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• This work introduces a reduced order model (ROM) of modeling thermal creep developed by dynamic mode decomposition (DMD). • The application of ROM allows for the rapid estimation of creep effects in complex structures, thereby improving the design efficiency. • The updated stress algorithm for the 316H unified visco-plastic constitutive equation in the 2023 edition ASME code are derived. Given the computational challenges associated with finite element methods in analyzing creep behavior in high-temperature components, this work presents an advanced method for modeling thermal creep in complex structures through a reduced order model (ROM) developed via dynamic mode decomposition (DMD). The results indicate that the ROM using DMD can predict long-term structural responses related to creep based on short-term data with high accuracy, enhancing significantly computational efficiency. The application of ROM allows for the rapid estimation of creep effects in complex structures, like monoliths in the MegaPower reactor, thereby improving the design efficiency. The eigenvalues of the creep related ROM all fall in the unit circle on the complex plane, indicating that creep is a stable development process. The DMD with improved time mode coefficient can reconstruct strain-rate related plastic deformation and cyclic visco-plastic deformation process. Additionally, we derive the necessary stress updating algorithm and consistent tangent operator matrix for the 316H unified visco-plastic constitutive equation in 2023 edition ASME code, ensuring accurate modeling of material creep behavior under high temperatures in this paper. This work provides a valuable tool for the safe design and operation of critical components in nuclear engineering and other high-temperature applications. [ABSTRACT FROM AUTHOR]

Fast simulation for stratified indoor airflow distributions is desired for various applications, such as design of advanced indoor environments, emergency management, and coupled annual energy simulation for buildings with stratified air distributions. Reduced order models trained by pre-computed computational fluid dynamics results are fast, but their prediction may be inaccurate when applied for conditions outside the training domain. To overcome this limitation, we propose a fast and self-learning model based on an in situ adaptive tabulation (ISAT) algorithm, which is trained by a fast fluid dynamics (FFD) model as an example. The idea is that the ISAT will retrieve the solutions from an existing data set if the estimated prediction error is within a pre-defined tolerance. Otherwise, the ISAT will execute the FFD simulation, which is accelerated by running in parallel on a graphics processing unit, for a full-scale simulation. This paper systematically investigates the feasibility of the ISAT for indoor airflow simulations by presenting the ISAT-FFD implementation alongside results related to its overall performance. Using a stratified indoor airflow as an example, we evaluated how the training time of ISAT was impacted by four factors (training methods, error tolerances, number of inputs, and number of outputs). Then we demonstrated that a trained ISAT model can predict the key information for inputs both inside and outside the training domain. The ISAT was able to answer query points both inside and close to training domain using retrieve actions within a time less than 0.001 s for each query. Finally, we provided suggestions for using the ISAT for building applications.

The high-speed train bogie is a typical underactuated mechanical system. It has been difficult to design controls to increase the stability against hunting motion with limited sensor measurements and actuation hardware. This paper develops a control design for the stability improvement of the bogie by making use of the balanced truncation reduced order model of the bogie. When the train travels at speed higher than the critical speed, the bogie has unstable modes. The balanced truncation model reduction (BTMR) is usually applied to stable systems. In this paper, we first apply the real Schur decomposition to separate the stable and unstable modes of the bogie. The BTMR is then carried out for the stable subsystem. An augmented X 0 -balanced truncation algorithm is considered to deal with the dependence of the BTMR on initial conditions. The reduced order subsystem is then combined with the unstable subsystem. A linear quadratic regulator control together with a Luenberger observer for the state estimation is designed for the bogie with non-zero initial conditions. Simulation results show that the control designed with the balanced truncation reduced order model performs very well in terms of the stability improvement by significantly increasing the critical train speed. [ABSTRACT FROM AUTHOR]

Rational approximation recently emerged as an efficient numerical tool for the solution of exterior wave propagation problems. Currently, this technique is limited to wave media which are invariant along the main propagation direction. We propose a new model order reduction-based approach for compressing unbounded waveguides with layered inclusions. It is based on the solution of a nonlinear rational least squares problem using the RKFIT method. We show that approximants can be converted into an accurate finite difference representation within a rational Krylov framework. Numerical experiments indicate that RKFIT computes more accurate grids than previous analytic approaches and even works in the presence of pronounced scattering resonances. Spectral adaptation effects allow for finite difference grids with dimensions near or even below the Nyquist limit. [ABSTRACT FROM AUTHOR]

