Abstracts
Abstracts
Keynote Talks 

Catherine Powell (Manchester University)  Intrusive Methods for Forward UQ in Engineering Applications Stochastic Galerkin (SG) approximation, also known as intrusive polynomial chaos approximation, can be used to facilitate forward uncertainty quantification (UQ) in models consisting of partial differential equations (PDEs) with uncertain inputs. Unlike conventional sampling methods, such as Monte Carlo, SG schemes yield approximations that are functions of the input random variables, leading to surrogate models. Although the study of intrusive SG methods is now mature for simple model problems, much work remains to be done to determine whether they can provide a computationally feasible framework for facilitating forward UQ in more complex PDE models arising in engineering applications. There are two key challenges  designing the polynomial space to ensure the resulting approximation is provably accurate and the efficient numerical solution of the associated (potentially huge) linear systems of equations. In this talk, we will give an introduction to SG methods for forward UQ in a simple PDE model and then discuss recent work on developing more advanced methods for linear elasticity and poroelasticity models. 
Keith Butler (STFC) 
Opening the Black Box: How Understanding And Interpreting Machine Learning Models can Enhance Materials Design and Characterisation Machine learning (ML) and artificial intelligence (AI) are the subjects of much debate as to potential impact for good or ill. Depending who we talk to ML is the solution to almost every human challenge, from open boarders to pandemic control, or presents an existential crises for the species. In materials science the polarisation is perhaps less extreme, but nonetheless pervasive. The numbers of ML related works experiences an explosion, yet one highly respected theoretical chemist recently pronounced “[a]t least 50% of the machine learning papers I see regarding electronic structure are junk”. A part of the issue that many detractors have with ML methods is related to their perception of the techniques as ‘blackbox’ approaches, at the same time, the same lack of understanding limitations of the models leads to some of the more outlandish boosterism surrounding the subject. In this talk I will discuss, with examples from our work, how we can open up the blackbox of ML methods, highlighting and understanding limitations, increasing trust in results, and potentially improving the methods themselves. 
Presentations from HetSys Cohort 1


Andrew Angus 
Modelling Stimulated Raman Scattering in Laser Directdrive Fusion Plasmas at Ignition Scale References 
Matthew Harrison  Quantification of Heterogeneity of Spatially Averaged Generalized subGaussian Random Fields While Gaussian models have been used to describe spatial heterogeneity of hydrogeological attributes, the Generalized subGaussian (GSG) model has been shown to be able to capture heavy tailed marginal distributions and simultaneous leptokurtic scaling of increment distributions of a broad range of hydrogeological variables. In this context, it can be noted that the main statistics characterizing the spatial heterogeneity of a given system attribute such as, e.g., permeability, depend on observation scale. A key parameter of the GSG model is a length scale which is proportional to the size of the volume associated with observations and can be characterized through standard inverse approaches. Here, we investigate the dependence of observation scale of the parameters of the GSG model, with speciﬁc focus on the way uncertainty propagates across random ﬁelds associated with diverse observation scales. We do so by analytically deriving expressions according to which the variance of a (two or threedimensional) GSG random ﬁeld varies as a function of the degree of spatial averaging. Our formulations enable one to estimate the level of heterogeneity (as quantiﬁed through the variance) at a given scale, as a result of averaging from a reference scale. Our analytical ﬁndings show that the level of heterogeneity in GSG ﬁelds (a Gaussian distribution being a special case thereof) is highest at the ﬁnest scale and decays towards zero as we increase the spatial averaging volume. As expected, the ﬁeld becomes homogeneous at the limit of complete spatial averaging. Our model for variance propagation across averaging scales allows eﬃcient estimation of residual heterogeneity retained at larger length scales, thus being of interest when formulating coarse grained hydrogeological ﬂow models. The model is ﬁrst veriﬁed through comparison with results achieved through a MonteCarlo numerical analysis and it is then applied to a comprehensive dataset composed of more than 2000 air permeability data collected at various observation scales on the surface of a block of Massilon Sandstone sample. 
