Showing 1–20 of 20 results for author: Pain, C C

Quantum Neural Physics: Solving Partial Differential Equations on Quantum Simulators using Quantum Convolutional Neural Networks

Authors: Jucai Zhai, Muhammad Abdullah, Boyang Chen, Fazal Chaudry, Paul N. Smith, Claire E. Heaney, Yanghua Wang, Jiansheng Xiang, Christopher C. Pain

Abstract: Neural Physics recasts local discretisations of partial differential equations (PDEs) as fixed convolutional operators, providing a physics-preserving alternative to data-driven surrogate modelling in scientific machine learning. However, existing realizations remain largely confined to classical AI hardware and do not directly connect to quantum structured operator design. To bridge this gap, we… ▽ More Neural Physics recasts local discretisations of partial differential equations (PDEs) as fixed convolutional operators, providing a physics-preserving alternative to data-driven surrogate modelling in scientific machine learning. However, existing realizations remain largely confined to classical AI hardware and do not directly connect to quantum structured operator design. To bridge this gap, we introduce a \emph{Quantum Neural Physics} framework and develop a Hybrid Quantum-Classical CNN Multigrid Solver (HQC-CNNMG). The proposed method maps analytically prescribed stencil operators to local quantum convolutional primitives and embeds them within a classical multilevel W-cycle architecture, combining the operator-centric view of scientific ML with the numerical rigor of multigrid solvers. Using amplitude encoding together with the Linear Combination of Unitaries (LCU) and the Quantum Fourier Transform (QFT), the resulting local quantum operators admit logarithmic-depth implementation, with circuit depth scaling as $\mathcal{O}(\log K)$ for an encoded block of size $K$ under the idealized parallel circuit model considered here. Numerical experiments on Poisson, transient diffusion, convection--diffusion, and incompressible Navier--Stokes problems demonstrate numerical consistency, stable multilevel behaviour, and workflow-level feasibility on noiseless simulators. Comparisons with representative quantum linear solver paradigms further show that the main strength of HQC-CNNMG lies in its balanced trade-off among local circuit depth, numerical robustness, and compatibility with PDE structure, rather than in fully quantum global inversion. △ Less

Submitted 20 June, 2026; v1 submitted 25 March, 2026; originally announced March 2026.

Comments: 25 pages and 8 figures

Surrogate models for Rock-Fluid Interaction: A Grid-Size-Invariant Approach

Authors: Nathalie C. Pinheiro, Donghu Guo, Hannah P. Menke, Aniket C. Joshi, Claire E. Heaney, Ahmed H. ElSheikh, Christopher C. Pain

Abstract: Modelling rock-fluid interaction requires solving a set of partial differential equations (PDEs) to predict the flow behaviour and the reactions of the fluid with the rock on the interfaces. Conventional high-fidelity numerical models require a high resolution to obtain reliable results, resulting in huge computational expense. This restricts the applicability of these models for multi-query probl… ▽ More Modelling rock-fluid interaction requires solving a set of partial differential equations (PDEs) to predict the flow behaviour and the reactions of the fluid with the rock on the interfaces. Conventional high-fidelity numerical models require a high resolution to obtain reliable results, resulting in huge computational expense. This restricts the applicability of these models for multi-query problems, such as uncertainty quantification and optimisation, which require running numerous scenarios. As a cheaper alternative to high-fidelity models, this work develops eight surrogate models for predicting the fluid flow in porous media. Four of these are reduced-order models (ROM) based on one neural network for compression and another for prediction. The other four are single neural networks with the property of grid-size invariance; a term which we use to refer to image-to-image models that are capable of inferring on computational domains that are larger than those used during training. In addition to the novel grid-size-invariant framework for surrogate models, we compare the predictive performance of UNet and UNet++ architectures, and demonstrate that UNet++ outperforms UNet for surrogate models. Furthermore, we show that the grid-size-invariant approach is a reliable way to reduce memory consumption during training, resulting in good correlation between predicted and ground-truth values and outperforming the ROMs analysed. The application analysed is particularly challenging because fluid-induced rock dissolution results in a non-static solid field and, consequently, it cannot be used to help in adjustments of the future prediction. △ Less

Submitted 23 June, 2026; v1 submitted 25 February, 2026; originally announced February 2026.

