The concept of a “digital twin” as a model for data-driven management and control of physical systems has emerged over the past decade in the domains of manufacturing, production, and operations. In the context of buildings and civil infrastructure, the notion of a digital twin remains ill-defined, with little or no consensus among researchers and practitioners of the ways in which digital twin processes and data-centric technologies can support design and construction. This paper builds on existing concepts of Building Information Modeling (BIM), lean project production systems, automated data acquisition from construction sites and supply chains, and artificial intelligence to formulate a mode of construction that applies digital twin information systems to achieve closed loop control systems. It contributes a set of four core information and control concepts for digital twin construction (DTC), which define the dimensions of the conceptual space for the information used in DTC workflows. Working from the core concepts, we propose a DTC information system workflow—including information stores, information processing functions, and monitoring technologies—according to three concentric control workflow cycles. DTC should be viewed as a comprehensive mode of construction that prioritizes closing the control loops rather than an extension of BIM tools integrated with sensing and monitoring technologies.

This paper introduces a dynamic knowledge-graph approach for digital twins and illustrates how this approach is by design naturally suited to realizing the vision of a Universal Digital Twin. The dynamic knowledge graph is implemented using technologies from the Semantic Web. It is composed of concepts and instances that are defined using ontologies, and of computational agents that operate on both the concepts and instances to update the dynamic knowledge graph. By construction, it is distributed, supports cross-domain interoperability, and ensures that data are connected, portable, discoverable, and queryable via a uniform interface. The knowledge graph includes the notions of a “base world” that describes the real world and that is maintained by agents that incorporate real-time data, and of “parallel worlds” that support the intelligent exploration of alternative designs without affecting the base world. Use cases are presented that demonstrate the ability of the dynamic knowledge graph to host geospatial and chemical data, control chemistry experiments, perform cross-domain simulations, and perform scenario analysis. The questions of how to make intelligent suggestions for alternative scenarios and how to ensure alignment between the scenarios considered by the knowledge graph and the goals of society are considered. Work to extend the dynamic knowledge graph to develop a digital twin of the UK to support the decarbonization of the energy system is discussed. Important directions for future research are highlighted.

This paper presents the development process of a digital twin of a unique hydroponic underground farm in London, Growing Underground (GU). Growing 12x more per unit area than traditional greenhouse farming in the UK, the farm also consumes 4x more energy per unit area. Key to the ongoing operational success of this farm and similar enterprises is finding ways to minimize the energy use while maximizing crop growth by maintaining optimal growing conditions. As such, it belongs to the class of Controlled Environment Agriculture, where indoor environments are carefully controlled to maximize crop growth by using artificial lighting and smart heating, ventilation, and air conditioning systems. We tracked changing environmental conditions and crop growth across 89 different variables, through a wireless sensor network and unstructured manual records, and combined all the data into a database. We show how the digital twin can provide enhanced outputs for a bespoke site like GU, by creating inferred data fields, and show the limitations of data collection in a commercial environment. For example, we find that lighting is the dominant environmental factor for temperature and thus crop growth in this farm, and that the effects of external temperature and ventilation are confounded. We combine information learned from historical data interpretation to create a bespoke temperature forecasting model (root mean squared error < 1.3°C), using a dynamic linear model with a data-centric lighting component. Finally, we present how the forecasting model can be integrated into the digital twin to provide feedback to the farmers for decision-making assistance.

The Poisson equation is commonly encountered in engineering, for instance, in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field. In the present work, we propose a novel fully convolutional neural network (CNN) architecture to infer the solution of the Poisson equation on a 2D Cartesian grid with different resolutions given the right-hand side term, arbitrary boundary conditions, and grid parameters. It provides unprecedented versatility for a CNN approach dealing with partial differential equations. The boundary conditions are handled using a novel approach by decomposing the original Poisson problem into a homogeneous Poisson problem plus four inhomogeneous Laplace subproblems. The model is trained using a novel loss function approximating the continuous $ {L}^p $ norm between the prediction and the target. Even when predicting on grids denser than previously encountered, our model demonstrates encouraging capacity to reproduce the correct solution profile. The proposed model, which outperforms well-known neural network models, can be included in a CFD solver to help with solving the Poisson equation. Analytical test cases indicate that our CNN architecture is capable of predicting the correct solution of a Poisson problem with mean percentage errors below 10%, an improvement by comparison to the first step of conventional iterative methods. Predictions from our model, used as the initial guess to iterative algorithms like Multigrid, can reduce the root mean square error after a single iteration by more than 90% compared to a zero initial guess.