Idil Ismail  Successes and challenges in using machinelearned activation energies in microkinetic simulations

Jingbang Liu  Modelling confined thinfilms at nanoscale A precises description of the behaviours of nanoscale thinfilms is key to various applications such as printable electronics, labonachip devices, spin coating as well as high performance lubricants. At such a small scale the free surface can be viewed as a collection of particles moving randomly (Brownian motion) generating nano waves and the continuum description of the fluid breaks down. Fluctuating hydrodynamics (the LandauLifstiz NavierStokes equations) have been raised to include the random motions and for thinfilms the stochastic lubriation equation (SLE) has been derived. Previous studies have focused on thinfilms with periodic boundary conditions assuming the film is unbounded, but this is not physical. In our study we examined both 2D and 3D thinfilms with two physically motivated contact line conditions where the free surface meets a confining solid wall: 90 degrees contact angle and pinned contact line. To understand the behaviour of the film, we run Molecular Dynamics (MD) simulations and rationalise the results of these using conventional mathematical techniques applied to SLE. For different boundary conditions, new wave modes are derived from linear stability analysis generating results that agree excellently with the MD. The results show that the effect of confining boundaries propagates across the free surface, even for relatively long films. And with 3D thinfilms we conclude with ideas as to how these results can be experimentally validated. 
Carlo Maino  Excited State Machine Learning for Chromophores in Complex Environments Accurate simulations of the excited state dynamics of chromophores in complex environments are a prerequisite to understanding important properties such as photostability, relaxation pathways, and excited state lifetimes. An atomistic understanding of these properties can aid in the design and study of useful chemical compounds such as novel sunscreen candidates. However, with an explicit representation of the solvent, there are conflicting requirements set by the need to follow individual trajectories over long timescales, to sample over the ensemble of solvent configurations, and to use a high level of theory to obtain good chemical accuracy. This puts such methods out of the reach of DFT or QC methods alone. Our ongoing work uses machine learning to approximate ground and excited state potential energy surfaces of chromophores in a variety of solvent environments. This allows for an acceleration of the dynamics simulations, while retaining the accuracy of DFT or higher level methods. Our workflow is based in ESTEEM: Explicit Solvent Toolkit for Electronic Excitations of Molecules. ESTEEM can call on a range of different electronic structure, molecular dynamics, machine learning codes, and spectroscopy postprocessing tools to calculate excited state and spectroscopic properties of molecules in solvent environments. 
Arre Rajkumar 
From selfassembly to mechanical behaviour: a datadriven framework for block copolymers. As inherently heterogeneous materials, block copolymers (BCPs) can demonstrate nontrivial mechanical behaviour such as hyperelasticity, viscoplasticity and hysteresis. Whilst there exist some continuum approaches to modelling the mechanical response of BCPs [12], models that encompass the full detail of the underlying polymer dynamics have not yet been developed. Of interest is the tendency of BCPs to selfassemble into welldefined morphologies and the effect that this selfassembly has on the mechanical response. We employ a computational framework that combines selfconsistent field theory simulations (SCFT) and molecular dynamics (MD). The use of SCFT enables us to obtain an equilibrium structure on the mesoscopic scale. Subsequently, the results of the SCFT calculation are used to generate density biased random walks (DBRW) to build a particlebased model [34], capturing a microstructure composed of glassy and rubbery phases. Furthermore, we present an improved DBRW algorithm that allows for the particlebased modelling of highly heterogeneous BCP systems such as ABC triblock copolymers. Coarsegrained MD is then employed to predict the mechanical deformation of BCP systems for selected microstructural parameters. We show how the obtained simulation data can then be used to train a Gaussian process regression model for the prediction of a variety of mechanical properties. We then demonstrate how this framework may be employed to model cyclic deformation as well as efficiently capture the hysteresis effects that emerge throughout. References [1] C. P. Buckley, D. S. A. De Focatiis and C. Prisacariu; In Constitutive Models for Rubber VII; 1st Ed.; S. Jerrams, N. Murphy, CRC Press: London, pp. 310, (2011) [2] Cho, H.; Mayer, S.; Pöselt, E.; Susoff, M.; Boyce, M. C., Polymer 128, 5 (2017) [3] A. F. Terzis, D. N. Theodorou, A. Stroeks, Macromolecules 33, 4, pp. 13851396 (2000) [4] T. Aoyagi, T. Honda, M. Doi, J. Chem. Phys. 117, 81538161 (2002) 
Christopher Woodgate 
ShortRange Order in HighEntropy Alloys: First Principles Theory and Atomistic Modelling ShortRange order (SRO) can be either beneficial or detrimental to the properties of novel high and mediumentropy alloys. An understanding of phase behaviour and underlying physical mechanisms driving ordering is therefore essential. We present results from an allelectron, first principles, Landautype theory which enables us to obtain SRO directly, and also to obtain parameters suitable for atomistic modelling to understand incipient order in these materials. As a case study, we present results on the prototypical facecentred cubic highentropy alloy, NiCoFeMnCr, and its derivatives, collectively referred to as the CantorWu alloys [1]. We are able to show that the dominant correlations in these systems are between Co and Cr, and that Fe and Mn dilute interactions and stabilise the disordered solid solution. Our approach not only provides insights into the physical origins of ordering, but is also exceptionally computationally efficient compared to conventional supercellbased approaches.

Talks and Posters from HetSys Cohort 2 

Connor Allen 
An Efficient Approach for Improving Phonon Representation in Machine Learned Potentials. Gaussian approximation potentials (GAP) have been trained on density functional theory (DFT) predictions for free energy and derivative quantities. We demonstrate a computationally economical means to capture the phonon representation in Al, Mg, Si and W, and also use GAP to investigate the ordering of a dilute amount of Al within hcpTi. Vibrational and elastic properties of Al, Mg, Si and W are reproduced with excellent accuracy as compared against DFT. From hybrid MonteCarlo molecular dynamics simulations, we find that Al preferentially orders itself in hcpTi such that AlAl nearest neighbours are disfavoured. 
Iain Best 
Uncertainty Quantification in Atomistic Simulations using Interatomic Potentials 
Adam Fisher 
Using kinetic Monte Carlo to investigate crystal growth in NiAl Superalloys. Superalloys can be used at a high percentage of their melting point with good resistance to fatigue and creep. NickelAluminium superalloys gain much of this resistance from the interaction between and phases. We aim to study the growth of from the phase at the atomistic level. We test the feasibility of using the kinetic ActivationRelaxation Technique (kART), an off lattice kinetic Monte Carlo (kMC) method. kART finds and catalogues the barriers within the system and evolves the system through a chain of metastable states. Using the barriers heights that separate the states, a rate is calculated based upon harmonic transition state theory (HTST). To examine the feasibility of using kART to study the growth of , a / interface was set up: 256 atoms of next to 256 atoms of random alloy, with one vacancy introduced to facilitate diffusive processes. The system was then evolved over 650 kMC steps at 900 K using a published potential for to calculate energies and forces. The study shows that kART evolves the system with the system lowering in energy over time, indicating that it is moving towards an equilibrium. However, there is no real order emerging within the test cell indicating access to longer time scales is required. Many areas for further research are identified including using growth rates learnt to parametrise a partial differential equation model to simulate the ageing processes on technologically relevant time and length scales. 
Joe Gilkes 
Towards Automatic Reaction Networking for Modelling LongTerm Degradation of Materials Knowing the pathways and products of material decomposition is of vital importance to industry, where environmental factors can cause accelerated aging within critical components. However, computationally modelling this molecular breakdown process requires expansive networks of reactions with accurate reaction rates, such that they can be propagated forwards through time to predict how a material will decompose under specific conditions. The creation and solving of such networks is a computationally expensive process. We employ a singleended graphdriven searching technique to programmatically build complete reaction networks for the breakdown of polyethylene (PE), using machine learning to efficiently predict reaction barriers. We then propagate these networks in time using differential equation solvers written in Julia, culminating in a highly efficient workflow that is capable of creating and exactly solving complete breakdown networks to predict how PE thermally decomposes over timespans of decades within just a few hours of compute time. We explore further improvements that could be made to the efficiency and accuracy of this method, as well as discussing how the method could be extended to elucidate longterm breakdown pathways due to other nonthermal environmental effects. 
