Full-order Model Research Articles

Inversion method of hydraulic conductivity for steady-state problem based on reduced-order model constructed by improved greedy sampling method

To solve the time-consuming parameter inversion problem based on swarm evolution algorithm, this study proposes an improved greedy sampling method (GSM) (IGSM) based on model reduction technology to rapidly estimate the hydraulic conductivity of steady-state seepage problem. Different from the traditional GSM, IGSM neither needs to estimate the posterior error bound of the reduced-order model (ROM) nor does it require a training sample set to train the ROM. Instead, the observation data are directly applied to the training process of ROM. Each iterative process of IGSM includes a parameter inversion process to obtain the parameters that best match the observation information and use it to update the current ROM. The improved differential evolution algorithm (e.g., MMRDE) is used as the search algorithm, and the resulting algorithm is denoted as IGSM-MMRDE. After comparative testing, IGSM-MMRDE was found to have higher accuracy and lower calculation cost than GSM-MMRDE. In addition, IGSM-MMRDE is also capable of high-dimensional parameter inversion problems and parameter inversion with a wider search range. After applying IGSM-MMRDE to the inversion of the rock mass hydraulic conductivity of the natural seepage field in the dam site area of a hydropower station, IGSM-MMRDE converges quickly and takes much less time than ADINA-MMRDE based on the full-order model (approximately 0.31% of ADINA-MMRDE). The performance results are even better than the ADINA-MMRDE using the fixed evolutionary generation. Therefore, the advantages of using IGSM in the rapid inversion of the initial seepage field of large-scale projects are extremely evident.

Adaptive surrogates of crashworthiness models for multi-purpose engineering analyses accounting for uncertainty

Uncertainty Quantification (UQ) is a booming discipline for complex computational models based on the analysis of robustness, reliability and credibility. UQ analysis for nonlinear crash models with high dimensional outputs presents important challenges. In crashworthiness, nonlinear structural behaviours with multiple hidden modes require expensive models (18 h for a single run). Surrogate models (metamodels) allow substituting the full order model, introducing a response surface for a reduced training set of numerical experiments. Moreover, uncertain input and large number of degrees of freedom result in high dimensional problems, which derives to a bottle neck that blocks the computational efficiency of the metamodels. Kernel Principal Component Analysis (kPCA) is a multidimensionality reduction technique for non-linear problems, with the advantage of capturing the most relevant information from the response and improving the efficiency of the metamodel. Aiming to compute the minimum number of samples with the full order model. The proposed methodology is tested with a practical industrial problem that arises from the automotive industry.

PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by means of partial differential equations (PDEs), to carry out the task at hand. The goal is to estimate the epicardial potential field from measurements of the electric potential at a discrete set of points on the body surface. The employment of deep learning techniques in this context is made difficult by the low amount of clinical data at disposal, as measuring cardiac potentials requires invasive procedures. Suitably exploiting the underlying physically based mathematical model allowed circumventing the data availability issue and led to the development of fast-training and low-complexity models. Physical awareness has been pursued by means of two elements: the projection of the epicardial potential onto a space-time reduced subspace, spanned by the numerical solutions of the governing PDEs, and the inclusion of a tensorial reduced basis solver of the forward problem in the network architecture. Numerical tests have been conducted only on synthetic data, obtained via a full order model approximation of the problem at hand, and two variants of the model have been addressed. Both proved to be accurate, up to an average $\ell^1$-norm relative error on epicardial activation maps of 3.5%, and both could be trained in $\approx$$15$ min. Nevertheless, some improvements, mostly concerning data generation, are necessary in order to bridge the gap with clinical applications.

Energy preserving reduced-order modeling of the rotating thermal shallow water equation

In this paper, reduced-order models (ROMs) are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with state-dependent Poisson matrix. The high fidelity full solutions are obtained by discretizing the RTSWE in space with skew-symmetric finite-differences, while preserving the Hamiltonian structure. The resulting skew-gradient system is integrated in time by the energy preserving average vector field (AVF) method. The ROM is constructed by applying proper orthogonal decomposition with the Galerkin projection, preserving the reduced skew-gradient structure, and integrating in time with the AVF method. The nonlinear terms of the Poisson matrix and Hamiltonian are approximated with the discrete empirical interpolation method to reduce the computational cost. The solutions of the resulting linear-quadratic reduced system are accelerated by the use of tensor techniques. The accuracy and computational efficiency of the ROMs are demonstrated for a numerical test problem. Preservation of the energy (Hamiltonian) and other conserved quantities, i.e., mass, buoyancy, and total vorticity, show that the reduced-order solutions ensure the long-term stability of the solutions while exhibiting several orders of magnitude computational speedup over the full-order model. Furthermore, we show that the ROMs are able to accurately predict the test and training data and capture the system behavior in the prediction phase.

