Supervisors: Radu Cimpeanu; James Sprittles; Albert Bartok-Partay

Student: Sebastian Dooley

This exciting project lives at the interface between multi-physics modelling, high performance computing and data-driven approaches. The 21st century has brought a revolution in micromanufacturing techniques (LCD, 3D printing etc.) that require understanding and efficient deployment of knowledge at scales below those currently accessible. Enter data-driven equation discovery techniques: novel surrogate modelling methods which can provide insight in scenarios in which simulation or experimental data are available, but traditional derivation approaches break down. Our challenge is to create a new computational framework that harnesses the power of these approaches towards generating new meaningful understanding of fluid flows at small scales.

The project will involve a productive interplay between mathematical modelling, asymptotic analysis, computational fluid dynamics and data-driven methods, as well as multi-physics elements and heterogeneous approaches more generally. Several useful resources are provided below, showcasing some of the capabilities of these techniques in related contexts, as well as providing a broader perspective into this rapidly evolving research area.

[1] Rudy et al., Data-driven discovery of partial differential equations, Science Advances 3: e1602614, 2017.

[2] Brunton et al., Machine learning for fluid mechanics, Annual Reviews of Fluid Mechanics 52: 477-508, 2020.

[3] Cimpeanu et al., Active control of liquid film flows: beyond reduced-order models, Nonlinear Dynamics 104: 267-287, 2021.

[4] Sprittles, Kinetic effects in dynamic wetting, Physical Review Letters 118: 114502, 2017.

[5] Bartok et al., Machine learning unifies the modeling of materials and molecules, Science Advances 3: e1701816, 2017.