Peter LewinJones 
Dynamic Leidenfrost Effects: Computational Modelling to Predict Transitions in Drop Impact When a liquid drop is placed gently on a sufficiently hot surface it is able to levitate on its own evaporative vapour cushion. This `Leidenfrost effect' is well understood and has been the focus of much research, motivated by its importance for numerous industrial applications where the dramatic decrease in thermal conductivity caused by it is often detrimental. Notably, however, many technologies, such as spray cooling, actually involve the impact of droplets in Leidenfrost conditions. Recently, experimental studies have probed the dynamic Leidenfrost effect, where droplets can be forced into contact when impact speeds are large enough, uncovering several interesting modes of contact and discovering new unexpected effects, such as an oscillating film height in certain regimes. To provide new insight into the physical mechanisms involved in such phenomena and as an important predictive tool, we have developed a novel computational model for the dynamic Leidenfrost process. This uses lubrication theory to model the evaporated vapour, and the finite element method to solve the NavierStokes equations in the drop, implemented in the open source library oomphlib and has passed a number of benchmarking tests. Our model enables us to explore the parameter space of impacting velocity and solid surface temperature, and probe different regimes of contact and vapour film behaviour, with the aim of predicting the critical impact speed at which contact will occur. 
Tadashmi Matsumoto 
Probabilistic Meshless Methods for Parabolic Partial Differential Equations (P.D.Es) When a physical phenomena is being modelled by a P.D.E we often have data that represents a partial solution to the P.D.E but not necessarily the parameters that describe the P.D.E, e.g the diffusivity coefficient in the heat equation. Currently, it is popular to use probabilistic methods like maximum likelyood estimation to estimate parameters as they can also provide a confidence interval of how accurate our estimation of the parameter is. Most of these methods use a 'forward solver' that solves the P.D.E for some set of parameters and then apply statistical techniques to determine which parameter is mostlikley based on the data. In my Ph.D I am developing a forward solver that is probabilistic in it self, as most solvers are determnistic. The main idea of the solver is based on the Kalman filter, which is an algorithm that uses a series of measurements observed over time to produce estimates of the unknown variables, by estimating a joint probability distribution over the variables for each timeframe. One assumes that the prior probability distribution of the unknown variables is a multivariate Gaussian and therefore the algorithm reduces to simply applying linear transformations and conditioning this multivariate Gaussian on the observed data. As we are interested in solutions to P.D.Es our unknown variables belong to some infitie dimensional function space, so we can no longer place a Gaussian prior on our solution space, so we use Gaussian processes instead. So far I have been developing this theory and currently I am trying to implement this Gaussian process based Kalman filter. 
Charlotte Rogerson 
Validating Hydrodynamic Codes for Inertial Confinement Fusion using experimental Shocktiming Data Nuclear fusion provides access to clean, unlimited, and reliable power source. One of the ways in which to achieve fusion here on Earth is through Inertial Confinement Fusion (ICF). The design and interpretation of ICF experiments depends on accurate, predictive numerical calculations, along with welldefined uncertainties. Success of these calculations depends on highquality equation of state (EoS) data. Out of several competing EoS models which currently exist, none of these do a good job at matching all the experimental data and only perform well in a subset of relevant parameter space. The hydrodynamic codes used to simulate ICF experiments also have many free parameters, and we need to quantify the uncertainty associated with them. One way in which the free parameters of hydrodynamic simulations are optimised are through large ensemble parameter scans. However, this can be computationally expensive given the dimensionality of parameter space for a full laserdriven fusion simulation. Therefore, this project focuses on the implementation of a Gaussian process (GP) surrogate which provides an inexpensive model from which a large number of samples can be obtained. The GP is trained using simulations from the 1D Lagrangian hydrodynamics code Freyja, simulating shocktiming experiments conducted by Cao et al (2018). These shocktiming experiments are commonly used to validate models used in ICF codes, and we aim to optimise 4 free parameters within Freyja which best match experimental results. Three EoS models are used in Freyja simulations, namely Ideal Gas, FEOS and FPEOS. 
Lakshmi Shenoy 
A machine learning interatomic potential for simulation of fracture in αiron Neutron irradiation and extreme temperature changes in reactor pressure vessels (RPV) lead to embrittlement of the RPV’s structural steel – a lowalloy of αiron. Large scale modelling of this phenomenon using local approach models to fracture [1] require accurate estimates of fracture effective surface energy γ_{fes} as an input. The γ_{fes} can be calculated from atomistic modelling of fracture, which in turn requires a reliable interatomic potential that is suitable for fracture simulation. In this work, we start by evaluating the crack simulations using two strong candidate machine learning potentials for αiron – a Gaussian approximation potential (GAP) by Dragoni et al. [2], and the quadraticnoise machine learning potential by Goryaeva et al. [3] – both of which were not trained specifically for crack properties. We then present iterative modifications of the GAP training database and kernel choices, to make it suitable for simulation of cracks and their interaction with simple radiationinduced point defects in αiron, such as vacancies and selfinterstitials. These results are a step towards modelling fracture in the lowalloy ferritic steels used in RPVs. References: [1] Mathieu, JeanPhilippe, et al. Journal of nuclear materials 406.1 (2010): 97112. [2] Dragoni, Daniele, et al. Physical Review Materials 2.1 (2018): 013808. [3] Goryaeva, Alexandra M., et al. Physical Review Materials 5.10 (2021): 103803. 