The monitoring of infrastructure assets using sensor networks is becoming increasingly prevalent. A digital twin in the form of a finite element (FE) model, as commonly used in design and construction, can help make sense of the copious amount of collected sensor data. This paper demonstrates the application of the statistical finite element method (statFEM), which provides a principled means of synthesizing data and physics-based models, in developing a digital twin of a self-sensing structure. As a case study, an instrumented steel railway bridge of $ 27.34\hskip1.5pt \mathrm{m} $ length located along the West Coast Mainline near Staffordshire in the UK is considered. Using strain data captured from fiber Bragg grating sensors at 108 locations along the bridge superstructure, statFEM can predict the “true” system response while taking into account the uncertainties in sensor readings, applied loading, and FE model misspecification errors. Longitudinal strain distributions along the two main I-beams are both measured and modeled during the passage of a passenger train. The statFEM digital twin is able to generate reasonable strain distribution predictions at locations where no measurement data are available, including at several points along the main I-beams and on structural elements on which sensors are not even installed. The implications for long-term structural health monitoring and assessment include optimization of sensor placement and performing more reliable what-if analyses at locations and under loading scenarios for which no measurement data are available.

Recent work has demonstrated the use of sparse sensors in combination with the proper orthogonal decomposition (POD) to produce data-driven reconstructions of the full velocity fields in a variety of flows. The present work investigates the fidelity of such techniques applied to a stalled NACA 0012 aerofoil at $ {Re}_c=75,000 $ at an angle of attack $ \alpha ={12}^{\circ } $ as measured experimentally using planar time-resolved particle image velocimetry. In contrast to many previous studies, the flow is absent of any dominant shedding frequency and exhibits a broad range of singular values due to the turbulence in the separated region. Several reconstruction methodologies for linear state estimation based on classical compressed sensing and extended POD methodologies are presented as well as nonlinear refinement through the use of a shallow neural network (SNN). It is found that the linear reconstructions inspired by the extended POD are inferior to the compressed sensing approach provided that the sparse sensors avoid regions of the flow with small variance across the global POD basis. Regardless of the linear method used, the nonlinear SNN gives strikingly similar performance in its refinement of the reconstructions. The capability of sparse sensors to reconstruct separated turbulent flow measurements is further discussed and directions for future work suggested.

Assimilation of continuously streamed monitored data is an essential component of a digital twin; the assimilated data are used to ensure the digital twin represents the monitored system as accurately as possible. One way this is achieved is by calibration of simulation models, whether data-derived or physics-based, or a combination of both. Traditional manual calibration is not possible in this context; hence, new methods are required for continuous calibration. In this paper, a particle filter methodology for continuous calibration of the physics-based model element of a digital twin is presented and applied to an example of an underground farm. The methodology is applied to a synthetic problem with known calibration parameter values prior to being used in conjunction with monitored data. The proposed methodology is compared against static and sequential Bayesian calibration approaches and compares favourably in terms of determination of the distribution of parameter values and analysis run times, both essential requirements. The methodology is shown to be potentially useful as a means to ensure continuing model fidelity.

