My research interests span multiple disciplines in engineering, all classifiable as inverse problems. Mathematical models of dynamical systems must be tuned using observational data for predictive and simulation based decision making purposes. In this framework, a physical system may be described by a forward model whose purpose is to provide an output/response given a set of parameters and inputs/excitations. The process of tuning such model involves solving the inverse problem of estimating the model inputs and/or parameters from observations (possibly sparse and/or noisy). Such problems arise frequently in science and engineering, with applications in weather forecasting, large-scale climate prediction, oil reservoir production forecasting, and stock market prediction being prominent examples. Inverse problems are normally ill-posed, having either no (unique) solution or a solution that is highly sensitive to the noise in the data. My current research focuses on refining the Bayesian approach to tackle ill-posed inverse problems. Bayesian inference provides the solution to the inverse problem in the form of probability distributions for the unknown parameters. To that extent, I rely heavily on utilizing efficient uncertainty quantification techniques and exploiting the state-of-the-art technology of high-performance computing to expedite this process.

My research experience spans the following fields:

  • Uncertainty quantification
  • Bayesian inference and stochastic inverse problems
  • Optimization under uncertainty
  • High performance computing and parallel algorithm design
  • Data assimilation in dynamical systems
  • Efficient representation of stochastic processes for numerical simulation purposes
  • Reduced-order modelling
  • Nonlinear dynamics, limit cycle oscillation, and chaos
  • Inverse problems in aeroelasticity
  • Time-series statistical modelling
  • Bayesian model selection and model averaging