To analyze the complex spatiotemporal evolution law of the high-speed jet flow field in a liquid-ring pump ejector, both the classic and spectral proper orthogonal decomposition (SPOD) methods were introduced to decompose the transient flow field based on the numerical large eddy simulation. The proper orthogonal decomposition (POD) reduced order model (ROM) of the complex flow in the ejector was established to analyze the transient characteristics and reconstruct the flow field. The spatial mode characteristics of density, pressure and vorticity field, and the frequency domain characteristics of mode coefficients were analyzed. The results show that the spatiotemporal decoupling analysis of a high-speed jet flow field can be accomplished by the POD and SPOD methods. A large-scale symmetric coherent structure is formed in the shear layer of the first two modes of vorticity, and a small-scale antisymmetric structure is formed at the trailing edge of the jet flow for the third and fourth modes. This reflects the evolutionary characteristics of the jet shear vortex. There is a significant spatial correlation between the density and pressure modes, reflecting that the evolution of the two structures has important correlation characteristics. The spectral analysis of the mode coefficients shows that the dominant frequencies of 1250 Hz and 18 kHz correspond to the self-excited oscillation frequency of shock waves and the vortex shedding frequency. The POD-ROM can reconstruct the high-speed flow field of the ejector with enough accuracy using the first 30-order modes, and the root mean square error and mean absolute percentage error for the velocity prediction are 0.48% and 0.24%, respectively. [ABSTRACT FROM AUTHOR]

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A reduced-order model (ROM) is developed for proton exchange membrane fuel cells (PEMFCs) considering the non-isothermal two-phase effects, with the goal of enhancing computational efficiency and thus accelerating fuel cell design development. Using analytical order reduction and approximation methods, the fluxes and source terms in conventional 1D conservation equations are reduced to six computing nodes at the interfaces between each cell component. The errors associated with order reduction are minimized by introducing new approximation methods for the potential distribution, the transport properties, and the membrane hydration status. The trade-off between model accuracy and computational efficiency is studied by comparing the simulation results and computational times of the new model with a full 1D model. The new model is nearly two orders of magnitude faster without sacrificing too much accuracy (<4% difference) compared to the 1D model. The new model is then used to analyze the influence of the membrane electrode assembly (MEA) design on cell performance and internal state distributions, offering insights into MEA structural optimization. The model can be readily extended to account for more detailed physico-chemical processes, such as Knudsen diffusion or the influence of micro-porous layers, and it can be an effective tool for understanding and designing PEMFCs. • A reduced-order model for PEM fuel cells is developed. • The model is two orders of magnitude faster than the conventional 1D model. • The model results agree well with the 1D model. • The influence of the membrane electrode assembly design is studied. • CL thickness is the dominant factor at low current density. [ABSTRACT FROM AUTHOR]

The aim of this study is to introduce the maximum torque per total ampere (MTPTA) control strategy for brushless doubly fed induction machine drives taking iron loss into account. In this regard, the condition for realizing the MTPTA is investigated in the presence of iron loss by a theoretical approach. It is shown the proposed strategy is realized when the MTPTA criterion tracks zero as reference signal. As a result, the current is not only shared between the stator windings fairly but also total stator currents are minimized for a given torque. The experimental results confirm the performance of the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the mathematical foundations of reduced order model (ROM) closures. First, we extend the verifiability concept from large eddy simulation to the ROM setting. Specifically, we call a ROM closure model verifiable if a small ROM closure model error (i.e., a small difference between the true ROM closure and the modeled ROM closure) implies a small ROM error. Second, we prove that the data-driven ROM closure studied here (i.e., the data-driven variational multiscale ROM) is verifiable. Finally, we investigate the verifiability of the data-driven variational multiscale ROM in the numerical simulation of the one-dimensional Burgers equation and a two-dimensional flow past a circular cylinder at Reynolds numbers R e = 100 and R e = 1000 . [ABSTRACT FROM AUTHOR]

In this article, we introduce a methodology for improving the accuracy and efficiency of reduced order models (ROMs) constructed using the least‐squares Petrov–Galerkin (LSPG) projection method through the introduction of preconditioning. Unlike prior related work, which focuses on preconditioning the linear systems arising within the ROM numerical solution procedure to improve linear solver performance, our approach leverages a preconditioning matrix directly within the minimization problem underlying the LSPG formulation. Applying preconditioning in this way has the potential to improve ROM accuracy for several reasons. First, preconditioning the LSPG formulation changes the norm defining the residual minimization, which can improve the residual‐based stability constant bounding the ROM solution's error. The incorporation of a preconditioner into the LSPG formulation can have the additional effect of scaling the components of the residual being minimized to make them roughly of the same magnitude, which can be beneficial when applying the LSPG method to problems with disparate scales (e.g., dimensional equations, multi‐physics problems). Importantly, we demonstrate that an "ideal preconditioned" LSPG ROM (a ROM in which the preconditioner is the inverse of the Jacobian of its corresponding full order model) emulates projection of the full order model solution increment onto the reduced basis. This quantity defines a lower bound on the error of a ROM solution for a given reduced basis. By designing preconditioners that approximate the Jacobian inverse—as is common in designing preconditioners for solving linear systems—it is possible to obtain a ROM whose error approaches this lower bound. The proposed approach is evaluated on several mechanical and thermo‐mechanical problems implemented within the Albany HPC code and run in the predictive regime, with prediction across material parameter space. We demonstrate numerically that the introduction of simple Jacobi, Gauss‐Seidel, and ILU preconditioners into the proper orthogonal decomposition/LSPG formulation reduces significantly the ROM solution error, the reduced Jacobian condition number, the number of nonlinear iterations required to reach convergence, and the wall time (thereby improving efficiency). Moreover, our numerical results reveal that the introduction of preconditioning can deliver a robust and accurate solution for test cases in which the unpreconditioned LSPG method fails to converge. [ABSTRACT FROM AUTHOR]