Physics-informed machine learning (PIML) has emerged as a promising new approach for simulating complex physical and biological systems that are governed by complex multiscale processes for which some data are also available. In some instances, the objective is to discover part of the hidden physics from the available data, and PIML has been shown to be particularly effective for such problems for which conventional methods may fail. Unlike commercial machine learning where training of deep neural networks requires big data, in PIML big data are not available. Instead, we can train such networks from additional information obtained by employing the physical laws and evaluating them at random points in the space–time domain. Such PIML integrates multimodality and multifidelity data with mathematical models, and implements them using neural networks or graph networks. Here, we review some of the prevailing trends in embedding physics into machine learning, using physics-informed neural networks (PINNs) based primarily on feed-forward neural networks and automatic differentiation. For more complex systems or systems of systems and unstructured data, graph neural networks (GNNs) present some distinct advantages, and here we review how physics-informed learning can be accomplished with GNNs based on graph exterior calculus to construct differential operators; we refer to these architectures as physics-informed graph networks (PIGNs). We present representative examples for both forward and inverse problems and discuss what advances are needed to scale up PINNs, PIGNs and more broadly GNNs for large-scale engineering problems.

This paper presents Parallel World Framework as a solution for simulations of complex systems within a time-varying knowledge graph and its application to the electric grid of Jurong Island in Singapore. The underlying modeling system is based on the Semantic Web Stack. Its linked data layer is described by means of ontologies, which span multiple domains. The framework is designed to allow what-if scenarios to be simulated generically, even for complex, inter-linked, cross-domain applications, as well as conducting multi-scale optimizations of complex superstructures within the system. Parallel world containers, introduced by the framework, ensure data separation and versioning of structures crossing various domain boundaries. Separation of operations, belonging to a particular version of the world, is taken care of by a scenario agent. It encapsulates functionality of operations on data and acts as a parallel world proxy to all of the other agents operating on the knowledge graph. Electric network optimization for carbon tax is demonstrated as a use case. The framework allows to model and evaluate electrical networks corresponding to set carbon tax values by retrofitting different types of power generators and optimizing the grid accordingly. The use case shows the possibility of using this solution as a tool for CO2 reduction modeling and planning at scale due to its distributed architecture.

A framework is proposed for generative models as a basis for digital twins or mirrors of structures. The proposal is based on the premise that deterministic models cannot account for the uncertainty present in most structural modeling applications. Two different types of generative models are considered here. The first is a physics-based model based on the stochastic finite element (SFE) method, which is widely used when modeling structures that have material and loading uncertainties imposed. Such models can be calibrated according to data from the structure and would be expected to outperform any other model if the modeling accurately captures the true underlying physics of the structure. The potential use of SFE models as digital mirrors is illustrated via application to a linear structure with stochastic material properties. For situations where the physical formulation of such models does not suffice, a data-driven framework is proposed, using machine learning and conditional generative adversarial networks (cGANs). The latter algorithm is used to learn the distribution of the quantity of interest in a structure with material nonlinearities and uncertainties. For the examples considered in this work, the data-driven cGANs model outperforms the physics-based approach. Finally, an example is shown where the two methods are coupled such that a hybrid model approach is demonstrated.

The search space for new thermoelectric oxides has been limited to the alloys of a few known systems, such as ZnO, SrTiO3, and CaMnO3. Notwithstanding the high power factor, their high thermal conductivity is a roadblock in achieving higher efficiency. In this paper, we apply machine learning (ML) models for discovering novel transition metal oxides with low lattice thermal conductivity ($ {k}_L $). A two-step process is proposed to address the problem of small datasets frequently encountered in material informatics. First, a gradient-boosted tree classifier is learnt to categorize unknown compounds into three categories of $ {k}_L $: low, medium, and high. In the second step, we fit regression models on the targeted class (i.e., low $ {k}_L $) to estimate $ {k}_L $ with an $ {R}^2>0.9 $. Gradient boosted tree model was also used to identify key material properties influencing classification of $ {k}_L $, namely lattice energy per atom, atom density, band gap, mass density, and ratio of oxygen by transition metal atoms. Only fundamental materials properties describing the crystal symmetry, compound chemistry, and interatomic bonding were used in the classification process, which can be readily used in the initial phases of materials design. The proposed two-step process addresses the problem of small datasets and improves the predictive accuracy. The ML approach adopted in the present work is generic in nature and can be combined with high-throughput computing for the rapid discovery of new materials for specific applications.

