Applied Interdisciplinary Mathematics (AIM) Seminar

Many engineering and scientific problems can be described by equations of fluid dynamics, namely, systems of time dependent nonlinear hyperbolic PDEs. The mathematical description of these processes, as well as the numerical discretisation of the resulting PDEs, will depend on the level of detail required to study them.

In this talk, I will present two approaches towards higher fidelity numerical simulations: 1) we develop a new variable shape parameter selection strategy for Radial Basis Function approximations using an unsupervised learning strategy, leading to an adaptive, parameter-free shape parameter estimation for RBFs. 2) we develop fast and accurate data-driven surrogate models to better describe planetary collisions and planetary system formation, by mimicking the coupling of two hydro-dynamics solvers through data-driven surrogate models.

I will finish by presenting some extensions to the frameworks presented, using uncertainty estimates to guide active learning strategies or to better sample datasets. Speaker(s): Maria Han Veiga (University of Michigan)