This paper presents a new nonlinear projection based model reduction using convolutional Variational AutoEncoders (VAEs). This framework is applied on transient incompressible flows. The accuracy is obtained thanks to the expression of the velocity and pressure fields in a nonlinear manifold maximising the likelihood on pre-computed data in the offline stage. A confidence interval is obtained for each time instant thanks to the definition of the reduced dynamic coefficients as independent random variables for which the posterior probability given the offline data is known. The parameters of the nonlinear manifold are optimized as the ones of the decoder layers of an autoencoder. The parameters of the conditional posterior probability of the reduced coefficients are the ones of the encoder layers of the same autoencoder. The optimization of both sets of the encoder and the decoder parameters is obtained thanks to the application of a variational Bayesian method, leading to variational autoencoders. This Reduced Order Model (ROM) is not a regression model over the offline pre-computed data. The numerical resolution of the ROM is based on the Chorin projection method. We apply this new nonlinear projection-based Reduced Order Modeling (ROM) for a 2D Karman Vortex street flow and a 3D incompressible and unsteady flow in an aeronautical injection system. [ABSTRACT FROM AUTHOR]

Simulation and numerical analysis of physical phenomena, especially for the unsteady problems due to the dependency of the numerical algorithms on the computer hardware and the large number of computational nodes, are the most important problems. For these reasons, the number of computations and computational costs increase. The order reduction method is the one that has been widely used in recent years to reduce computational time. In this way, by reducing the constraints of the system without changing the inherent features of the problem, the computational efficiency will dramatically increase. In this study, using the basic concepts of dynamical systems, the thermal diffusion problem is investigated using the dynamic modes decomposition method. Then, a reduced order model is established for the related governing equation of this phenomenon. Accordingly, based on the projection of the governing equation in the vector space of modes, by using dynamic modes, a reduced order model is obtained with respect to the properties of dynamic modes. The obtained model to simulate the time evolution and parametric variations can be properly replaced with the original equation and predict the behavior of the system with very good accuracy. A comparison between the results of the present reduced order models and the simulations of the exact solution shows high computation accuracy.

Data-driven researches based on various machine learning techniques, are being actively explored in science and technology areas. In the area of computational fluid dynamics, several studies have already been conducted in a reduced order modeling technique using principal orthogonal basis called proper orthogonal decomposition (POD). Recently the application of machine learning techniques represented by deep learning or deep neural network (DNN) to the existing reduced order model methods is increasingly drawing attention with the development of processor hardware technology such as GPU. This study, based on the data produced by a state-of-the-art flow solver, examined both POD and DNN techniques to three different methods: a) classical non-intrusive POD with local linear regression, b) fully-connected DNN, and c) mixed POD-DNN. Method a) and c) have difference in computing superposed time expansion coefficients. The target problem is unsteady aerodynamic simulation of a two dimensional airfoil with fixed angle-of-attack and three grid and flow condition sets: (structured grid, inviscid flow, Mach 0.2), (structured grid, turbulent flow, Mach 0.6, Reynolds 1×105), and (unstructured grid, laminar flow, Mach 0.4). The comparison items were flow fields of velocity/pressure for all cases and aerodynamic lift/drag performances only for the structured grid system respectively. In these computations the overall tendencies of aerodynamic lift and drag are similar, but the POD with existing local linear regression method in calculating time coefficients was found to show the highly robust and moderately accurate predictions. The direct DNN method was judged to be able to be used as a feasible reduced order model since it overcomes linearity error at both extracting POD basis and determining coefficients and has an advantage to be able to infer flow variables in arbitrary spatial locations. It showed better level of error than the classical POD method, but had model optimization cost to tune hyper-parameters and determine how many training data should be obtained to mitigate partial error. As an intermediate way, the mixed POD-DNN provided a robust reduced model of airfoil aerodynamic simulation due to the moderate computational cost and better accuracy comparing to the two other methods, but it had a shortcoming of fixed spatial coordinates like the classical POD method because the POD basis has fixed dimension of vector. In conclusion, fully-connected deep neural network method is helpful to predict flow field distribution as a universal field approximator in accordance with time and space such as fluid field simulation in this study, and, what is better, using POD basis will augment the accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

