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An athlete's posture has a significant impact on aerodynamic drag. Although aerodynamic drag in different sports has been studied extensively, most studies have analysed only a limited number of positions, and no generalized methods for optimization are available. In this work, we present a methodology to perform athlete posture optimization with respect to aerodynamic drag reduction. The method combines the virtual skeleton methodology to adjust the athlete's posture, CFD simulations to evaluate the drag for a given posture, and efficient global optimization to find the optimum position. We demonstrate the method by optimizing the time trial position for a cyclist. The cyclist position was parameterized with 6 design parameters, and the optimization required 41 CFD simulations to converge. The optimal posture yielded a reduction in drag of 17 % compared to the initial posture (disregarding bicycle drag). The method has potential to make posture optimization more accessible across a wide range of sports, and lead to insight into the aerodynamic influence of posture in general.

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Physics-based models are computationally time-consuming and infeasible for real-time scenarios of urban drainage networks, and a surrogate model is needed to accelerate the online predictive modelling. Fully-connected neural networks (NNs) are potential surrogate models, but may suffer from low interpretability and efficiency in fitting complex targets. Owing to the state-of-the-art modelling power of graph neural networks (GNNs) and their match with urban drainage networks in the graph structure, this work proposes a GNN-based surrogate of the flow routing model for the hydraulic prediction problem of drainage networks, which regards recent hydraulic states as initial conditions, and future runoff and control policy as boundary conditions. To incorporate hydraulic constraints and physical relationships into drainage modelling, physics-guided mechanisms are designed on top of the surrogate model to restrict the prediction variables with flow balance and flooding occurrence constraints. According to case results in a stormwater network, the GNN-based model is more cost-effective with better hydraulic prediction accuracy than the NN-based model after equal training epochs, and the designed mechanisms further limit prediction errors with interpretable domain knowledge. As the model structure adheres to the flow routing mechanisms and hydraulic constraints in urban drainage networks, it provides an interpretable and effective solution for data-driven surrogate modelling. Simultaneously, the surrogate model accelerates the predictive modelling of urban drainage networks for real-time use compared with the physics-based model.

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A high failure rate is associated with fracture plates in proximal humerus fractures. The causes of failure remain unclear due to the complexity of the problem including the number and position of the screws, their length and orientation in the space. Finite element (FE) analysis has been used for the analysis of plating of proximal humeral fractures, but due to computational costs is unable to fully explore all potential screw combinations. Surrogate modelling is a viable solution, having the potential to significantly reduce the computational cost whilst requiring a moderate number of training sets. This study aimed to develop adaptive neural network (ANN)-based surrogate models to predict the strain in the humeral bone as a result of changing the length of the screws. The ANN models were trained using data from FE simulations of a single humerus, and after defining the best training sample size, multiple and single-output models were developed. The best performing ANN model was used to predict all the possible screw length configurations. The ANN predictions were compared with the FE results of unseen data, showing a good correlation (R2 = 0.99) and low levels of error (RMSE = 0.51%-1.83% strain). The ANN predictions of all possible screw length configurations showed that the screw that provided the medial support was the most influential on the predicted strain. Overall, the ANN-based surrogate model accurately captured bone strains and has the potential to be used for more complex problems with a larger number of variables.

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We developed a high-resolution machine learning based surrogate model to identify a robust land-use future for Australia which meets multiple UN Sustainable Development Goals. We compared machine learning models with different architectures to pick the best performing model considering the data type, accuracy metrics, ability to handle uncertainty and computational overhead requirement. The surrogate model, called ML-LUTO Spatial, was trained on the Land-Use Trade-Offs (version 1.0) model of Australian agricultural land system sustainability. Using the surrogate model, we generated projections of land-use futures at 1.1 km resolution with 95% classification accuracy, and which far surpassed the computational benchmarks of the original model. This efficiency enabled the generation of numerous SDG-compliant (SDGs 2, 6, 7, 13, 15) future land-use maps on a standard laptop, a task previously dependent upon high-performance computing clusters. Combining these projections, we derived a single, robust land-use future and quantified the uncertainty. Our findings indicate that while agricultural land-use remains dominant in all Australian regions, extensive carbon plantings were identified in Queensland and environmental plantings played a role across the study area, reflecting a growing urgency for offsetting greenhouse gas emissions and the restoration of ecosystems to support biodiversity across Australia to meet the 2050 Sustainable Development Goals.

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Accurately describing the evolution of water droplet size distribution in crude oil is fundamental for evaluating the water separation efficiency in dehydration systems. Enhancing the separation of an aqueous phase dispersed in a dielectric oil phase, which has a significantly lower dielectric constant than the dispersed phase, can be achieved by increasing the water droplet size through the application of an electrostatic field in the pipeline. Mathematical models, while being accurate, are computationally expensive. Herein, we introduced a constrained machine learning (ML) surrogate model developed based on a population balance model. This model serves as a practical alternative, facilitating fast and accurate predictions. The constrained ML model, utilizing an extreme gradient boosting (XGBoost) algorithm tuned with a genetic algorithm (GA), incorporates the key parameters of the electrostatic dehydration process, including droplet diameter, voltage, crude oil properties, temperature, and residence time as input variables, with the output being the number of water droplets per unit volume. Furthermore, we modified the objective function of the XGBoost algorithm by incorporating two penalty terms to ensure the model's predictions adhere to physical principles. The constrained model demonstrated accuracy on the test set, with a mean squared error of 0.005 and a coefficient of determination of 0.998. The efficiency of the model was validated through comparison with the experimental data and the results of the population balance mathematical model. The analysis shows that the initial droplet diameter and voltage have the highest influence on the model, which aligns with the observed behaviour in the real-world process.

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Excitable systems give rise to important phenomena such as heat waves, epidemics and cardiac arrhythmias. Understanding, forecasting and controlling such systems requires reliable mathematical representations. For cardiac tissue, computational models are commonly generated in a reaction-diffusion framework based on detailed measurements of ionic currents in dedicated single-cell experiments. Here, we show that recorded movies at the tissue-level of stochastic pacing in a single variable are sufficient to generate a mathematical model. Via exponentially weighed moving averages, we create additional state variables, and use simple polynomial regression in the augmented state space to quantify excitation wave dynamics. A spatial gradient-sensing term replaces the classical diffusion as it is more robust to noise. Our pipeline for model creation is demonstrated for an in-silico model and optical voltage mapping recordings of cultured human atrial myocytes and only takes a few minutes. Our findings have the potential for widespread generation, use and on-the-fly refinement of personalised computer models for non-linear phenomena in biology and medicine, such as predictive cardiac digital twins.

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In response to growing concerns surrounding the relationship between climate change and escalating flood risk, there is an increasing urgency to develop precise and rapid flood prediction models. Although high-resolution flood simulations have made notable advancements, they remain computationally expensive, underscoring the need for efficient machine learning surrogate models. As a result of sparse empirical observation and expensive data collection, there is a growing need for the models to perform effectively in 'small-data' contexts, a characteristic typical of many scientific problems. This research combines the latest developments in surrogate modelling and physics-informed machine learning to propose a novel Physics-Informed Neural Network-based surrogate model for hydrodynamic simulators governed by Shallow Water Equations. The proposed method incorporates physics-based prior information into the neural network structure by encoding the conservation of mass into the model without relying on calculating continuous derivatives in the loss function. The method is demonstrated for a high-resolution inland flood simulation model and a large-scale regional tidal model. The proposed method outperforms the existing state-of-the-art data-driven approaches by up to 25 %. This research demonstrates the benefits and robustness of physics-informed approaches in surrogate modelling for flood and hydroclimatic modelling problems.

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Pollution source identification is vital in water safety management. An integrated simulation-optimization modelling framework comprising a process-based hydrodynamic water quality model, artificial neural network surrogate model and particle swarm optimization (PSO) was proposed to achieve rapid, accurate and reliable pollution source identification. In this study, the hydrodynamics and water quality processes in a straight lab-based flume were simulated to test pollution source identification under steady flow conditions. Additionally, the pollution source identification in the unsteady flow conditions was examined using a real-life estuary, specifically the Yangtze River estuary. First, we developed two process-based models to simulate hydrodynamics and water quality in the flume and estuary. Then, the data generated from the process-based models were used to develop surrogate models. Three typical artificial neural networks (ANNs) algorithms: backpropagation (BP), radial basis function (RBF) and general regression neural networks (GRNN) were selected to develop surrogates for process-based models (PBMs), and they were coupled with PSO algorithm to achieve the hybrid modelling framework for pollution source identification. Our results showed that hybrid PBM-ANNs-PSO models could be applied to identify the pollution source and quantify release intensity in spatial distribution when the discharge type was assumed as the point source with a continuous release. Multiple-performance criteria metrics, in terms of the coefficient of determination, root-mean-square error, mean absolute error, evaluated the model performance as "Excellent prediction". The BP-PSO models consistently appear to be the top-performing source identification model within the developed models, with most cases of relative error (RE) values lower than 5%. The new insights from the hybrid modelling framework would provide useful information for the local government agency to make reasonable decisions regarding pollution source identification issues.

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A novel type of neural network with an architecture based on physics is proposed. The network structure builds on a body of analytical modifications of classical numerical methods. A feature of the constructed neural networks is defining parameters of the governing equations as trainable parameters. Constructing the network is carried out in three stages. In the first step, a neural network solution to an equation corresponding to a numerical scheme is constructed. It allows for forming an initial low-fidelity neural network solution to the original problem. At the second stage, the network with physics-based architecture (PBA) is further trained to solve the differential equation by minimising the loss function, as is typical in works devoted to physics-informed neural networks (PINNs). In the third stage, the physics-informed neural network with architecture based on physics (PBA-PINN) is trained on high-fidelity sensor data, parameters are identified, or another task of interest is solved. This approach makes it possible to solve insufficiently studied PINN problems: selecting neural network architecture and successfully initialising network weights corresponding to the problem being solved that ensure rapid convergence to the loss function minimum. It is advisable to use the devised PBA-PINNs in the problems of surrogate modelling and modelling real objects with multi-fidelity data. The effectiveness of the approach proposed is demonstrated using the problem of modelling processes in a chemical reactor. Experiments show that subsequent retraining of the initial low-fidelity PBA model based on a few high-accuracy data leads to the achievement of relatively high accuracy.

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Self-expandable transcatheter aortic valves (TAVs) elastically resume their initial shape when implanted without the need for balloon inflation by virtue of the nickel-titanium (NiTi) frame super-elastic properties. Experimental findings suggest that NiTi mechanical properties can vary markedly because of a strong dependence on the chemical composition and processing operations. In this context, this study presents a computational framework to investigate the impact of the NiTi super-elastic material properties on the TAV mechanical performance. Finite element (FE) analyses of TAV implantation were performed considering two different TAV frames and three idealized aortic root anatomies, evaluating the device mechanical response in terms of pullout force magnitude exerted by the TAV frame and peak maximum principal stress within the aortic root. The widely adopted NiTi constitute model by Auricchio and Taylor (1997) was used. A multi-parametric sensitivity analysis and a multi-objective optimization of the TAV mechanical performance were conducted in relation to the parameters of the NiTi constitutive model. The results highlighted that: five NiTi material model parameters (EA, σtLS, σtUS, σtUE and σcLS) are significantly correlated with the FE outputs; the TAV frame geometry and aortic root anatomy have a marginal effect on the level of influence of each NiTi material parameter; NiTi alloy candidates with pareto-optimal characteristics in terms of TAV mechanical performance can be successfully identified. In conclusion, the proposed computational framework supports the TAV design phase, providing information on the relationship between the super-elastic behavior of the supplied NiTi alloys and the device mechanical response.

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Myriad natural protective structures consist of bone plates joined by convoluted unmineralized (soft) collagenous sutures. Examples of such protective structures include: shells of turtles, craniums of almost all animals (including humans), alligator armour, armadillo armour, and others. The function of sutures has been well researched. However, whether, and if so how, sutures improve protective performance during a predator attack has received limited attention. Sutures are ubiquitous in protective structures, and this motivates the question as to whether sutures optimize the protective function of the structure. Hence, in this work the behaviour of structures that contain sutures during predator attacks is investigated. We show that sutures decrease the maximum strain energy density that turtle shells experience during predator attacks by more than an order of magnitude. Hence, sutures make turtle shells far more resilient to material failure, such as, fracture, damage, and plastic deformations. Additionally, sutures increase the viscous behaviour of the shell causing increased dissipation of energy during predator attacks. Further investigations into the influence of sutures on behaviour during locomotion and breathing are also presented. The results presented in this work motivate the inclusion of sutures in biomimetically designed protective structures, such as helmets and protective clothing. STATEMENT OF SIGNIFICANCE: Myriad bony protective structures contain networks of sutures, that is con- voluted soft collagenous tissue. Their ubiquity motivates the question, whether, and if so how, sutures improve protective performance. Hence, this work inves- tigates how sutures affect protective performance using computational experi- ments. Due to the length scale of sutures being far smaller than the structures in which they reside, classical modelling approaches are prohibitively expensive. Hence, in this work, a multiscale approach is taken. To our knowledge, this is the first multiscale investigation of structures that contain sutures. Among other insights, we show that sutures decrease the maximum strain energy density in structures during predator attacks by over an order of mag- nitude. Hence, sutures make structures far more resilient to failure.

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In-stent restenosis is a recurrence of coronary artery narrowing due to vascular injury caused by balloon dilation and stent placement. It may lead to the relapse of angina symptoms or to an acute coronary syndrome. An uncertainty quantification of a model for in-stent restenosis with four uncertain parameters (endothelium regeneration time, the threshold strain for smooth muscle cell bond breaking, blood flow velocity and the percentage of fenestration in the internal elastic lamina) is presented. Two quantities of interest were studied, namely the average cross-sectional area and the maximum relative area loss in a vessel. Owing to the high computational cost required for uncertainty quantification, a surrogate model, based on Gaussian process regression with proper orthogonal decomposition, was developed and subsequently used for model response evaluation in the uncertainty quantification. A detailed analysis of the uncertainty propagation is presented. Around 11% and 16% uncertainty is observed on the two quantities of interest, respectively, and the uncertainty estimates show that a higher fenestration mainly determines the uncertainty in the neointimal growth at the initial stage of the process. The uncertainties in blood flow velocity and endothelium regeneration time mainly determine the uncertainty in the quantities of interest at the later, clinically relevant stages of the restenosis process.

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Plastic-metal joints with a laser-structured metal surface have a high potential to reduce cost and weight compared to conventional joining technologies. However, their application is currently inhibited due to the absence of simulation methods and models for mechanical design. Thus, this paper presents a model-based approach for the strength estimation of laser-based plastic-metal joints. The approach aims to provide a methodology for the efficient creation of surrogate models, which can capture the influence of the microstructure parameters on the joint strength. A parametrization rule for the shape of the microstructure is developed using microsection analysis. Then, a parameterized finite element (FE) model of the joining zone on micro level is developed. Different statistical plans and model fits are tested, and the predicted strength of the FE model and the surrogate models are compared against experiments for different microstructure geometries. The joint strength is predicted by the FE model with a 3.7% error. Surrogate modelling using half-factorial experimental design and linear regression shows the best accuracy (6.2% error). This surrogate model can be efficiently created as only 16 samples are required. Furthermore, the surrogate model is provided as an equation, offering the designer a convenient tool to estimate parameter sensitivities.

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Uncertainty quantification (UQ) is a key component when using computational models that involve uncertainties, e.g. in decision-making scenarios. In this work, we present uncertainty quantification patterns (UQPs) that are designed to support the analysis of uncertainty in coupled multi-scale and multi-domain applications. UQPs provide the basic building blocks to create tailored UQ for multiscale models. The UQPs are implemented as generic templates, which can then be customized and aggregated to create a dedicated UQ procedure for multiscale applications. We present the implementation of the UQPs with multiscale coupling toolkit Multiscale Coupling Library and Environment 3. Potential speed-up for UQPs has been derived as well. As a proof of concept, two examples of multiscale applications using UQPs are presented. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

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The use of high-fidelity computational simulations promises to enable high-throughput hypothesis testing and optimisation of cancer therapies. However, increasing realism comes at the cost of increasing computational requirements. This article explores the use of surrogate-assisted evolutionary algorithms to optimise the targeted delivery of a therapeutic compound to cancerous tumour cells with the multicellular simulator, PhysiCell. The use of both Gaussian process models and multi-layer perceptron neural network surrogate models are investigated. We find that evolutionary algorithms are able to effectively explore the parameter space of biophysical properties within the agent-based simulations, minimising the resulting number of cancerous cells after a period of simulated treatment. Both model-assisted algorithms are found to outperform a standard evolutionary algorithm, demonstrating their ability to perform a more effective search within the very small evaluation budget. This represents the first use of efficient evolutionary algorithms within a high-throughput multicellular computing approach to find therapeutic design optima that maximise tumour regression.

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Head injury in childhood is the most common cause of death or permanent disability from injury. However, insufficient understanding exists of the response of a child's head to injurious loading scenarios to establish cause and effect relationships to assist forensic and safetly investigations. Largely as a result of a lack of availability of paediatric clinical and Post-Mortem-Human-Surrogate (PMHS) experimental data, a new approach to infant head injury experimentation has been developed. A coupled-methodology, combining a physical infant head surrogate, producing "real world" global, regional and localised impact response data and a computational Finite-Element (FE-head) model was created and validated against available PMHS and physical model global impact response data. Experimental impact simulations were performed to investigate regional and localised injury vulnerability. Different regions of the head produced accelerations significantly greater than those calculated using the currently available method of measuring the global, whole head response. The majority of material strain was produced within the relatively elastic suture and fontanelle regions, rather than the skull bones. A subsequent parametric analysis was conducted to provide a correlation between fall height and areas of maximum-stress-response and fracture-risk-probability. The FE-head was further applied to investigating fracture risk, simulating injurious PMHS impacts and a good qualitative match was observed. The FE-head shows significant potential for the study of infant head injury and is anticipated to be a motivating tool for the improvement of head injury understanding across a range of potentially injurious head loading scenarios.

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Poor air quality and related health impacts are still an issue in many cities and regions worldwide. Integrated assessment models (IAMs) can support the design of measures to reduce the emissions of precursors affecting air pollution. In this study, we apply the SHERPA (screening for high emission reduction potentials for air quality) model to compare spatial and sectoral emission reductions, given country-scale emission targets. Different approaches are tested: (a) country "uniform" emission reductions, (b) emission reductions targeting urban areas, (c) emission reductions targeting preferential sectors. As a case study, we apply the approaches to the implementation of the National Emission Ceiling Directive. Results are evaluated in terms of the reduction in average population exposure to PM2.5 overall in a country and in its main cities. Results indicate that the reduction of population exposure to PM2.5 highly depends on the way emission reductions are implemented. This work also shows the usefulness of the SHERPA model to support national authorities implementing national emission reduction targets while, at the same time, addressing their local air quality issues.

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Sparse grid interpolation is a popular numerical discretization technique for the treatment of high dimensional, multivariate problems. We consider the case of using time-series data to calibrate epidemiological models from both phenomenological and mechanistic perspectives using this computational tool. By capturing the dynamics underlying both global and local spaces, our algorithm identifies potentially optimal regions of the parameter space and directs computational effort towards resolving the dynamics and resulting fits of these regions. We demonstrate how sparse grid interpolants can be effectively deployed to fit available data and discriminate between competing hypotheses to explain the current cholera epidemic in Yemen.

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Head injury in childhood is the single most common cause of death or permanent disability from injury. However, despite its frequency and significance, there is little understanding of the response of a child's head to injurious loading. This is a significant limitation when making early diagnoses, informing clinical and/or forensic management or injury prevention strategies. With respect to impact vulnerability, current understanding is predominantly based on a few post-mortem-human-surrogate (PMHS) experiments. Researchers, out of experimental necessity, typically derive acceleration data, currently an established measure for head impact vulnerability, by calculation. Impact force is divided by the head mass, to produce a "global approximation", a single-generalised head response acceleration value. A need exists for a new experimental methodology, which can provide specific regional or localised response data. A surrogate infant head, was created from high resolution computer tomography scans with properties closely matched to tissue response data and validated against PMHS head impact acceleration data. The skull was 3D-printed from co-polymer materials. The brain, represented as a lumped mass, comprised of an injected gelatin/water mix. High-Speed Digital-Image-Correlation optically measured linear and angular velocities and accelerations, strains and strain rates. The "global approximation" was challenged by comparison with regional and local acceleration data. During impacts, perpendicular (at 90°) to a surface, regional and local accelerations were up to three times greater than the concomitant "global" accelerations. Differential acceleration patterns were very sensitive to impact location. Suture and fontanelle regions demonstrated ten times more strain (103%/s) than bone, resulting in skull deformations similar in magnitude to those observed during child birth, but at much higher rates. Surprisingly, perpendicular impacts produced significantly greater rotational velocities and accelerations, which are closer to current published injury thresholds than expected, seemingly as a result of deformational changes to the complex skull geometry. The methodology has proven a significant new step in characterising and understanding infant head injury mechanics.

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Osteoporosis and related bone fractures are an increasing global burden in our ageing society. Areal bone mineral density assessed through dual energy X-ray absorptiometry (DEXA), the clinically accepted and most used method, is not sufficient to assess fracture risk individually. Finite element (FE) modelling has shown improvements in prediction of fracture risk, better than aBMD from DEXA, but is not practical for widespread clinical use. The aim of this study was to develop an adaptive neural network (ANN)-based surrogate model to predict femoral neck strains and fracture loads obtained from a previously developed population-based FE model. The surrogate model performance was assessed in simulating two loading conditions: the stance phase of gait and a fall. The surrogate model successfully predicted strains estimated by FE (r2=0.90-0.98 for level gait load case, r2=0.92-0.96 for the fall load case). Moreover, an ANN model based on three measurements obtainable in clinics (femoral neck length (level gait) or maximum femoral neck diameter (fall), femoral neck bone mass, body weight) was able to give reasonable predictions (r2=0.84-0.94) for all of the strain metrics and the estimated femoral neck fracture load. Overall, the surrogate model has potential for clinical applications as they are based on simple measures of geometry and bone mass which can be derived from DEXA images, accurately predicting FE model outcomes, with advantages over FE models as they are quicker and easier to perform.

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