Solving PDE-constrained inverse problems using FEniCS

Inversion of the Antarctic basal sliding parameter field from surface velocity observations. Figure from Isaac et. al 2015.

Course advisor - Dr. Omar Ghattas

We tackled the following problems:

• Analysis of exponentially ill-posed heat equation (parabolic PDE)
• Using autograd to minimize energy of a hanging chain subject to length constraints
• Image denoising while preserving sharp edges; formulated as infinite dimensionsal minimization problem
• Inverting advection-diffusion-reaction PDE for reaction coefficient
• An inverse problem for the Burger’s equation
• Frequency domain inverse wave propagation for multiple sources and frequencies

The code and reports can be found here.