Journal ref: Published in Engineering with Computers 42, 131 (2026)

An AI-driven framework for the prediction of personalised health response to air pollution

Authors: Nazanin Zounemat-Kermani, Sadjad Naderi, Claire H. Dilliway, Claire E. Heaney, Shrreya Behll, Boyang Chen, Hisham Abubakar-Waziri, Alexandra E. Porter, Marc Chadeau-Hyam, Fangxin Fang, Ian M. Adcock, Kian Fan Chung, Christopher C. Pain

Abstract: Air pollution is a growing global health threat, exacerbated by climate change and linked to cardiovascular and respiratory diseases. While personal sensing devices enable real-time physiological monitoring, their integration with environmental data for individualised health prediction remains underdeveloped. Here, we present a modular, cloud-based framework that predicts personalised physiologica… ▽ More Air pollution is a growing global health threat, exacerbated by climate change and linked to cardiovascular and respiratory diseases. While personal sensing devices enable real-time physiological monitoring, their integration with environmental data for individualised health prediction remains underdeveloped. Here, we present a modular, cloud-based framework that predicts personalised physiological responses to pollution by combining wearable-derived data with real-time environmental exposures. At its core is an Adversarial Autoencoder (AAE), initially trained on high-resolution pollution-health data from the INHALE study and fine-tuned using smartwatch data via transfer learning to capture individual-specific patterns. Consistent with changes in pollution levels commonly observed in the real-world, simulated pollution spikes (+100%) revealed modest but measurable increases in vital signs (e.g., +2.5% heart rate, +3.5% breathing rate). To assess clinical relevance, we analysed U-BIOPRED data and found that individuals with such subclinical vital sign elevations had higher asthma burden scores or elevated Fractional Exhaled Nitric Oxide (FeNO), supporting the physiological validity of these AI-predicted responses. This integrative approach demonstrates the feasibility of anticipatory, personalised health modelling in response to environmental challenges, offering a scalable and secure infrastructure for AI-driven environmental health monitoring. △ Less

Submitted 13 January, 2026; v1 submitted 15 May, 2025; originally announced May 2025.

Comments: Zounemat-Kermani and Naderi share first authorship. 22 pages, 5 figures and 1 table

Online learning to accelerate nonlinear PDE solvers: applied to multiphase porous media flow

Authors: Vinicius L S Silva, Pablo Salinas, Claire E Heaney, Matthew Jackson, Christopher C Pain

Abstract: We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed method rely on four pillars: (i) dimensionless numbers as input parameters for the machine learning model, (ii) simplified numerical model (two-dimensional) fo… ▽ More We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed method rely on four pillars: (i) dimensionless numbers as input parameters for the machine learning model, (ii) simplified numerical model (two-dimensional) for the offline training, (iii) dynamic control of a nonlinear solver tuning parameter (numerical relaxation), (iv) and online learning for real-time improvement of the machine learning model. This strategy decreases the number of nonlinear iterations by dynamically modifying a single global parameter, the relaxation factor, and by adaptively learning the attributes of each numerical model on-the-run. Furthermore, this work performs a sensitivity study in the dimensionless parameters (machine learning features), assess the efficacy of various machine learning models, demonstrate a decrease in nonlinear iterations using our method in more intricate, realistic three-dimensional models, and fully couple a machine learning model into an open-source multiphase flow simulator achieving up to 85\% reduction in computational time. △ Less

Submitted 25 April, 2025; originally announced April 2025.

Rapid modelling of reactive transport in porous media using machine learning: limitations and solutions

Authors: Vinicius L S Silva, Geraldine Regnier, Pablo Salinas, Claire E Heaney, Matthew D Jackson, Christopher C Pain

Abstract: Reactive transport in porous media plays a pivotal role in subsurface reservoir processes, influencing fluid properties and geochemical characteristics. However, coupling fluid flow and transport with geochemical reactions is computationally intensive, requiring geochemical calculations at each grid cell and each time step within a discretized simulation domain. Although recent advancements have i… ▽ More Reactive transport in porous media plays a pivotal role in subsurface reservoir processes, influencing fluid properties and geochemical characteristics. However, coupling fluid flow and transport with geochemical reactions is computationally intensive, requiring geochemical calculations at each grid cell and each time step within a discretized simulation domain. Although recent advancements have integrated machine learning techniques as surrogates for geochemical simulations, ensuring computational efficiency and accuracy remains a challenge. This work investigates machine learning models as replacements for a geochemical module in a simulation of reactive transport in porous media. As a proof of concept, we test this approach on a well-documented cation exchange problem. While the surrogate models excel in isolated predictions, they fall short in rollout predictions over successive time steps. By introducing modifications, including physics-based constraints and tailored dataset generation strategies, we show that machine learning surrogates can achieve accurate rollout predictions. Our findings emphasize that even for a simple sorption equilibrium reaction (cation exchange problem), machine learning surrogates alone fail in predicting over successive time-steps. Incorporating simple physics-based modifications enables us to overcome this limitation. A detailed analysis of the limitations and potential mitigation strategies is presented in this work. △ Less

Submitted 25 April, 2025; v1 submitted 23 May, 2024; originally announced May 2024.

Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamics

Authors: Boyang Chen, Claire E. Heaney, Christopher C. Pain

Abstract: Numerical discretisations of partial differential equations (PDEs) can be written as discrete convolutions, which, themselves, are a key tool in AI libraries and used in convolutional neural networks (CNNs). We therefore propose to implement numerical discretisations as convolutional layers of a neural network, where the weights or filters are determined analytically rather than by training. Furth… ▽ More Numerical discretisations of partial differential equations (PDEs) can be written as discrete convolutions, which, themselves, are a key tool in AI libraries and used in convolutional neural networks (CNNs). We therefore propose to implement numerical discretisations as convolutional layers of a neural network, where the weights or filters are determined analytically rather than by training. Furthermore, we demonstrate that these systems can be solved entirely by functions in AI libraries, either by using Jacobi iteration or multigrid methods, the latter realised through a U-Net architecture. Some advantages of the Neural Physics approach are that (1) the methods are platform agnostic; (2) the resulting solvers are fully differentiable, ideal for optimisation tasks; and (3) writing CFD solvers as (untrained) neural networks means that they can be seamlessly integrated with trained neural networks to form hybrid models. We demonstrate the proposed approach on a number of test cases of increasing complexity from advection-diffusion problems, the non-linear Burgers equation to the Navier-Stokes equations. We validate the approach by comparing our results with solutions obtained from traditionally written code and common benchmarks from the literature. We show that the proposed methodology can solve all these problems using repurposed AI libraries in an efficient way, without training, and presents a new avenue to explore in the development of methods to solve PDEs with implicit methods. △ Less

Submitted 4 November, 2025; v1 submitted 27 February, 2024; originally announced February 2024.

Comments: 28 pages, 14 figures

Solving the Discretised Multiphase Flow Equations with Interface Capturing on Structured Grids Using Machine Learning Libraries

Authors: Boyang Chen, Claire E. Heaney, Jefferson L. M. A. Gomes, Omar K. Matar, Christopher C. Pain

Abstract: This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network whose weights are determined by the numerical method, rather than by training, and hence, we refer to this approach as Neural Networks for PDEs (NN4PDEs). To sol… ▽ More This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network whose weights are determined by the numerical method, rather than by training, and hence, we refer to this approach as Neural Networks for PDEs (NN4PDEs). To solve the discretised multiphase flow equations, a multigrid solver is implemented through a convolutional neural network with a U-Net architecture. Immiscible two-phase flow is modelled by the 3D incompressible Navier-Stokes equations with surface tension and advection of a volume fraction field, which describes the interface between the fluids. A new compressive algebraic volume-of-fluids method is introduced, based on a residual formulation using Petrov-Galerkin for accuracy and designed with NN4PDEs in mind. High-order finite-element based schemes are chosen to model a collapsing water column and a rising bubble. Results compare well with experimental data and other numerical results from the literature, demonstrating that, for the first time, finite element discretisations of multiphase flows can be solved using an approach based on (untrained) convolutional neural networks. A benefit of expressing numerical discretisations as neural networks is that the code can run, without modification, on CPUs, GPUs or the latest accelerators designed especially to run AI codes. △ Less

Submitted 3 March, 2024; v1 submitted 12 January, 2024; originally announced January 2024.

Comments: 34 pages, 18 figures, 4 tables

Solving the Discretised Boltzmann Transport Equations using Neural Networks: Applications in Neutron Transport

Authors: T. R. F. Phillips, C. E. Heaney, C. Boyang, A. G. Buchan, C. C. Pain

Abstract: In this paper we solve the Boltzmann transport equation using AI libraries. The reason why this is attractive is because it enables one to use the highly optimised software within AI libraries, enabling one to run on different computer architectures and enables one to tap into the vast quantity of community based software that has been developed for AI and ML applications e.g. mixed arithmetic pre… ▽ More In this paper we solve the Boltzmann transport equation using AI libraries. The reason why this is attractive is because it enables one to use the highly optimised software within AI libraries, enabling one to run on different computer architectures and enables one to tap into the vast quantity of community based software that has been developed for AI and ML applications e.g. mixed arithmetic precision or model parallelism. Here we take the first steps towards developing this approach for the Boltzmann transport equation and develop the necessary methods in order to do that effectively. This includes: 1) A space-angle multigrid solution method that can extract the level of parallelism necessary to run efficiently on GPUs or new AI computers. 2) A new Convolutional Finite Element Method (ConvFEM) that greatly simplifies the implementation of high order finite elements (quadratic to quintic, say). 3) A new non-linear Petrov-Galerkin method that introduces dissipation anisotropically. △ Less

Submitted 25 January, 2023; v1 submitted 24 January, 2023; originally announced January 2023.

Solving the Discretised Neutron Diffusion Equations using Neural Networks

Authors: T. R. F. Phillips, C. E. Heaney, C. Boyang, A. G. Buchan, C. C. Pain

Abstract: This paper presents a new approach which uses the tools within Artificial Intelligence (AI) software libraries as an alternative way of solving partial differential equations (PDEs) that have been discretised using standard numerical methods. In particular, we describe how to represent numerical discretisations arising from the finite volume and finite element methods by pre-determining the weight… ▽ More This paper presents a new approach which uses the tools within Artificial Intelligence (AI) software libraries as an alternative way of solving partial differential equations (PDEs) that have been discretised using standard numerical methods. In particular, we describe how to represent numerical discretisations arising from the finite volume and finite element methods by pre-determining the weights of convolutional layers within a neural network. As the weights are defined by the discretisation scheme, no training of the network is required and the solutions obtained are identical (accounting for solver tolerances) to those obtained with standard codes often written in Fortran or C++. We also explain how to implement the Jacobi method and a multigrid solver using the functions available in AI libraries. For the latter, we use a U-Net architecture which is able to represent a sawtooth multigrid method. A benefit of using AI libraries in this way is that one can exploit their power and their built-in technologies. For example, their executions are already optimised for different computer architectures, whether it be CPUs, GPUs or new-generation AI processors. In this article, we apply the proposed approach to eigenvalue problems in reactor physics where neutron transport is described by diffusion theory. For a fuel assembly benchmark, we demonstrate that the solution obtained from our new approach is the same (accounting for solver tolerances) as that obtained from the same discretisation coded in a standard way using Fortran. We then proceed to solve a reactor core benchmark using the new approach. △ Less

Submitted 24 January, 2023; originally announced January 2023.

Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models

Authors: Sibo Cheng, Jianhua Chen, Charitos Anastasiou, Panagiota Angeli, Omar K. Matar, Yi-Ke Guo, Christopher C. Pain, Rossella Arcucci

Abstract: Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a system which combines reduced-order surrogate models with a novel data assimilation (DA) technique used to incorporate real-time observations from different physical… ▽ More Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a system which combines reduced-order surrogate models with a novel data assimilation (DA) technique used to incorporate real-time observations from different physical spaces. We make use of local smooth surrogate functions which link the space of encoded system variables and the one of current observations to perform variational DA with a low computational cost. The new system, named Generalised Latent Assimilation can benefit both the efficiency provided by the reduced-order modelling and the accuracy of data assimilation. A theoretical analysis of the difference between surrogate and original assimilation cost function is also provided in this paper where an upper bound, depending on the size of the local training set, is given. The new approach is tested on a high-dimensional CFD application of a two-phase liquid flow with non-linear observation operators that current Latent Assimilation methods can not handle. Numerical results demonstrate that the proposed assimilation approach can significantly improve the reconstruction and prediction accuracy of the deep learning surrogate model which is nearly 1000 times faster than the CFD simulation. △ Less

Submitted 8 April, 2022; v1 submitted 7 April, 2022; originally announced April 2022.

An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes

Authors: Claire E. Heaney, Zef Wolffs, Jón Atli Tómasson, Lyes Kahouadji, Pablo Salinas, André Nicolle, Omar K. Matar, Ionel M. Navon, Narakorn Srinil, Christopher C. Pain

Abstract: The modelling of multiphase flow in a pipe presents a significant challenge for high-resolution computational fluid dynamics (CFD) models due to the high aspect ratio (length over diameter) of the domain. In subsea applications, the pipe length can be several hundreds of kilometres versus a pipe diameter of just a few inches. In this paper, we present a new AI-based non-intrusive reduced-order mod… ▽ More The modelling of multiphase flow in a pipe presents a significant challenge for high-resolution computational fluid dynamics (CFD) models due to the high aspect ratio (length over diameter) of the domain. In subsea applications, the pipe length can be several hundreds of kilometres versus a pipe diameter of just a few inches. In this paper, we present a new AI-based non-intrusive reduced-order model within a domain decomposition framework (AI-DDNIROM) which is capable of making predictions for domains significantly larger than the domain used in training. This is achieved by using domain decomposition; dimensionality reduction; training a neural network to make predictions for a single subdomain; and by using an iteration-by-subdomain technique to converge the solution over the whole domain. To find the low-dimensional space, we explore several types of autoencoder networks, known for their ability to compress information accurately and compactly. The performance of the autoencoders is assessed on two advection-dominated problems: flow past a cylinder and slug flow in a pipe. To make predictions in time, we exploit an adversarial network which aims to learn the distribution of the training data, in addition to learning the mapping between particular inputs and outputs. This type of network has shown the potential to produce realistic outputs. The whole framework is applied to multiphase slug flow in a horizontal pipe for which an AI-DDNIROM is trained on high-fidelity CFD simulations of a pipe of length 10 m with an aspect ratio of 13:1, and tested by simulating the flow for a pipe of length 98 m with an aspect ratio of almost 130:1. Statistics of the flows obtained from the CFD simulations are compared to those of the AI-DDNIROM predictions to demonstrate the success of our approach. △ Less

Submitted 12 February, 2022; originally announced February 2022.

Comments: 38 pages, 11 figures

Generative Network-Based Reduced-Order Model for Prediction, Data Assimilation and Uncertainty Quantification

Authors: Vinicius L. S. Silva, Claire E. Heaney, Nenko Nenov, Christopher C. Pain

Abstract: We propose a new method in which a generative network (GN) integrate into a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and estimate the corresponding uncertainties associated with the states and parameters of a numerical physical simulation. The GN is trained using only unconditional sim… ▽ More We propose a new method in which a generative network (GN) integrate into a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and estimate the corresponding uncertainties associated with the states and parameters of a numerical physical simulation. The GN is trained using only unconditional simulations of the discretized PDE model. We compare the proposed method with the golden standard Markov chain Monte Carlo. We apply the proposed approaches to a spatio-temporal compartmental model in epidemiology. The results show that the proposed GN-based ROM can efficiently quantify uncertainty and accurately match the measurements and the golden standard, using only a few unconditional simulations of the full-order numerical PDE model. △ Less

Submitted 5 September, 2023; v1 submitted 28 May, 2021; originally announced May 2021.

Comments: arXiv admin note: text overlap with arXiv:2105.07729

Journal ref: Journal of Computational Science Volume 83, December 2024, 102451

Data Assimilation Predictive GAN (DA-PredGAN): applied to determine the spread of COVID-19

Authors: Vinicius L. S. Silva, Claire E. Heaney, Yaqi Li, Christopher C. Pain

Abstract: We propose the novel use of a generative adversarial network (GAN) (i) to make predictions in time (PredGAN) and (ii) to assimilate measurements (DA-PredGAN). In the latter case, we take advantage of the natural adjoint-like properties of generative models and the ability to simulate forwards and backwards in time. GANs have received much attention recently, after achieving excellent results for t… ▽ More We propose the novel use of a generative adversarial network (GAN) (i) to make predictions in time (PredGAN) and (ii) to assimilate measurements (DA-PredGAN). In the latter case, we take advantage of the natural adjoint-like properties of generative models and the ability to simulate forwards and backwards in time. GANs have received much attention recently, after achieving excellent results for their generation of realistic-looking images. We wish to explore how this property translates to new applications in computational modelling and to exploit the adjoint-like properties for efficient data assimilation. To predict the spread of COVID-19 in an idealised town, we apply these methods to a compartmental model in epidemiology that is able to model space and time variations. To do this, the GAN is set within a reduced-order model (ROM), which uses a low-dimensional space for the spatial distribution of the simulation states. Then the GAN learns the evolution of the low-dimensional states over time. The results show that the proposed methods can accurately predict the evolution of the high-fidelity numerical simulation, and can efficiently assimilate observed data and determine the corresponding model parameters. △ Less

Submitted 18 June, 2021; v1 submitted 17 May, 2021; originally announced May 2021.

Journal ref: Journal of Scientific Computing, 94(1), p.25. 2023

Real-time Updating of Dynamic Social Networks for COVID-19 Vaccination Strategies

Authors: Sibo Cheng, Christopher C. Pain, Yi-Ke Guo, Rossella Arcucci

Abstract: Vaccination strategy is crucial in fighting against the COVID-19 pandemic. Since the supply is limited, contact network-based interventions can be most powerful to set an optimal strategy by identifying high-risk individuals or communities. However, due to the high dimension, only partial and noisy network information can be available in practice, especially for dynamical systems where the contact… ▽ More Vaccination strategy is crucial in fighting against the COVID-19 pandemic. Since the supply is limited, contact network-based interventions can be most powerful to set an optimal strategy by identifying high-risk individuals or communities. However, due to the high dimension, only partial and noisy network information can be available in practice, especially for dynamical systems where the contact networks are highly time-variant. Furthermore, numerous mutations of SARS-CoV-2 impact considerably the current infectious probability, requiring real-time network updating algorithms. In this study, we propose a sequential network updating approach based on data assimilation techniques to combine different sources of temporal information. We then prioritise the individuals with high-degree or high-centrality, obtained from the assimilated networks, for vaccination. The assimilation-based approach is compared with the standard method (based on partially observed networks) and a random selection strategy in terms of vaccination effectiveness in a SIR model. The numerical comparison is first carried out using real-world face-to-face dynamical networks collected in a high school, following by sequential multi-layer networks, generated relying on the Barabasi-Albert model emulating the department of Computing at Imperial College London in the UK as an example. △ Less

Submitted 9 August, 2021; v1 submitted 19 February, 2021; originally announced March 2021.

Numerical study of COVID-19 spatial-temporal spreading in London

Authors: J. Zheng, X. Wu, F. Fang, J. Li, Z. Wang, H. Xiao, J. Zhu, C. C. Pain, P. F. Linden, B. Xiang

Abstract: Recent study reported that an aerosolised virus (COVID-19) can survive in the air for a few hours. It is highly possible that people get infected with the disease by breathing and contact with items contaminated by the aerosolised virus. However, the aerosolised virus transmission and trajectories in various meteorological environments remain unclear. This paper has investigated the movement of ae… ▽ More Recent study reported that an aerosolised virus (COVID-19) can survive in the air for a few hours. It is highly possible that people get infected with the disease by breathing and contact with items contaminated by the aerosolised virus. However, the aerosolised virus transmission and trajectories in various meteorological environments remain unclear. This paper has investigated the movement of aerosolised viruses from a high concentration source across a dense urban area. The case study looks at the highly air polluted areas of London: University College Hospital (UCH) and King Cross and St Pancras International Station (KCSPI). We explored the spread and decay of COVID-19 released from the hospital and railway stations with the prescribed meteorological conditions. The study has three key findings: the primary result is that it is possible for the virus to travel from meters up to hundred meters from the source location. The secondary finding shows viruses released into the atmosphere from entry and exit points at KCSPI remain trapped within a small radial distance of < 50m. This strengthens the case for the use of face coverings to reduce the infection rate. The final finding shows that there are different levels of risk at various door locations for UCH, depending on which door is used there can be a higher concentration of COVID-19. Although our results are based on London, since the fundamental knowledge processes are the same, our study can be further extended to other locations (especially the highly air polluted areas) in the world. △ Less

Submitted 22 February, 2021; v1 submitted 19 February, 2021; originally announced February 2021.