This paper describes a new efficient method for the construction of an approximately balanced aerodynamic Reduced Order Model (ROM) via the frequency domain using Computational Fluid Dynamics data. Time domain ROM construction requires CFD data, which is obtained from the DLR TAU RANS or Euler Linearised Frequency Domain (LFD) solver. The ROMs produced with this approach, using a small number of frequency simulations, are shown to exhibit a strong ability to reconstruct the system response for inviscid flow about the NLR7301 aerofoil and the FFAST wing; and viscous flow about the NASA Common Research Model. The latter demonstrates that the reduced order model approach can reconstruct the full order frequency response of a viscous aircraft configuration with excellent accuracy using a strip wise approach. The time domain models are built using the frequency domain, but also give promising results when applied to reconstruct non-periodic motions. Results are compared to time domain simulations, showing good agreement even with small ROM sizes, but with a substantial reduction in calculation time. The main advantage of the current model order reduction approach is that the method does not require the formation and storage of large matrices, such as in POD approaches. [ABSTRACT FROM AUTHOR]

This article presents a new reduced order model (ROM) for the angular discretization of the Boltzmann transport equation. The angular ROM is built over a partitioning of the space‐angle phase‐space, by generating independent, optimized angular basis function sets for each partition. The advantage is that each basis function set is optimized to represent the neutron flux distribution in a particular partition of space and angle, rather than being optimized for the entire domain. This serves to reduce the total number of basis functions required, and therefore the solve time. Two numerical examples are presented to demonstrate the efficacy of the methods—a dog‐leg duct problem, involving particle streaming, and the Watanabe–Maynard problem, which includes significant particle scattering. In both cases, it is shown that the method reduces the angular flux error, for a given basis size or solve time, by around an order of magnitude in comparison to other, similar ROM methods. An adaptive version of the method is also presented, whereby the number of basis functions within each space‐angle partition can vary independently. It is shown to potentially provide further significant reductions in error. [ABSTRACT FROM AUTHOR]

In this paper, we formulate three nonintrusive methods and systematically explore their performance in terms of the ability to reconstruct the quantities of interest and their predictive capabilities. The methods include deterministic dynamic mode decomposition, randomised dynamic mode decomposition and nonlinear proper orthogonal decomposition (NLPOD). We apply these methods to a convection dominated fluid flow problem governed by the Boussinesq equations. We analyse the reconstruction results primarily at two different times for considering different noise levels synthetically added into the data snapshots. Overall, our results indicate that, with a proper selection of the number of retained modes and neural network architectures, all three approaches make predictions that are in a good agreement with the full order model solution. However, we find that the NLPOD approach seems more robust for higher noise levels compared to both dynamic mode decomposition approaches. [ABSTRACT FROM AUTHOR]

This work presents the application of a recently developed parametric, non-intrusive, and multi-fidelity reduced-order modeling method on high-dimensional displacement and stress fields arising from the structural analysis of geometries that differ in the size of discretization and structural topology. The proposed approach leverages manifold alignment to fuse inconsistent field outputs from high- and low-fidelity simulations by individually projecting their solution onto a common subspace. The effectiveness of the method is demonstrated on two multi-fidelity scenarios involving the structural analysis of a benchmark wing geometry. Results show that outputs from structural simulations using incompatible grids, or related yet different topologies, are easily combined into a single predictive model, thus eliminating the need for additional pre-processing of the data. The new multi-fidelity reduced-order model achieves a relatively higher predictive accuracy at a lower computational cost when compared to a single-fidelity model. [ABSTRACT FROM AUTHOR]

In this paper, to evaluate the residual stress of welded structures efficiently, we propose a welding simulation method utilizing a reduced order model. To construct the reduced order model, a finite element model is divided into a target part and an omitted part. For the heat transfer analysis, a thermal boundary condition is newly defined and applied to the target part, to compensate for the heat loss induced by neglecting the omitted part. For the thermal elastic plastic analysis, a reduced model for the target part is constructed using the automated static condensation method. The performance of the proposed welding simulation method adopting the reduced order model is verified by solving severalwelding problems, and it effectively reduces computational costs while predicting the residual stress with little loss of accuracy. [ABSTRACT FROM AUTHOR]

Recently, the reduced order model (ROM) has been applied to reduce the computational cost of numerical methods. Merging this approach with the lattice Boltzmann method (LBM) as a powerful mesoscale fluid solver seems promising. Dealing with this idea requires a matrix form for the LBM. This matrix form must represent all the LBM's algorithm steps (including boundary condition implementation) to just one specific matrix-vector relation. Furthermore, the LBM contains some nonlinear parts inside the equilibrium distribution function (EDF), which must be treated with a nonlinear ROM like the discrete empirical interpolation method (DEIM). So, in this paper, we discuss proper orthogonal decomposition (POD)-ROM LBM in the general form, present an appropriate matrix form for the LBM as explained, and implement POD or DEIM on that matrix form. In the end, the ability of this scheme is challenged with solving the urban air pollutant transition problem over some canyons areas as a practical problem. [ABSTRACT FROM AUTHOR]

