On-going Research I: Statistical Learning for Nonlinear Dynamical Systems

Objectives: to develop a physics-informed statistical learning approach capable of 

• learning nonlinear dynamics by utilizing data generated from computer models as well as the fundamental physics laws of nonlinear dynamics, and 

• predicting nonlinear dynamics for new parameters (i.e., out-of-sample prediction) in a computationally-efficient manner that needs to be significantly faster than direct numerical solutions.

Application: physics-informed statistical modeling approach for aircraft-UAV (Unmanned Aerial Vehicle) collision severity assessment, which aims to predict aircraft surface deformation due to collisions under a range of impact parameters (e.g., impact  attitude, speed, position, altitude, etc.).

Challenges: (i) conventional high-fidelity Finite Element Analysis (FEA) is computationally too expensive; (ii) the data-driven model needs to incorporate fundamental structural dynamics for such a high-stake applications.

Illustration: