The present study evaluates a parameter discovery approach based on a lumped parameter model of the cardiovascular system in conjunction with optimization to approximate important cardiac parameters, including simulated left ventricle elastances. Important parameters pertaining to ventricular function were estimated using gradient optimization and synthetically generated measurements. Forward-mode automatic differentiation was used to estimate the cost function-parameter matrices and compared to the common finite differences approach. Synthetic data of healthy and diseased hearts were generated as proxies for noninvasive clinical measurements and used to evaluate the algorithm. Twelve parameters including left ventricle elastances were selected for optimization based on 99% explained variation in mean left ventricle pressure and volume. The hybrid optimization strategy yielded the best overall results compared to 1st order optimization with automatic differentiation and finite difference approaches, with mean absolute percentage errors ranging from 6.67% to 14.14%. Errors in left ventricle elastance estimates for simulated aortic stenosis and mitral regurgitation were smallest when including synthetic measurements for arterial pressure and valvular flow rate at approximately 2% and degraded to roughly 5% when including volume trends as well. However, the latter resulted in better tracking of the left ventricle pressure waveforms and may be considered when the necessary equipment is available.

Valvular heart diseases are growing concern in impoverished parts of the world, such as Southern-Africa, claiming more than 31 % of total deaths related to cardiovascular diseases. The ability to model the effects of regurgitant and obstructive lesions on the valve body can assist clinicians in preparing personalised treatments. In the present work, a multi-compartment lumped parameter model of the human cardiovascular system is developed, with a newly proposed valve modelling approach which accounts for geometry and flow regime dependent pressure drops along with the valve cusp motion. The model is applied to study various degrees of aortic stenosis using typical human cardiovascular parameters. The predicted transvalvular pressure drops for the different modelling approaches are compared to typical measured mean and peak gradients found in literature for severely stenosed aortic valves. The comparison between the predicted and measured values show that the previously published valve models under predicts expected severely stenosed peak and mean transvalvular pressure drops by approximately 47% and 25% respectively, whereas the newly proposed model under predicts the peak pressure drop by 25% and over predicts mean pressure drop by 7%.

Integrated whole-boiler process models are useful in the design of biomass and coal-fired boilers, and they can also be used to analyse different scenarios such as low load operation and alternate fuel firing. Whereas CFD models are typically applied to analyse the detail heat transfer phenomena in furnaces, analysis of the integrated whole-boiler performance requires one-dimensional thermofluid network models. These incorporate zero-dimensional furnace models combined with the solution of the fundamental mass, energy, and momentum balance equations for the different heat exchangers and fluid streams. This approach is not new, and there is a large amount of information available in textbooks and technical papers. However, the information is fragmented and incomplete and therefore difficult to follow and apply. The aim of this review paper is therefore to: (i) provide a review of recent literature to show how the different approaches to boiler modelling have been applied; (ii) to provide a review and clear description of the thermofluid network modelling methodology, including the simplifying assumptions and its implications; and (iii) to demonstrate the methodology by applying it to two case study boilers with different geometries, firing systems and fuels at various loads, and comparing the results to site measurements, which highlight important aspects of the methodology. The model results compare well with values obtained from site measurements and detail CFD models for full load and part load operation. The results show the importance of utilising the high particle load model for the effective emissivity and absorptivity of the flue gas and particle suspension rather than the standard model, especially in the case of a high ash fuel. It also shows that the projected method provides better results than the direct method for the furnace water wall heat transfer.

Physics-Informed Neural Networks (PINNs) are a new class of machine learning algorithms that are capable of accurately solving complex partial differential equations (PDEs) without training data. By introducing a new methodology for fluid simulation, PINNs provide the opportunity to address challenges that were previously intractable, such as PDE problems that are ill-posed. PINNs can also solve parameterized problems in a parallel manner, which results in favorable scaling of the associated computational cost. The full potential of the application of PINNs to solving fluid dynamics problems is still unknown, as the method is still in early development: many issues remain to be addressed, such as the numerical stiffness of the training dynamics, the shortage of methods for simulating turbulent flows and the uncertainty surrounding what model hyperparameters perform best. In this paper, we investigated the accuracy and efficiency of PINNs for modeling aortic transvalvular blood flow in the laminar and turbulent regimes, using various techniques from the literature to improve the simulation accuracy of PINNs. Almost no work has been published, to date, on solving turbulent flows using PINNs without training data, as this regime has proved difficult. This paper aims to address this gap in the literature, by providing an illustrative example of such an application. The simulation results are discussed, and compared to results from the Finite Volume Method (FVM). It is shown that PINNs can closely match the FVM solution for laminar flow, with normalized maximum velocity and normalized maximum pressure errors as low as $5.74\%$ and $9.29\%$, respectively. The simulation of turbulent flow is shown to be a greater challenge, with normalized maximum velocity and normalized maximum pressure errors only as low as $41.8\%$ and $113\%$, respectively.

Physics-informed neural networks (PINNs) were developed to overcome the limitations associated with the acquisition of large training data sets that are commonly encountered when using purely data-driven machine learning methods. This paper proposes a PINN surrogate modeling methodology for steady-state integrated thermofluid systems modeling based on the mass, energy, and momentum balance equations, combined with the relevant component characteristics and fluid property relationships. The methodology is applied to two thermofluid systems that encapsulate the important phenomena typically encountered, namely: (i) a heat exchanger network with two different fluid streams and components linked in series and parallel; and (ii) a recuperated closed Brayton cycle with various turbomachines and heat exchangers. The results generated with the PINN models were compared to benchmark solutions generated via conventional, physics-based thermofluid process models. The largest average relative errors are 0.17% and 0.93% for the heat exchanger network and Brayton cycle, respectively. It was shown that the use of a hybrid Adam-TNC optimizer requires between 180 and 690 fewer iterations during the training process, thus providing a significant computational advantage over a pure Adam optimization approach. The resulting PINN models can make predictions 75 to 88 times faster than their respective conventional process models. This highlights the potential for PINN surrogate models as a valuable engineering tool in component and system design and optimization, as well as in real-time simulation for anomaly detection, diagnosis, and forecasting.