Nonlinear Dynamics Project Proposal

In many disciplines of science and engineering, the systems of interest are often modeled as dynamical systems (such as ordinary differential equations, partial differential equations, etc.). Some physical quantities depend on the solution of such dynamical systems, which indirectly depend on the parameters of the problems. Given the desired properties of such quantities, solving for the correct parameters is commonly known as a inverse problem. In this project, I am trying to solve several inverse problems of my current interest through the principles of differentiable programming, where we can define adjoint operations of dynamical evolutions for efficient model construction and optimization. This will help us to use adequate constraints and/or empirical data to refine our models, and therefore provide more insight in fields like design and fabrication. The differentiable programming paradigm will be based on the current Julia ecosystem which has a great ecosystem for scientific modeling and optimization.