applications such as geotechnical engineering (e.g. soils), structural engineering (e.g. concrete, composites), environmental engineering (e.g. groundwater ow through a porous medium). In addition, new materials of this type are constantly being developed for aerospace components, biomedical applications etc as they exhibit favorable properties (i.e. increased stiffness, lower weight, higher durability). I have attempted to address questions related to the probabilistic characterization and simulation based on macroscale statistics. I have also proposed a novel multiscale analysis framework that is based on learning from data collected experimentally or generated computationally. It employs information theoretic concepts and tools in order to quantify the informational content of the microstructural details and find ways to condense it, while assessing quantitatively the approximation introduced. For that purpose, I have adapted techniques from vector quantization in order to develop a consistent theoretical and computational framework for upscaling in random microstructures.

c) Fracture and Fatigue Modeling

I have investigated the numerical modeling of fracture processes particularly in the context of assessing the reliability of aircraft fuselages. Despite the progress in material science and computational mechanics, fatigue life prediction has been based primarily on empirical laws and experimental results. The difficulty in addressing this problem stems from its inherent multi-scale nature. The phenomena associated with fatigue failure transverse multiple length and time scales. Hence, it is particularly important to adopt models that can accurately describe the fracture initiation process as well as the subsequent damage accumulation and crack propagation. Undeniably, uncertainties play a pivotal role in the prediction of fatigue life.

d) System Identification and Model Validation

We utilize Bayesian techniques in order to solve inverse problems and perform system identification. Traditionally, validation of material models and testing of various components has been performed using fairly large specimens which however, do not provide information about all the parameters in the material model at the scale of interest, particularly in heterogeneous materials. To that end, we have been working on the problem of accounting for material varia ability at various length scales from disparate measurements and experimental observations at a macro-scale. This provides a sound theoretical framework of fusing experiments and advanced computational models.

e) Interdisciplinary research

I am particularly interested in interdisciplinary research topics especially pertaining to the general themes of statistical inference and probabilistic modeling. One of the projects I was recently involved deals with the stochastic analysis of energy models for the United States and the determination of future policies through numerical optimization techniques in the presence of uncertainty.

In other research endeavors, I have focused on more abstract machine learning tasks and in particular in the areas of information extraction, pattern discovery and prediction in relational databases using hierarchical, nonparametric Bayesian models.