Alisdair Soppitt 
Simulation of turbulent mixing in channels with reactive boundary conditions 
James M Targett 
Quantum Interference Enhanced Thermopower in Single Molecules My PhD aims to exploit the electronic and vibrational properties of nanoscale materials that are 1000 times smaller than the diameter of a human hair to discover new materials for energy harvesting and cooling in consumer electronics such as mobile phones and laptops. The ultimate goal of the research is to understand quantum and phonon transport through molecular structures for thermoelectricity and thermal management. One of the projects currently being carried out is to see how quantum interferences affect the thermopower in molecular junctions like single molecules. Molecular junctions usually comprise a bridge, anchors and electrodes, and gold electrodes and SCH3 (SMe) anchors have been chosen for this project. Our molecular junctions demonstrated improved Seebeck coefficients, which is desirable. All the theoretical predictions are obtained using computational material modelling and quantum transport simulation methods such as SIETA [1], GOLLUM [2], tightbinding model (TB) and Dr Sadeghi’s tutorial [3]. And these results have been confirmed by collaborators from experimental groups in the UK and China. [1] J. M. Soler et al., J. Phys. Condens. Matter, 2002, 14, 2745–2779. [2] J. Ferrer et al., New J. Phys., 2014, 16, 093029. [3] H. Sadeghi, Nanotechnology, 2018, 29, 373001. 
Steven Tseng 
A SOAP Opera: Methods for Modeling the Relationship Between Molecular Structure and Solubility 
Flash Presentations and Slides from HetSys Cohort 3 

Geraldine Anis 
Title: TBC 
Ziad Fakhoury 
Title: TBC 
Ben Gosling 
Title: Using surrogate models to optimise designs for laserdriven fusion power production Laserplasma experiments in fusion research trigger kinetic scale (picosecond timescale) instabilities, whose effects need to be included in largerscale fluid models (nanosecond timescales) to predict ICF experiments accurately. These laserplasma instabilities are threewave parametric couplings that can lead to the generation of ’Hot electrons’, which reduces the efficiency of the ICF process. Given the significant difference in time and length scales for kinetic and hydrodynamic processes, suitable surrogate models must be found to include the laserplasma instability information in largescale hydrodynamic implosion models. In this short talk, I will aim to give a very brief overview of the impact of laserplasma instabilities and what I have been working on for the past month, which is the development of metrics to be used to build a Gaussian process surrogate. 
Oscar Holroyd 
Hierarchical Modelling Approaches to Manipulating Thin Liquid Films. 
Dylan Morgan 
Title: TBC 
Matt Nutter 
Title: TBC 
Matyas Parrag 
Using machine learning to predict cardiolipin binding sites on bacterial membrane proteins Lipid binding sites play an important role in the function of bacterial membrane proteins and are often targets for antibiotics. Being able to quickly predict their locations from the protein structure would expedite the discovery of antibiotic pharmaceuticals. Currently computational methods used to identify binding sites involve expensive MD simulations and analysis of the resulting trajectories. Using machine learning methods, such as Gaussian processes and deep neural networks, I hope to predict cardiolipin (CDL) binding sites at a fraction of the computational cost. 
Thomas Rocke 
Atomistic Modelling of IIIV Semiconductor Device Failure IIIV alloys are common in semiconductor optoelectronic devices. The high energy conditions during device operation lead to growth of crystal dislocations, which cause loss of efficiency and eventual failure of the active region. Using Gaussian Approximation Potentials, we hope to atomistically model absorption of point defects into the dislocation core at nearquantum accuracy in order to better understand the mechanisms behind dislocation growth in these devices. 
Anas Siddiqui 
Title: TBC 
Jeremy Thorn 
Title: TBC 