To enable multi-query analyses, such as optimisations of large-scale crashworthiness problems, a numerically efficient model is crucial for the development process. Therefore, data-driven Model Order Reduction (MOR) aims at generating low-fidelity models that approximate the solution while strongly reducing the computational cost. MOR methods for crashworthiness became only available in recent years; a detailed and comparative assessment of their potential is still lacking. Hence, this work evaluates the advantages and drawbacks of intrusive and non-intrusive projection based MOR methods in the framework of non-linear structural transient analysis. Both schemes rely on the collection of full-order training simulations and a subsequent subspace construction via Singular Value Decomposition. The intrusive MOR is based on a Galerkin projection and a consecutive hyper-reduction step. In this work, its inter-and extrapolation abilities are compared to the non-intrusive technique, which combines the subspace approach with machine learning methods. Moreover, an optimisation analysis incorporating the MOR methods is proposed and discussed for a crashworthiness example. [ABSTRACT FROM AUTHOR]

• Reduced order modeling approach for rotating bladed disks under varying speeds. • Mistuning identification method for rotating bladed disks with variable speed. • Numerical verification results show the effectiveness and accuracy of the method. As a critical component in turbomachinery, such as aero-engines, bladed disks frequently experience mistuning due to various factors, leading to localized vibrations and increased risk of high-cycle fatigue. To enable online mistuning identification and dynamic response prediction of rotating bladed disks, this paper proposes a variable-speed reduced order model (VSROM) that accounts for varying rotational speeds and a response-based mistuning identification method. By parameterizing the stiffness matrix of the bladed disk as a polynomial and assuming the tuned system's mode shapes are minimally affected by speed, the VSROM can be developed using the Component Mode Mistuning method. Additionally, leveraging the VSROM, a response-based mistuning identification method is proposed, capable of identifying mistuning at any speed. The effectiveness and accuracy of the VSROM and mistuning identification method are validated through numerical simulations. The dynamic response of the mistuned system is predicted using the VSROM, and the results are compared with those obtained from the existing reduced order model that accounts for varying speeds, as well as from the full-order finite element model. The results demonstrate that the proposed VSROM offers superior prediction accuracy and computational efficiency. Moreover, mistuning identification at different speeds shows good agreement with the actual mistuning values. The proposed VSROM and mistuning identification method hold significant potential for online vibration monitoring of rotating bladed disks. [ABSTRACT FROM AUTHOR]

Regularized reduced order models (Reg-ROMs) are stabilization strategies that leverage spatial filtering to alleviate the spurious numerical oscillations generally displayed by the classical Galerkin ROM (G-ROM) in under-resolved numerical simulations of turbulent flows. In this paper, we propose a new Reg-ROM, the time-relaxation ROM (TR-ROM), which filters the marginally resolved scales. We compare the new TR-ROM with the two other Reg-ROMs in current use, i.e., the Leray ROM (L-ROM) and the evolve-filter-relax ROM (EFR-ROM) and one eddy viscosity model, the mixing-length model, in the numerical simulation of the turbulent channel flow at R e τ = 180 and R e τ = 395 in both the reproduction and the predictive regimes. For each Reg-ROM, we investigate two different filters: (i) the differential filter (DF), and (ii) the higher-order algebraic filter (HOAF). In our numerical investigation, we monitor the Reg-ROM performance with respect to the ROM dimension, N , and the filter order. We also perform sensitivity studies of the three Reg-ROMs with respect to the time interval, relaxation parameter, and filter radius. The numerical results yield the following conclusions: (i) All three Reg-ROMs are significantly more accurate than the G-ROM. (ii) All three Reg-ROMs are more accurate than the ROM projection in terms of Reynolds stresses. (iii) With the optimal parameter values, the new TR-ROM yields more accurate results than the L-ROM and the EFR-ROM in all tests. (iv) The new TR-ROM is more accurate than the mixing-length ROM. (v) For most N values, DF yields the most accurate results for all three Reg-ROMs. (vi) The optimal parameters trained in the reproduction regime are also optimal for the predictive regime for most N values, demonstrating the Reg-ROM predictive capabilities. (vii) All three Reg-ROMs are sensitive to the filter order and the filter radius, and the EFR-ROM and the TR-ROM are sensitive to the relaxation parameter. (viii) The optimal range for the filter radius and the effect of relaxation parameter are similar for the two R e τ values. • A new regularized reduced order model (ROM), the time-relaxation ROM, is proposed. • Several regularized ROMs are compared for the turbulent channel flow. • Sensitivity studies with respect to regularization parameters are presented. • Robustness of regularized ROMs' parameters for the predictive problem is established. • With respect to Reynolds shear and normal stresses, the new time-relaxation ROM is the most accurate model. [ABSTRACT FROM AUTHOR]

• The highlights of this manuscript can be summarized as. • Two finite element models are presented to simulate coated blisks under elastic support. • Reduced order models are developed for coated blisks with random mistuning and variable support stiffness. • New phenomena are observed for tuned, deterministic and randomly mistuned blisks and the mechanism is explained. Boundary conditions significantly affect the vibration characteristics of mechanical structures. Hard coatings are applied to reduce the vibration levels of blisks, and the modelling methods and vibration characteristics of mistuned coated blisks have been investigated under hard-support boundary conditions. However, the behavior of coated blisks under elastic support has not been previously studied. This paper presents a finite element model to simulate elastic support using two methods and develops reduced-order models to analyze coated blisks under elastic support. Furthermore, the effects of elastic support on the vibration characteristics of tuned, deterministic, and randomly mistuned blisks are investigated with a detailed discussion of the underlying mechanisms. The results indicate that elastic support has a notable impact on the natural frequencies and resonant responses at nodal diameters 1 and 2 in tuned-coated blisks. For deterministic mistuned blisks, the amplitude amplification factor varies in frequency-veering regions and frequency-intersecting regions with increasing support stiffness. Elastic support can reduce the forced responses of randomly mistuned blisks, and the well-known peak-value phenomenon is not observed in some cases based on statistical analyses. [ABSTRACT FROM AUTHOR]

The radial basis function network (RBFN) is compared with gappy interpolation for sparse reconstruction of a reduced order model (ROM) for an industrial natural gas boiler. It is a non-intrusive method based on proper orthogonal decomposition (POD) and sensor measurements substituted by full order model (FOM) results at specified locations. The FOM was formed by steady-state computational fluid dynamic simulation at training and validation points selected by Latin hypercube and adaptive sampling in the 2D parameter space. Parametric study was performed for a varying number of sensors located on the boiler walls as a realistic measurement option. The optimal numbers of training samples and truncated eigenmodes were determined according to the relative L2 norm error between FOM and ROM by the truncated eigenmodes. Results showed RBFN outperforming gappy interpolation with a lower relative L2 norm error and less dependence on the number of sensors for both temperature and nitric oxide concentration fields. The RBFN may be a better choice for reconstruction of multidimensional scalar fields as a digital twin through fusion of simulation and online data for smart operation of complicated thermofluid facilities.

• Very slow dynamics of slag layer govern the responses of slag thickness and heat duty. • Characteristic time of heat duty was 4 min, half or less than that for slag thickness. • Lower operating load and slag fluidity extend the characteristic times. • Short O/C fluctuations minimally impact slag thickness, less than Q wall. • Long, large O/C dips form thick slag layers, complicating bottom slag discharge. In commercial coal gasifiers, the oxygen/coal (O/C) ratio is the key operation variable representing the reaction stoichiometry and is carefully controlled considering coal properties and operation load in commercial coal gasifiers. However, the O/C ratio fluctuates frequently from the target value, which causes variations of the gasification performance. In this study, the dynamic response of a commercial Shell coal gasifier to changes in the O/C ratio were investigated using a pseudo-2D reduced-order model (ROM) with focus on three key performance parameters: exit gas temperature (T g,exit), heat duty (Q wall), and slag thickness at the slag tap (δ tap). The ROM was validated for two actual operation cases of the plant and used to analyze the response of the parameters to various simulated cases with step changes, peaks, and dips in the O/C ratio. T g,exit responded almost immediately to the change in the O/C ratio; however, the slow change in the slag layer on the wall with a residence time >20 min considerably influenced the dynamic responses of Q wall and δ tap. The characteristic times of Q wall and δ tap at an operation load of 85 % were approximately 4 and 9 min, respectively. Therefore, usual fluctuations in the O/C ratio with periods much shorter than the characteristic times have a minimal impact on δ tap , which is considerably smaller than that of Q wall monitored by the operators. However, larger fluctuations with periods comparable to the characteristic times can cause changes in Q wall and δ tap significantly larger than the variations in the O/C ratio. In particular, a long, large dip in the O/C ratio should be avoided for coal with low slag fluidity at low loads to prevent the formation of an excessively thick slag layer, which can cause issues in the bottom slag discharge. The dynamic behaviors of the key parameters provide physical insights for improved operational control of the gasifier in which Q wall is the only parameter measured directly. [ABSTRACT FROM AUTHOR]

The pre-operative planning and intra-operative navigation of the endovascular aneurysm repair (EVAR) procedure are currently challenged by the aortic deformations that occur due to the insertion of a stiff guidewire. Hence, a fast and accurate predictive tool may help clinicians in the decision-making process and during surgical navigation, potentially reducing the radiations and contrast dose. To this aim, we generated a reduced order model (ROM) trained on parametric finite element simulations of the aortic wall-guidewire interaction. A Design of Experiments (DOE) consisting of 300 scenarios was created spanning over seven parameters. Radial basis functions were used to achieve a morphological parametrization of the aortic geometry. The ROM was built using 200 scenarios for training and the remaining 100 for validation. The developed ROM estimated the displacement of aortic nodes with a relative error below 5.5% for all the considered validation cases. From a preliminary analysis, the aortic elasticity, the stiffness of the guidewire and the tortuosity of the cannulated iliac artery proved to be the most influential parameters. Once built, the ROM provided almost real-time and accurate estimations of the guidewire-induced aortic displacement field, thus potentially being a promising pre- and intra-operative tool for clinicians. • A methodology for a reduced order model (ROM) to estimate the guidewire-induced displacement of abdominal aorta during EVAR is obtained. • The workflow to obtain the ROM from CT images can be executed within 3 hours and 15 minutes, given access to HPC resources. • The obtained ROM allows to explore with sufficient accuracy different scenarios, varying seven parameters of interest. [ABSTRACT FROM AUTHOR]

