TBA

Several physical models are available to understand the dynamics of fluid mixtures, including the so-called Baer-Nunziato models. The partial differential equations associated with these models look like those of Navier-Stokes, with the addition of new relaxation terms. One strategy to obtain these models is homogenisation: starting from a mesoscopic mixture, where two pure fluids satisfying the compressible Navier-Stokes equations share the space between them, a change of scale is performed to obtain a macroscopic mixture, where the two fluids can coexist at any point in space.

This problem concerns the study of the Navier-Stokes equations with strongly oscillating initial data. We'll start by explaining some results in this framework, in one dimension of space and on the torus, for barotropic fluids. We will then detail the various steps involved in demonstrating homogenisation. Finally, we'll explain how to adapt this reasoning to homogenisation for perfect gases, with and without heat conduction.

Predictions of complex flows remain a significant challenge for engineering systems. Computationally affordable predictions of turbulent flows generally require Reynolds-Averaged Navier–Stokes (RANS) simulations and Large-Eddy Simulation (LES), the predictive accuracy of which can be insufficient due to non-Boussinesq turbulence and/or unresolved multiphysics that preclude qualitative fidelity in certain regimes. For example, in turbulent combustion, flame–turbulence interactions can lead to inverse-cascade energy transfer, which violates the assumptions of many RANS and LES closures. We present an adjoint-based, solver-embedded data assimilation method to augment the RANS and LES equations using trusted data. This is accomplished using Python-native flow solvers that leverage differentiable programming techniques to construct the adjoint equations needed for optimization. We present applications to shock-tube ignition delay predictions, turbulent premixed jet flames, and shock-dominated nonequilibrium flows and discuss the potential of adjoint-based approaches for future machine learning applications.

TBA

Numerically solving PDEs typically requires compressing infinite information into a finite system of algebraic equations. Pragmatically, we usually follow a recipe: “Assume solutions of form X; substitute into PDE Y; discard terms by rule Z.” In contrast, Lanczos’s pioneering “tau method” prescribes modifying the PDE to form an exact finite system. Crucially, any recipe-based method can be viewed as adding a small equation correction, enabling us to compare multiple schemes independently of the solver. 

This talk also addresses a paradox: PDEs often admit infinitely many solutions, but finite systems produce only a finite set. When we include a “small” correction, the missing solutions are effectively hidden. I will discuss how tau methods frame this perspective and outline proposals for systematically studying and optimising various residuals.

to follow

During the talk I will describe my research on host-pathogen interactions during lung infections. Various modelling approaches have been used, including a hybrid multiscale individual-based model that we have developed, which simulates pulmonary infection spread, immune response and treatment within in a section of human lung. The model contains discrete agents which model the spatio-temporal interactions (migration, binding, killing etc.) of the pathogen and immune cells. Cytokine and oxygen dynamics are also included, as well as Pharmacokinetic/Pharmacodynamic models, which are incorporated via PDEs. I will also describe ongoing work to develop a continuum model, comparing the spatial dynamics resulting from these different modelling approaches.  I will focus in the most part on two infectious diseases: Tuberculosis and COVID-19.

We will review physics-informed neural networks (NNs) and summarize available extensions for applications in computational science and engineering. We will also introduce new NNs that learn functionals and nonlinear operators from functions and corresponding responses for system identification. 

These two key developments have formed the backbone of scientific machine learning that has disrupted the path of computational science and engineering and has created new opportunities for all scientific domains. We will discuss some of these opportunities in digital twins, autonomy, materials discovery, etc.

Moreover, we will discuss bio-inspired solutions, e.g., spiking neural networks and neuromorphic computing.

It’s a busy and stressful term for a lot of us so come and take a break and do some colouring and origami with us. Venting is very much encouraged.

TBC

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TBA

TBA

Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. 

This work demonstrates that when the matrix coefficients of the equation are quasiseparable, the solution also exhibits numerical quasiseparability. This property enables us to develop two efficient Riccati solvers. The first solver is applicable to the general quasiseparable case, while the second is tailored to the particular case of banded coefficients. Numerical experiments confirm the effectiveness of the proposed algorithms on both synthetic examples and case studies from the control of partial differential equations and agent-based models. 

The rheological (deformation and flow) properties of biological tissues  are important in processes such as embryo development, wound healing and 
tumour invasion. Indeed, processes such as these spontaneously generate  stresses within living tissue via active process at the single cell level. 
Tissues are also continually subject to external stresses and deformations  from surrounding tissues and organs. The success of numerous physiological 
functions relies on the ability of cells to withstand stress under some conditions, yet to flow collectively under others. Biological tissue is 
furthermore inherently viscoelastic, with a slow time-dependent mechanics.  Despite this rich phenomenology, the mechanisms that govern the 
transmission of stress within biological tissue, and its response to bulk deformation, remain poorly understood to date.

This talk will describe three recent research projects in modelling the rheology of biological tissue. The first predicts a strain-induced 
stiffening transition in a sheared tissue [1]. The second elucidates the interplay of external deformations applied to a tissue as a whole with 
internal active stresses that arise locally at the cellular level, and shows how this interplay leads to a host of fascinating rheological 
phenomena such as yielding, shear thinning, and continuous or discontinuous shear thickening [2]. The third concerns the formulation of 
a continuum constitutive model that captures several of these linear and nonlinear rheological phenomena [3].

[1] J. Huang, J. O. Cochran, S. M. Fielding, M. C. Marchetti and D. Bi, 
Physical Review Letters 128 (2022) 178001

[2] M. J. Hertaeg, S. M. Fielding and D. Bi, Physical Review X 14 (2024) 
011017.

[3] S. M. Fielding, J. O. Cochran, J. Huang, D. Bi, M. C. Marchetti, 
Physical Review E (Letter) 108 (2023) L042602.

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I will present some ongoing work on solving parametric linear systems arising from the application of the finite elements method on elliptic partial differential trial equations. The focus of the talk will be on leveraging randomised numerical linear algebra to solve these equations in high-dimensional parameter spaces with special emphasis on the multi-query context where optimal sampling is not practical. In this context I will discuss some ideas on choosing a suitable low-dimensional approximation of the solution, as well as reducing the variance of the sketched systems. This research aims at exploring the potential of randomisation as a probabilistic framework for model order reduction, with potential applications to online simulations, uncertainty quantification and inverse problems, via the research grant EPSRC EP/V028618/1

Bio: Nick Polydorides is a professor in computational engineering at the University of Edinburgh and has interests in randomised numerical linear algebra, inverse problems and edge computing. Previously, he was a faculty at the Cyprus Institute, and a postdoctoral fellow at MIT’s lab for Information and Decision Systems. He has a PhD in Electrical Engineering from the University of Manchester.