Projection-Based Model Reduction for Coupled Conduction—Enclosure Radiation Systems

Abstract A projection-based reduced order model (pROM) methodology has been developed for transient heat transfer problems involving coupled conduction and enclosure radiation. The approach was demonstrated on two test problems of varying complexity. The reduced order models demonstrated substantial speedups (up to 185×) relative to the full order model with good accuracy (less than 3% L∞ error). An attractive feature of pROMs is that there is a natural error indicator for the ROM solution: the final residual norm at each time-step of the converged ROM solution. Using example test cases, we discuss how to interpret this error indicator to assess the accuracy of the ROM solution. The approach shows promise for many-query applications, such as uncertainty quantification and optimization. The reduced computational cost of the ROM relative to the full-order model (FOM) can enable the analysis of larger and more complex systems as well as the exploration of larger parameter spaces.

A reduced order modeling method based on GNAT-embedded hybrid snapshot simulation

This paper presents a method to embed the Gauss–Newton approximated tensor (GNAT) reduced order model (ROM) into the hybrid snapshot simulation to enhance generation speed and representation of snapshot data for constructing GNAT ROMs. The snapshot simulation is divided into multiple temporal intervals, each of which is simulated by one of three numerical models: the full order model (FOM), the local ROM based on Petrov–Galerkin projection (ROM-PG), or the local ROM based on GNAT (ROM-GNAT). New model switch criteria are proposed to determine alternation among FOM, ROM-PG and ROM-GNAT in the simulation on-the-fly, which not only expedites snapshot data generation, but also preserves its underlying subspace representation. In contrast to existing GNAT approaches, the proper orthogonal decomposition (POD) modes of the residual and the column-reduced Jacobian in our local ROM-GNATs are continuously updated by the incremental singular value decomposition (iSVD) of the snapshot data generated by both the FOM and the local ROM-PG in the preceding intervals. The GNAT-embedded snapshot simulation is implemented for the recently proposed finite volume discretization of the 2D Burgers equation, and demonstrated for flow with weak divergence (Re≤100). Compared with its traditional counterparts, the proposed method accelerates the snapshot simulation by 33% while keeping the numerical error (RMSE) around 10−3. In online simulation, the ROM-GNAT constructed using the proposed hybrid snapshot method is compared with the high fidelity FOM. It is found that the ROM-GNAT is 70% faster and the numerical error (RMSE) is less than 10−2 relative to the FOM in the online simulation.

Consistency of the full and reduced order models for evolve-filter-relax regularization of convection-dominated, marginally-resolved flows.

Numerical stabilization is often used to eliminate (alleviate) the spurious oscillations generally produced by full order models (FOMs) in under‐resolved or marginally‐resolved simulations of convection‐dominated flows. In this article, we investigate the role of numerical stabilization in reduced order models (ROMs) of marginally‐resolved, convection‐dominated incompressible flows. Specifically, we investigate the FOM–ROM consistency, that is, whether the numerical stabilization is beneficial both at the FOM and the ROM level. As a numerical stabilization strategy, we focus on the evolve‐filter‐relax (EFR) regularization algorithm, which centers around spatial filtering. To investigate the FOM‐ROM consistency, we consider two ROM strategies: (i) the EFR‐noEFR, in which the EFR stabilization is used at the FOM level, but not at the ROM level; and (ii) the EFR‐EFR, in which the EFR stabilization is used both at the FOM and at the ROM level. We compare the EFR‐noEFR with the EFR‐EFR in the numerical simulation of a 2D incompressible flow past a circular cylinder in the convection‐dominated, marginally‐resolved regime. We also perform model reduction with respect to both time and Reynolds number. Our numerical investigation shows that the EFR‐EFR is more accurate than the EFR‐noEFR, which suggests that FOM‐ROM consistency is beneficial in convection‐dominated, marginally‐resolved flows.

A machine learning method for real-time numerical simulations of cardiac electromechanics

