Multi-Resolution Modeling; Uncertainty Propagation; Data Assimilation
The main focus of Dr. Singla’s research efforts is on developing an analytical and computational framework that enables the construction of multiresolution models from input-output data, characterization and propagation of uncertainty in the mathematical models, and data assimilation of irregularly spaced noisy data to determine optimal and multi-hypothesis estimates of the actual physical phenomenon. The central idea is to replace evolution of initial conditions for a large dynamical system by evolution of probability density functions (pdf) for state variables. A novel feature of this research work is to pose the pdf evolution problem as a convex optimization problem with guaranteed convergence while making use of Kolmogorov equation. Furthermore, Bayesian framework is used to assimilate the noisy observation data with uncertain model forecast to reduce the uncertainty associated with state estimates. Application of interest include: predicting the probability of collision of asteroid with Earth, diffusion of chemical plumes through air, and control of movement and planning of actions of autonomous systems in disaster areas.