A machine learning framework is developed to compute the aerodynamic forces and moment coefficients for a pitching NACA0012 airfoil incurring in light and deep dynamic stall. Four deep neural network frameworks of increasing complexity are investigated: two multilayer perceptrons and two convolutional neural networks. The convolutional framework, in addition to the standard mean squared error loss, features an improved loss function to compute the airfoil loads. In total, five models are investigated of increasingly complexity. The convolutional model, coupled with the loss function based on force and moment coefficients and embedding the attention mechanism, is found to robustly and efficiently predict pressure and skin friction distributions over the airfoil over the entire pitching cycle. Periodic conditions are implemented to grant the physical smoothness of the model output both in space and time. An analysis of the training dataset point distributions is performed to point out the effects of adopting low discrepancy sequences, such as Latin hypercube, Sobol', and Halton, compared to random and uniform sequences. The current model shows improved performances in predicting forces and pitching moment in a broad range of operating conditions. • Reduced order model for unsteady aerodynamics. • Small oscillations, light and deep dynamic stall. • Effects of low-discrepancy sequences distributions. [ABSTRACT FROM AUTHOR]

This paper introduces a new series of methods which combine modal decomposition algorithms, such as singular value decomposition and high-order singular value decomposition, and deep learning architectures to repair, enhance, and increase the quality and precision of numerical and experimental data. A combination of two- and three-dimensional, numerical and experimental datasets are used to demonstrate the reconstruction capacity of the presented methods, showing that these methods can be used to reconstruct any type of dataset, showing outstanding results when applied to highly complex data, which is noisy. The combination of benefits of these techniques results in a series of data-driven methods which are capable of repairing and/or enhancing the resolution of a dataset by identifying the underlying physics that define the data, which is incomplete or under-resolved, filtering any existing noise. These methods and the Python codes are included in the first release of ModelFLOWs-app. 1 1 The website of the software is available at https://modelflows.github.io/modelflowsapp/. • Effective data-driven reconstruction methods for 2D/3D, laminar/turbulent datasets. • Reconstruction tasks complete missing data and enhance resolution from sparse data. • Modal decomposition techniques and hybrid ROMs enhance datasets by filtering noise. • DL superresolution excels in reconstruction, adapting through hyperparameter tuning. • Different error evaluation techniques show the methods' robustness and versatility. [ABSTRACT FROM AUTHOR]

The main goal of this work is to develop a data-driven Reduced Order Model (ROM) strategy from high-fidelity simulation result data of a Full Order Model (FOM). The goal is to predict at lower computational cost the time evolution of solutions of Fluid–Structure Interaction (FSI) problems. For some FSI applications, the elastic solid FOM (often chosen as quasi-static) can take far more computational time than the fluid one. In this context, for the sake of performance one could only derive a ROM for the structure and try to achieve a partitioned FOM fluid solver coupled with a ROM solid one. In this paper, we present a data-driven partitioned ROM on two study cases: (i) a simplified 1D-1D FSI problem representing an axisymmetric elastic model of an arterial vessel, coupled with an incompressible fluid flow; (ii) an incompressible 2 D wake flow over a cylinder facing an elastic solid with two flaps. We evaluate the accuracy and performance of the proposed ROM-FOM strategy on these cases while investigating the effects of the model's hyperparameters. We demonstrate a high prediction accuracy and significant speedup achievements using this strategy. • A data-driven reduced order model for partitioned fluid–structure interactions. • A new approach, coupling a reduced order solid model, and a full order fluid model. • Reduction of elastic quasi-static solid models coupled with less expensive fluid models. • Linear and nonlinear dimensionality reduction for forces and displacement fields. • Parsimonious regression models to learn the solid model in the latent space. [Display omitted] [ABSTRACT FROM AUTHOR]

Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and time-consuming. An alternative, the pilot-scale model, relies on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, physics-constrained reduced order model (ROM) method. The ROM identifies critical physics modes from small-scale unit components, projecting governing equations onto these modes to create a reduced model that retains essential physics details. We also employ Discontinuous Galerkin Domain Decomposition (DG-DD) to apply ROM to unit components and interfaces, enabling the construction of large-scale global systems without data at such large scales. This method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about 15–40 times faster with only ∼ 1% relative error. Furthermore, ROM takes one order of magnitude less memory than the full order model, enabling larger scale predictions at a given memory limitation. • Developed a novel component reduced order model. • Identifies important physics modes from small-scale sample data. • Constructs the large-scale reduced order model only with small-scale data. • Provides efficient and robust predictions at large scales. • Demonstrated on Poisson, Stokes and advection-diffusion equation. [ABSTRACT FROM AUTHOR]

