Finite Element and Discrete Time Methods for Partial Differential Equations with Memory.
Such models occur in the continuum mechanics of biotissue and polymers, and also in the electromagnetism of lossy dielectrics. Some example projects:
- Implementation and analysis of fully discrete approximations to partial differential equations with exponentially fading memory
- Implementation and analysis of fully discrete approximations to partial differential equations with fractional calculus memory
- Use of forward problem simulation to generate training data for machine learning applications
- 3D modelling of the time dependent motion of a human chest
Deep Neural Networks for Inverse Problems
Funded Opportunity (closes 26 June 2020): https://www.findaphd.com/phds/project/deep-learning-for-inverse-scattering-problems/?p121459
There is a lot more scope in this area of research. Please contact me if you are interested.