The focus of this effort is on developing comprehensive means for dynamic data-driven modeling of engineering systems. At the heart of our approach is a powerful averaging pro- cess that allows us to construct a global family of local independent approximations with a desired order of continuity and quantifying error bounds, while retaining the freedom to vary in a general way the resolution (e.g., degrees of freedom) of local approximations. These independent local approximations can be constructed intelligently by incorporating any a-priori information about the modeling process or extracting local spatial information by the use of methods like principal component analysis or sparse approximation. Another important aspect of this research effort is to quantify approximation error and formulate adaptive (dynamic) error feedback learning algorithms for robust performance. This framework has been successfully used to generate data driven local maps of Earth’s magnetic filed and to seamlessly integrate data-driven local maps with the global maps (i.e. World Magnetic Model (WMM)) in collaboration with Prof. Manoranjan Majji at Texas A&M.
We have also used these tools to derive tumor motion models correlating respiratory motion to the motion of the tumor from imaging data to enable real-time adaptive conformal radiation therapy in collaboration with my colleague Prof. Tarunraj Singh and researchers from Roswell Park Cancer Institute (RPCI). Adaptive radiation therapy with high-fidelity target tracking can facilitate in reducing toxicity, bounds on the size of the necessary margins, and hence the risk for complications.