Comments: 15 pages, 6 figures

Digital twins based on bidirectional LSTM and GAN for modelling the COVID-19 pandemic

Authors: César Quilodrán-Casas, Vinicius Santos Silva, Rossella Arcucci, Claire E. Heaney, Yike Guo, Christopher C. Pain

Abstract: The outbreak of the coronavirus disease 2019 (COVID-19) has now spread throughout the globe infecting over 150 million people and causing the death of over 3.2 million people. Thus, there is an urgent need to study the dynamics of epidemiological models to gain a better understanding of how such diseases spread. While epidemiological models can be computationally expensive, recent advances in mach… ▽ More The outbreak of the coronavirus disease 2019 (COVID-19) has now spread throughout the globe infecting over 150 million people and causing the death of over 3.2 million people. Thus, there is an urgent need to study the dynamics of epidemiological models to gain a better understanding of how such diseases spread. While epidemiological models can be computationally expensive, recent advances in machine learning techniques have given rise to neural networks with the ability to learn and predict complex dynamics at reduced computational costs. Here we introduce two digital twins of a SEIRS model applied to an idealised town. The SEIRS model has been modified to take account of spatial variation and, where possible, the model parameters are based on official virus spreading data from the UK. We compare predictions from a data-corrected Bidirectional Long Short-Term Memory network and a predictive Generative Adversarial Network. The predictions given by these two frameworks are accurate when compared to the original SEIRS model data. Additionally, these frameworks are data-agnostic and could be applied to towns, idealised or real, in the UK or in other countries. Also, more compartments could be included in the SEIRS model, in order to study more realistic epidemiological behaviour. △ Less

Submitted 7 May, 2021; v1 submitted 3 February, 2021; originally announced February 2021.

Comments: 44 pages, 17 figures, 3 tables

Applying Convolutional Neural Networks to Data on Unstructured Meshes with Space-Filling Curves

Authors: Claire E. Heaney, Yuling Li, Omar K. Matar, Christopher C. Pain

Abstract: This paper presents the first classical Convolutional Neural Network (CNN) that can be applied directly to data from unstructured finite element meshes or control volume grids. CNNs have been hugely influential in the areas of image classification and image compression, both of which typically deal with data on structured grids. Unstructured meshes are frequently used to solve partial differential… ▽ More This paper presents the first classical Convolutional Neural Network (CNN) that can be applied directly to data from unstructured finite element meshes or control volume grids. CNNs have been hugely influential in the areas of image classification and image compression, both of which typically deal with data on structured grids. Unstructured meshes are frequently used to solve partial differential equations and are particularly suitable for problems that require the mesh to conform to complex geometries or for problems that require variable mesh resolution. Central to the approach are space-filling curves, which traverse the nodes or cells of a mesh tracing out a path that is as short as possible (in terms of numbers of edges) and that visits each node or cell exactly once. The space-filling curves (SFCs) are used to find an ordering of the nodes or cells that can transform multi-dimensional solutions on unstructured meshes into a one-dimensional (1D) representation, to which 1D convolutional layers can then be applied. Although developed in two dimensions, the approach is applicable to higher dimensional problems. To demonstrate the approach, the network we choose is a convolutional autoencoder (CAE) although other types of CNN could be used. The approach is tested by applying CAEs to data sets that have been reordered with an SFC. Sparse layers are used at the input and output of the autoencoder, and the use of multiple SFCs is explored. We compare the accuracy of the SFC-based CAE with that of a classical CAE applied to two idealised problems on structured meshes, and then apply the approach to solutions of flow past a cylinder obtained using the finite-element method and an unstructured mesh. △ Less

Submitted 4 January, 2021; v1 submitted 23 November, 2020; originally announced November 2020.

Comments: 17 figures, 52 pages

An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion

Authors: Toby Phillips, Claire E. Heaney, Paul N. Smith, Christopher C. Pain

Abstract: Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional space in which a high-dimensional system is approximated. Proper orthogonal decomposition (POD) and singular value decomposition (SVD) are often used for this pu… ▽ More Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional space in which a high-dimensional system is approximated. Proper orthogonal decomposition (POD) and singular value decomposition (SVD) are often used for this purpose and yield an optimal linear subspace. Autoencoders provide a nonlinear alternative to POD/SVD, that may capture, more efficiently, features or patterns in the high-fidelity model results. Reduced-order models based on an autoencoder and a novel hybrid SVD-autoencoder are developed. These methods are compared with the standard POD-Galerkin approach and are applied to two test cases taken from the field of nuclear reactor physics. △ Less

Submitted 15 August, 2020; originally announced August 2020.