This article develops an ontological description of land use and applies it to incorporate geospatial information describing land coverage into a knowledge-graph-based Universal Digital Twin. Sources of data relating to land use in the UK have been surveyed. The Crop Map of England (CROME) is produced annually by the UK Government and was identified as a valuable source of open data. Formal ontologies to represent land use and the geospatial data arising from such surveys have been developed. The ontologies have been deployed using a high-performance graph database. A customized vocabulary was developed to extend the geospatial capabilities of the graph database to support the CROME data. The integration of the CROME data into the Universal Digital Twin is demonstrated in two use cases that show the potential of the Universal Digital Twin to share data across sectors. The first use case combines data about land use with a geospatial analysis of scenarios for energy provision. The second illustrates how the Universal Digital Twin could use the land use data to support the cross-domain analysis of flood risk. Opportunities for the extension and enrichment of the ontologies, and further development of the Universal Digital Twin are discussed.

Conveyor belt wear is an important consideration in the bulk materials handling industry. We define four belt wear rate metrics and develop a model to predict wear rates of new conveyor configurations using an industry dataset that includes ultrasonic thickness measurements, conveyor attributes, and conveyor throughput. All variables are expected to contribute in some way to explaining wear rate and are included in modeling. One specific metric, the maximum throughput-based wear rate, is selected as the prediction target, and cross-validation is used to evaluate the out-of-sample performance of random forest and linear regression algorithms. The random forest approach achieves a lower error of 0.152 mm/megatons (standard deviation [SD] = 0.0648). Permutation importance and partial dependence plots are computed to provide insights into the relationship between conveyor parameters and wear rate. This work demonstrates how belt wear rate can be quantified from imprecise thickness testing methods and provides a transparent modeling framework applicable to other supervised learning problems in risk and reliability.

The digital twin concept has developed as a method for extracting value from data, and is being developed as a new technique for the design and asset management of high-value engineering systems such as aircraft, energy generating plant, and wind turbines. In terms of implementation, many proprietary digital twin software solutions have been marketed in this domain. In contrast, this paper describes a recently released open-source software framework for digital twins, which provides a browser-based operational platform using Python and Flask. The new platform is intended to maximize connectivity between users and data obtained from the physical twin. This paper describes how this type of digital twin operational platform (DTOP) can be used to connect the physical twin and other Internet-of-Things devices to both users and cloud computing services. The current release of the software—DTOP-Cristallo—uses the example of a three-storey structure as the engineering asset to be managed. Within DTOP-Cristallo, specific engineering software tools have been developed for use in the digital twin, and these are used to demonstrate the concept. At this stage, the framework presented is a prototype. However, the potential for open-source digital twin software using network connectivity is a very large area for future research and development.

The concept of “hybrid twin” (HT) has recently received a growing interest thanks to the availability of powerful machine learning techniques. This twin concept combines physics-based models within a model order reduction framework—to obtain real-time feedback rates—and data science. Thus, the main idea of the HT is to develop on-the-fly data-driven models to correct possible deviations between measurements and physics-based model predictions. This paper is focused on the computation of stable, fast, and accurate corrections in the HT framework. Furthermore, regarding the delicate and important problem of stability, a new approach is proposed, introducing several subvariants and guaranteeing a low computational cost as well as the achievement of a stable time-integration.

Accurate prediction of laminar-turbulent transition is a critical element of computational fluid dynamics simulations for aerodynamic design across multiple flow regimes. Traditional methods of transition prediction cannot be easily extended to flow configurations where the transition process depends on a large set of parameters. In comparison, neural network methods allow higher dimensional input features to be considered without compromising the efficiency and accuracy of the traditional data-driven models. Neural network methods proposed earlier follow a cumbersome methodology of predicting instability growth rates over a broad range of frequencies, which are then processed to obtain the N-factor envelope, and then, the transition location based on the correlating N-factor. This paper presents an end-to-end transition model based on a recurrent neural network, which sequentially processes the mean boundary-layer profiles along the surface of the aerodynamic body to directly predict the N-factor envelope and the transition locations over a two-dimensional airfoil. The proposed transition model has been developed and assessed using a large database of 53 airfoils over a wide range of chord Reynolds numbers and angles of attack. The large universe of airfoils encountered in various applications causes additional difficulties. As such, we provide further insights on selecting training datasets from large amounts of available data. Although the proposed model has been analyzed for two-dimensional boundary layers in this paper, it can be easily generalized to other flows due to embedded feature extraction capability of convolutional neural network in the model.

