Mihalis Kavousanakis

Methods such as physics-informed neural networks (PINNs), operator learning and hybrid modeling can help reduce reliance on massive datasets while ensuring predictions that respect fundamental scientific laws. Applications of scientific machine learning span a broad range including reactive flows, pollution dispersion models, materials design, etc.

Cancer growth is the result of cell-level processes during which an individual cell interacts with its micro-environment. To accelerate and thus enable the more efficient study of such models we employ multi-scale methods.

Projective integration is one technique of the computational framework, which wraps around cell-level simulators, and enables the acceleration of computations by carrying out "jumps" in time.

Monte Carlo models require substantial computational time and multi-scale techniques can be employed to accelerate simulations and perform systems level analysis. We have successfully applied this multi-scale computational framework in populations of coagulating and sintering solid particles.

Partial integro-differential equations is an alternative modelling approach, which requires the solution of a difficult class of problems. We have demonstrated how this category of problems can be solved within the environment of commercial software packages specializing in solving differential equations (COMSOL Multiphysics (R)) and how this software can be embedded in a computational framework which allows the application of bifurcation and stability analysis. Such an analysis has been applied in cell populations carrying the lac operon gene regulatory network, which encodes the proteins for lactose metabolism.

In a vertical-axisymmetric-stagnation point chemical vapor deposition reactor, 3d computations (exploiting commercial fluid dynamics code) reveal a rich solution space with multiple co-existing steady-state solutions (axisymmetric and non-axisymmetric), as well as periodic solutions.

Our goal is to investigate the critical operating conditions which combine high deposition rate, and film uniformity. In order to do so, the computed flow and temperature field is coupled with chemicaly reacting species that lead to the deposition of thin films.

Through this investigation, which employs an arsenal of computational tools borrowed from numerical analysis (bifurcation and stability analysis), we can identify parametric regions which allow the co-existence of different wetting states and furthermore we can identify - through eigenvalue analysis -the directions along which a perturbation should be applied for the most efficient wetting state transition.