Data-driven mesh adaptation =========================== Main contribution ^^^^^^^^^^^^^^^^^ I am involved in a research project base at `Imperial College London `__ on various advanced topics related to mesh adaptation as a consultant. In the first half on data-driven methods, we investigated how mesh movement methods such as those implemented in `Movement <../movement.html>`__ might be swapped out for machine learning (ML) approaches, to accelerate the mesh adaptation process and overcome certain limitation associated with classical mesh movement methods. In :cite:`ZK24`, we established an approach termed UM2N ('Universal Mesh Movement Networks'). When a classical mesh movement method was swapped out for UM2N, the computational cost was reduced by several orders of magnitude, since we were able to avoid expensive auxiliary PDE solves, such as Monge-Ampère type equations. Moreover, we found that UM2N was able to overcome the limitation of Monge-Ampère type methods being restricted to convex domains. The 'universal' part of the acronym refers to the fact that the data-driven approach can be trained once and then deployed for any (physical) PDE - a great advantage over other approaches, such as our previous work in :cite:`SZ22`, in which the ML model is trained per physical PDE. Funding information """"""""""""""""""" This project is funded by `Huawei Corporation Ltd. `__ and involves collaboration with the Noah's Ark Lab. Resources """"""""" * NeurIPS spotlight paper: :cite:`ZK24`. * Previous work investigating data-driven mesh movement: :cite:`SZ22`. * `Second half of the project `__ on combining mesh adaptation with PDE-constrained optimisation methods.