Available Projects

At the nanoscale, liquids jiggle: random molecular motion controls how jets break up, films rupture and droplets merge. Adding noise to the Navier–Stokes equations captures this for simple liquids like water, but no equations exist for complex liquids such as polymers, inks and biological fluids. You will use physics-informed machine learning, trained on molecular simulations, to discover them, and release the result as open-source software.

Primary supervisor: Duncan Lockerby - Duncan.Lockerby@warwick.ac.uk
Co-supervisor: James Sprittles (Mathematics)

Project detail:
Shrink a flow far enough and something remarkable happens: the liquid starts to jiggle. At the nanoscale, the random thermal motion of molecules is no longer a negligible background but a driving force, deciding how thin liquid jets break into droplets, how nanoscale films rupture, and how droplets merge. Our group has shown that capturing these effects means going beyond the Navier–Stokes equations that underpin classical fluid dynamics, by adding carefully constructed random 'noise' terms, an approach known as fluctuating hydrodynamics. It lets us simulate nanoscale flows at a tiny fraction of the cost of tracking every molecule.

But there is a catch: this only works for simple liquids like water. Many of the liquids that matter most in technology and biology are complex: polymer solutions and melts, lubricants, inks, mucus, and the protein-rich fluids inside cells. They have memory and elasticity, and at the nanoscale nobody knows what equations describe them, let alone what form their noise should take. Today they can only be studied with molecular dynamics, which is limited to tiny volumes and fleeting timescales. This holds back progress in areas from nanoscale 3D printing and inkjet technology to lubrication in micro-devices, and from DNA sequencing in nanopores to targeted drug delivery.

This project will use machine learning to discover the missing equations. You will propose a flexible family of fluctuating equations for complex liquids and train them on molecular simulations, so that they reproduce the true nanoscale behaviour at a fraction of the cost. The twist is that the quantities these equations need cannot be measured directly from molecular data: it is an inverse problem. You will solve it with Gaussian-process machine learning, which learns the link between what can be observed and what the model requires, and tells you how much to trust the answer.

The project is co-supervised across Engineering and Mathematics, in a group with a strong track record in nanoscale fluid dynamics and international collaborators. Your results will be released as open-source software within the widely used Basilisk flow solver. You will develop rare and highly employable skills in scientific machine learning, uncertainty quantification, molecular and continuum simulation, and research software engineering. The project suits a strong graduate in engineering, physics, mathematics or computer science who enjoys both equations and code.

How to apply for admission: www.warwick.ac.uk/pgrengineering