We apply deep kernel learning (DKL), which can be viewed as a combination of a Gaussian process (GP) and a deep neural network (DNN), to compression ignition engine emissions and compare its performance to a selection of other surrogate models on the same dataset. Surrogate models are a class of computationally cheaper alternatives to physics-based models. High-dimensional model representation (HDMR) is also briefly discussed and acts as a benchmark model for comparison. We apply the considered methods to a dataset, which was obtained from a compression ignition engine and includes as outputs soot and NOx emissions as functions of 14 engine operating condition variables. We combine a quasi-random global search with a conventional grid-optimization method in order to identify suitable values for several DKL hyperparameters, which include network architecture, kernel, and learning parameters. The performance of DKL, HDMR, plain GPs, and plain DNNs is compared in terms of the root mean squared error (RMSE) of the predictions as well as computational expense of training and evaluation. It is shown that DKL performs best in terms of RMSE in the predictions whilst maintaining the computational cost at a reasonable level, and DKL predictions are in good agreement with the experimental emissions data.

Patient-specific surgical simulations require the patient-specific identification of the constitutive parameters. The sparsity of the experimental data and the substantial noise in the data (e.g., recovered during surgery) cause considerable uncertainty in the identification. In this exploratory work, parameter uncertainty for incompressible hyperelasticity, often used for soft tissues, is addressed by a probabilistic identification approach based on Bayesian inference. Our study particularly focuses on the uncertainty of the model: we investigate how the identified uncertainties of the constitutive parameters behave when different forms of model uncertainty are considered. The model uncertainty formulations range from uninformative ones to more accurate ones that incorporate more detailed extensions of incompressible hyperelasticity. The study shows that incorporating model uncertainty may improve the results, but this is not guaranteed.

This article applies a knowledge graph-based approach to unify multiple heterogeneous domains inherent in climate and energy supply research. Existing approaches that rely on bespoke models with spreadsheet-type inputs are noninterpretable, static and make it difficult to combine existing domain specific models. The difficulties inherent to this approach become increasingly prevalent as energy supply models gain complexity while society pursues a net-zero future. In this work, we develop new ontologies to extend the World Avatar knowledge graph to represent gas grids, gas consumption statistics, and climate data. Using a combination of the new and existing ontologies we construct a Universal Digital Twin that integrates data describing the systems of interest and specifies respective links between domains. We represent the UK gas transmission system, and HadUK-Grid climate data set as linked data for the first time, formally associating the data with the statistical output areas used to report governmental administrative data throughout the UK. We demonstrate how computational agents contained within the World Avatar can operate on the knowledge graph, incorporating live feeds of data such as instantaneous gas flow rates, as well as parsing information into interpretable forms such as interactive visualizations. Through this approach, we enable a dynamic, interpretable, modular, and cross-domain representation of the UK that enables domain specific experts to contribute toward a national-scale digital twin.

Data assimilation of flow measurements is an essential tool for extracting information in fluid dynamics problems. Recent works have shown that the physics-informed neural networks (PINNs) enable the reconstruction of unsteady fluid flows, governed by the Navier–Stokes equations, if the network is given enough flow measurements that are appropriately distributed in time and space. In many practical applications, however, experimental measurements involve only time-averaged quantities or their higher order statistics which are governed by the under-determined Reynolds-averaged Navier–Stokes (RANS) equations. In this study, we perform PINN-based reconstruction of time-averaged quantities of an unsteady flow from sparse velocity data. The applied technique leverages the time-averaged velocity data to infer unknown closure quantities (curl of unsteady RANS forcing), as well as to interpolate the fields from sparse measurements. Furthermore, the method’s capabilities are extended further to the assimilation of Reynolds stresses where PINNs successfully interpolate the data to complete the velocity as well as the stresses fields and gain insight into the pressure field of the investigated flow.