alexandros kontogiannis

Hopkinson Lab (ISO-40)

CUED Trumpington Street

Cambridge CB2 1PZ UK

ak2239@cam.ac.uk

I am EPSRC research fellow in fluid dynamics and applied mathematics at Cambridge University Engineering Department.

I am currently working on Bayesian inverse problems in fluid dynamics for magnetic resonance velocimetry. In the past, I have worked on aerodynamic modelling, fluid-structure interaction, simulations of ice accretion on aircraft wings, and aerodynamic shape optimisation.

My main research concerns the formulation of new machine learning methods that automatically reconstruct corrupted flowfields. These methods learn the most probable simulation that corresponds to the corrupted flowfield, and, at the same time, infer unknown quantities (e.g. pressure) that are either hard or impossible to measure otherwise.

In a nutshell, I develop algorithms that learn the most probable physical model (aka digital twin) of the flowfield dynamics from data.

selected publications

2024

Bayesian inference of mean velocity fields and turbulence models from flow MRI

A. Kontogiannis, P. Nair, M. Loecher, D. B. Ennis, and 2 more authors

2024

Abs arXiv

We solve a Bayesian inverse Reynolds-averaged Navier-Stokes (RANS) problem that assimilates mean flow data by jointly reconstructing the mean flow field and learning its unknown RANS parameters. We devise an algorithm that learns the most likely parameters of an algebraic effective viscosity model, and estimates their uncertainties, from mean flow data of a turbulent flow. We conduct a flow MRI experiment to obtain mean flow data of a confined turbulent jet in an idealized medical device known as the FDA (Food and Drug Administration) nozzle. The algorithm successfully reconstructs the mean flow field and learns the most likely turbulence model parameters without overfitting. The methodology accepts any turbulence model, be it algebraic (explicit) or multi-equation (implicit), as long as the model is differentiable, and naturally extends to unsteady turbulent flows.
Learning rheological parameters of non-Newtonian fluids from velocimetry data

A. Kontogiannis, R. Hodgkinson, and E. L. Manchester

2024

Abs arXiv

We solve a Bayesian inverse Navier-Stokes (N-S) problem that assimilates velocimetry data in order to jointly reconstruct the flow field and learn the unknown N-S parameters. By incorporating a Carreau shear-thinning viscosity model into the N-S problem, we devise an algorithm that learns the most likely Carreau parameters of a shear-thinning fluid, and estimates their uncertainties, from velocimetry data alone. We then conduct a flow-MRI experiment to obtain velocimetry data of an axisymmetric laminar jet through an idealised medical device (FDA nozzle) for a blood analogue fluid. We show that the algorithm can successfully reconstruct the flow field by learning the most likely Carreau parameters, and that the learned parameters are in very good agreement with rheometry measurements. The algorithm accepts any algebraic effective viscosity model, as long as the model is differentiable, and it can be extended to more complicated non-Newtonian fluids (e.g. Oldroyd-B fluid) if a viscoelastic model is incorporated into the N-S problem.
Bayesian inverse Navier–Stokes problems: joint flow field reconstruction and parameter learning

A. Kontogiannis, S. V. Elgersma, A. J. Sederman, and M. P. Juniper

Inverse Problems, Dec 2024

Abs HTML

We formulate and solve a Bayesian inverse Navier–Stokes (N–S) problem that assimilates velocimetry data in order to jointly reconstruct a 3D flow field and learn the unknown N–S parameters, including the boundary position. By hardwiring a generalised N–S problem, and regularising its unknown parameters using Gaussian prior distributions, we learn the most likely parameters in a collapsed search space. The most likely flow field reconstruction is then the N–S solution that corresponds to the learned parameters. We develop the method in the variational setting and use a stabilised Nitsche weak form of the N–S problem that permits the control of all N–S parameters. To regularise the inferred geometry, we use a viscous signed distance field as an auxiliary variable, which is given as the solution of a viscous Eikonal boundary value problem. We devise an algorithm that solves this inverse problem, and numerically implement it using an adjoint-consistent stabilised cut-cell finite element method. We then use this method to reconstruct magnetic resonance velocimetry (flow-MRI) data of a 3D steady laminar flow through a physical model of an aortic arch for two different Reynolds numbers and signal-to-noise ratio (SNR) levels (low/high). We find that the method can accurately (i) reconstruct the low SNR data by filtering out the noise/artefacts and recovering flow features that are obscured by noise, and (ii) reproduce the high SNR data without overfitting. Although the framework that we develop applies to 3D steady laminar flows in complex geometries, it readily extends to time-dependent laminar and Reynolds-averaged turbulent flows, as well as non-Newtonian (e.g. viscoelastic) fluids.

2023

Physics-informed compressed sensing for PC-MRI: an inverse Navier-Stokes problem

A. Kontogiannis, and M. P. Juniper

IEEE Transactions on Image Processing, Jan 2023

Abs arXiv HTML

We formulate a physics-informed compressed sensing (PICS) method for the reconstruction of velocity fields from noisy and sparse phase-contrast magnetic resonance signals. The method solves an inverse Navier-Stokes boundary value problem, which permits us to jointly reconstruct and segment the velocity field, and at the same time infer hidden quantities such as the hydrodynamic pressure and the wall shear stress. Using a Bayesian framework, we regularize the problem by introducing a priori information about the unknown parameters in the form of Gaussian random fields. This prior information is updated using the Navier-Stokes problem, an energy-based segmentation functional, and by requiring that the reconstruction is consistent with the k -space signals. We create an algorithm that solves this inverse problem, and test it for noisy and sparse k -space signals of the flow through a converging nozzle. We find that the method is capable of reconstructing and segmenting the velocity fields from sparsely-sampled (15% k -space coverage), low ( ∼10 ) signal-to-noise ratio (SNR) signals, and that the reconstructed velocity field compares well with that derived from fully-sampled (100% k -space coverage) high ( >40 ) SNR signals of the same flow.

2022

Joint reconstruction and segmentation of noisy velocity images as an inverse Navier–Stokes problem

A. Kontogiannis, S. V. Elgersma, A. J. Sederman, and M. P. Juniper

Journal of Fluid Mechanics, Jul 2022

Abs arXiv HTML

We formulate and solve a generalized inverse Navier–Stokes problem for the joint velocity field reconstruction and boundary segmentation of noisy flow velocity images. To regularize the problem, we use a Bayesian framework with Gaussian random fields. This allows us to estimate the uncertainties of the unknowns by approximating their posterior covariance with a quasi-Newton method. We first test the method for synthetic noisy images of two-dimensional (2-D) flows and observe that the method successfully reconstructs and segments the noisy synthetic images with a signal-to-noise ratio (SNR) of three. Then we conduct a magnetic resonance velocimetry (MRV) experiment to acquire images of an axisymmetric flow for low (≃6) and high (>30) SNRs. We show that the method is capable of reconstructing and segmenting the low SNR images, producing noiseless velocity fields and a smooth segmentation, with negligible errors compared with the high SNR images. This amounts to a reduction of the total scanning time by a factor of 27. At the same time, the method provides additional knowledge about the physics of the flow (e.g. pressure) and addresses the shortcomings of MRV (i.e. low spatial resolution and partial volume effects) that otherwise hinder the accurate estimation of wall shear stresses. Although the implementation of the method is restricted to 2-D steady planar and axisymmetric flows, the formulation applies immediately to three-dimensional (3-D) steady flows and naturally extends to 3-D periodic and unsteady flows.