Comments: 35 pages, 33 figures

Data-driven modelling of nonlinear spatio-temporal fluid flows using a deep convolutional generative adversarial network

Authors: M. Cheng, F. Fang, C. C. Pain, I. M. Navon

Abstract: Deep learning techniques for improving fluid flow modelling have gained significant attention in recent years. Advanced deep learning techniques achieve great progress in rapidly predicting fluid flows without prior knowledge of the underlying physical relationships. Advanced deep learning techniques achieve great progress in rapidly predicting fluid flows without prior knowledge of the underlying… ▽ More Deep learning techniques for improving fluid flow modelling have gained significant attention in recent years. Advanced deep learning techniques achieve great progress in rapidly predicting fluid flows without prior knowledge of the underlying physical relationships. Advanced deep learning techniques achieve great progress in rapidly predicting fluid flows without prior knowledge of the underlying physical relationships. However, most of existing researches focused mainly on either sequence learning or spatial learning, rarely on both spatial and temporal dynamics of fluid flows (Reichstein et al., 2019). In this work, an Artificial Intelligence (AI) fluid model based on a general deep convolutional generative adversarial network (DCGAN) has been developed for predicting spatio-temporal flow distributions. In deep convolutional networks, the high-dimensional flows can be converted into the low-dimensional "latent" representations. The complex features of flow dynamics can be captured by the adversarial networks. The above DCGAN fluid model enables us to provide reasonable predictive accuracy of flow fields while maintaining a high computational efficiency. The performance of the DCGAN is illustrated for two test cases of Hokkaido tsunami with different incoming waves along the coastal line. It is demonstrated that the results from the DCGAN are comparable with those from the original high fidelity model (Fluidity). The spatio-temporal flow features have been represented as the flow evolves, especially, the wave phases and flow peaks can be captured accurately. In addition, the results illustrate that the online CPU cost is reduced by five orders of magnitude compared to the original high fidelity model simulations. The promising results show that the DCGAN can provide rapid and reliable spatio-temporal prediction for nonlinear fluid flows. △ Less

Submitted 12 March, 2020; originally announced April 2020.

Goal-based sensitivity maps using time windows and ensemble perturbations

Authors: C. E. Heaney, P. Salinas, F. Fang, C. C. Pain, I. M. Navon

Abstract: We present an approach for forming sensitivity maps (or sensitivites) using ensembles. The method is an alternative to using an adjoint, which can be very challenging to formulate and also computationally expensive to solve. The main novelties of the presented approach are: 1) the use of goals, weighting the perturbation to help resolve the most important sensitivities, 2) the use of time windows,… ▽ More We present an approach for forming sensitivity maps (or sensitivites) using ensembles. The method is an alternative to using an adjoint, which can be very challenging to formulate and also computationally expensive to solve. The main novelties of the presented approach are: 1) the use of goals, weighting the perturbation to help resolve the most important sensitivities, 2) the use of time windows, which enable the perturbations to be optimised independently for each window and 3) re-orthogonalisation of the solution through time, which helps optimise each perturbation when calculating sensitivity maps. These novel methods greatly reduce the number of ensembles required to form the sensitivity maps as demonstrated in this paper. As the presented method relies solely on ensembles obtained from the forward model, it can therefore be applied directly to forward models of arbitrary complexity arising from, for example, multi-physics coupling, legacy codes or model chains. It can also be applied to compute sensitivities for optimisation of sensor placement, optimisation for design or control, goal-based mesh adaptivity, assessment of goals (e.g. hazard assessment and mitigation in the natural environment), determining the worth of current data and data assimilation. We analyse and demonstrate the efficiency of the approach by applying the method to advection problems and also a non-linear heterogeneous multi-phase porous media problem, showing, in all cases, that the number of ensembles required to obtain accurate sensitivity maps is relatively low, in the order of 10s. △ Less

Submitted 20 September, 2018; v1 submitted 12 April, 2018; originally announced April 2018.

Comments: 35 pages, 13 figures. Submitted to JCP in September 2018 Changes: additional context given in the introduction, additional explanation given in section 2.2, some changes to equations. Results unchanged