Major concerns of carbon dioxide (CO2) sequestration in subsurface formations are knowledge of the well injectivity and gas storage capacity of the formation, the CO2 pressure and saturation plume extensions during and after injection, and the risks associated with CO2 leakage and fault reactivation. Saline reservoirs are considered as one of the target formations for CO2 sequestration through structural, residual, dissolution, and mineral trapping mechanisms. The boundary condition of the saline reservoir dictates the pressure and saturation plume extension of the injected supercritical CO2 that could expand over large distances. This can lead to sources of risk, e.g., leakage and/or fault reactivation due to presence of wells, thief zones, and geological discontinuities. Therefore, there is a critical need to develop a model that describes how risk-related performance metrics (i.e., the CO2 saturation plume size, the pressure differential plume area, and the pressure differential at specific locations) vary as a function of the size of injection, time following injection, injection operations, and geologic environment. In this study, a systematic reservoir modeling studies of anthropogenic CO2 sequestration in Citronelle dome, Alabama, was performed where all relevant scenarios and conditions to address the questions of the saturation and pressure plume size in the area of review (AoR) and post-injection site care (PISC) are considered. The objective for this study was firstly to systematically simulate CO2 sequestration, i.e., saturation dynamics, and pressure behavior over a range of operational and geological conditions and to derive conclusions about the factors influencing saturation and pressure plume size, post-injection behavior, and the risk associated with them, by developing third-generation reduced order models (ROMs) for reservoir behavior. Finally, to assess the uncertainty associated with our studies, Latin Hypercube Sampling (LHS) together with an experimental design technique, i.e., Plackett–Burman design, was used. Application of Pareto charts and respond surfaces enabled us to determine the most important parameters impacting saturation and pressure plume sizes and to quantify the auto- and cross-correlation among different parameters in both history-matched and upscaled models.

This paper introduces a new reduction method for linear time-invariant continuous and discrete-time systems. The method is created considering only the effect of the dominance pole to get the reduced-order model. The denominator coefficient of reduced order model (ROM) is obtained by conserving the dominant poles of a higher order system while the numerator polynomial of the reduced model is found by comparing the original system transfer function with the transfer function of desired reduced order model. Five standard numeric examples are examined from literature considering single input single output (SISO) and discrete systems. To prove the validity, accuracy and simplicity of the proposed method, the results obtained are compared with other recent established and well-known techniques like Truncation and Routh Stability methods. [ABSTRACT FROM AUTHOR]

Electromagnetic (EM) systems are prone to parameter variations and their impact help in predictive analysis. In this letter, proper orthogonal decomposition is proposed as a fast uncertainty quantification method, which can efficiently handle a large number of stochastic parameters, without any restriction on the levels of variations. The performance of the approach is evaluated in a frequency domain stochastic EM problem employing vector finite element method and having permittivity variations. The computational time increases by only 15% even with a fivefold increase in the stochastic variables. [ABSTRACT FROM AUTHOR]

The early detection of terrorist threat objects, such as guns and knives, through improved metal detection, has the potential to reduce the number of attacks and improve public safety and security. To achieve this, there is considerable potential to use the fields applied and measured by a metal detector to discriminate between different shapes and different metals since, hidden within the field perturbation, is object characterization information. The magnetic polarizability tensor (MPT) offers an economical characterization of metallic objects and its spectral signature provides additional object characterization information. The MPT spectral signature can be determined from measurements of the induced voltage over a range of frequencies in a metal signature for a hidden object. With classification in mind, it can also be computed in advance for different threat and non‐threat objects. In this article, we evaluate the performance of probabilistic and non‐probabilistic machine learning algorithms, trained using a dictionary of computed MPT spectral signatures, to classify objects for metal detection. We discuss the importance of using appropriate features and selecting an appropriate algorithm depending on the classification problem being solved, and we present numerical results for a range of practically motivated metal detection classification problems. [ABSTRACT FROM AUTHOR]

The paper studies the fault identification problem for nonlinear control systems under unmatched disturbances. A novel approach to construct a sliding mode observer is proposed for systems that do not satisfy common conditions required for fault estimation, in particular matching condition, minimum phase condition, and detectability conditions. The suggested approach is based on the reduced order model of the original system and on the canonical form of matrices describing such a model. This allows to reduce the complexity of sliding mode observers and relax the limitations imposed on the original system. Three different cases for disturbances are considered and the appropriate solutions are suggested. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for reduction of commensurate fractional-order single-input-single-output systems. The minimization in the frequency response error of the reduced order model (ROM) relative to the original system is carried out in the F-plane. A constrained optimization technique is introduced to satisfy the angle criteria for F-domain stability of the proposed ROM. Significant improvements in both the time- and frequency-responses over the recently published literature are illustrated using several numerical examples. [ABSTRACT FROM AUTHOR]