Research

Research interests:

  • Inverse problems (PDE-constrained optimization, Bayesian estimation)

  • Uncertainty quantification and management (risk metrics, probabilistic sensitivity analyses, optimization under uncertainty)

  • Computational physics (wave propagation and dynamics, fracture mechanics, heat conduction)

  • Machine learning (including physics-informed machine learning)

  • Digital twins

Application areas:

  • Mechanical system operational optimization (enhanced oil recovery, digital twins, power grids)

  • Structural health monitoring

  • Manufacturing (real-time sure monitoring, multi-fidelity modeling for additive manufacturing)

Wave energy focusing for enhanced oil recovery

  • Wave energy focusing in heterogeneous, elastic media

  • PDE-constrained optimization to arrive at optimal wave source locations, time signals

  • Quantify uncertainty in wave energy delivery

Non-destructive condition assessment for framed structures

  • Timoshenko beam model to accurately simulate high-frequency waves

  • PDE-constrained optimization for material profile reconstruction

  • Tikhonov (TN) and total-variation (TV) regularization

  • Regularization factor continuation schemes