We propose a machine learning-based method to build a system of differential equations that approximates the dynamics of 3D electromechanical models for the human heart, accounting for the dependence on a set of parameters. Specifically, our method permits to create a reduced-order model (ROM), written as a system of Ordinary Differential Equations (ODEs) wherein the forcing term, given by the right-hand side, consists of an Artificial Neural Network (ANN), that possibly depends on a set of parameters associated with the electromechanical model to be surrogated. This method is non-intrusive, as it only requires a collection of pressure and volume transients obtained from the full-order model (FOM) of cardiac electromechanics. Once trained, the ANN-based ROM can be coupled with hemodynamic models for the blood circulation external to the heart, in the same manner as the original electromechanical model, but at a dramatically lower computational cost. Indeed, our method allows for real-time numerical simulations of the cardiac function. Our results show that the ANN-based ROM is accurate with respect to the FOM (relative error between 10−3 and 10−2 for biomarkers of clinical interest), while requiring very small training datasets (30–40 samples). We demonstrate the effectiveness of the proposed method on two relevant contexts in cardiac modeling. First, we employ the ANN-based ROM to perform a global sensitivity analysis on both the electromechanical and hemodynamic models. Second, we perform a Bayesian estimation of two parameters starting from noisy measurements of two scalar outputs. In both these cases, replacing the FOM of cardiac electromechanics with the ANN-based ROM makes it possible to perform in a few hours of computational time all the numerical simulations that would be otherwise unaffordable, because of their overwhelming computational cost, if carried out with the FOM. As a matter of fact, our ANN-based ROM is able to speedup the numerical simulations by more than three orders of magnitude.

Projection-tree reduced-order modeling for fast N-body computations

This work presents a data-driven reduced-order modeling framework to accelerate the computations of nonlocal and N-body methods that model dynamical systems. The proposed framework differs from traditional acceleration methods, like the Barnes–Hut method, which requires online tree building of the state space, or the fast-multipole method, which requires rigorous a priori analysis of governing kernels and online tree building. Our approach combines Barnes–Hut hierarchical decomposition, projection-based reduced-order modeling via the least-squares Petrov–Galerkin (LSPG) projection, and hyper-reduction by way of the Gauss–Newton with approximated tensor (GNAT) approach. The resulting projection-tree reduced-order model (PTROM) enables a drastic reduction in operational count complexity by constructing sparse hyper-reduced pairwise interactions of the non-compact N-body dynamical system. As a result, the presented framework is capable of achieving an operational count complexity that is independent of N, the number of bodies in the numerical domain. Capabilities of the PTROM method are demonstrated on the two-dimensional fluid-dynamic Biot–Savart kernel within a parametric and reproductive setting. Results show the PTROM is capable of achieving over 2000× wall-time speed-up with respect to the full-order model, where the speed-up increases with N. The resulting solution delivers quantities of interest with errors that are less than 0.1% with respect to full-order model.

Reduced Order Modeling of Deformable Tire-Soil Interaction With Proper Orthogonal Decomposition

AbstractIn this study, model order reduction of high-fidelity off-road mobility models is explored to address the computational intensity of nonlinear finite element deformable tire–soil interaction models. To this end, a model order reduction procedure for the tire–soil interaction model is developed with the proper orthogonal decomposition (POD), and it is integrated into the off-road mobility simulation framework, leveraging high-performance computing. The POD is, however, limited in that the modes are dependent on snapshot data collected during the running of a full order model, limiting the modes to being accurate only for the specific scenario from which they were collected. Due to this limitation, a method of mode adaptation through interpolation on a tangent space of the Grassmann manifold is investigated to allow modes to be predicted for cases in which a full order model has not been run. It is demonstrated by several numerical examples that the POD modes are effective at retaining predictive accuracy while reducing computational time. The results show that adapted POD modes are more capable of characterizing the behavior of the model than modes produced at a different value of the simulation parameter. The POD-based reduced order modeling approach is further extended to the full vehicle simulation on deformable terrain through the co-simulation coupling algorithm by leveraging the high-performance computing technique.

A sample-efficient deep learning method for multivariate uncertainty qualification of acoustic–vibration interaction problems

We propose an efficient Monte Carlo simulation method to address the multivariate uncertainties in acoustic–vibration interaction systems. The deep neural network acts as a general surrogate model to enhance the sampling efficiency of Monte Carlo Simulation. Singular Value Decomposition - Radial Basis Functions (SVD-RBF) acts as a bridge between the original full model and the neural network, enabling the training datasets of the neural network to be evaluated rapidly from a reduced-order model. The snapshots of full order models are obtained with isogeometric analysis, in which we couple two numerical schemes for vibro–acoustic interaction problems: the isogeometric finite element method for simulating vibration of Kirchhoff–Love shells and isogeometric boundary element method for exterior acoustic waves. Numerical results show that the proposed algorithm can significantly improve the efficiency of uncertainty analysis.

Large-eddy simulation and challenges for projection-based reduced-order modeling of a gas turbine model combustor

Computationally efficient modeling of gas turbine combustion is challenging due to the chaotic multi-scale physics and the complex non-linear interactions between acoustic, hydrodynamic, and chemical processes. A large-eddy simulation, referred to as the full order model (FOM), is performed for a gas turbine model combustor with turbulent combustion effects modeled using a flamelet-based method. Modal analysis reveals a high degree of correlation with averaged and instantaneous high-frequency particle image velocimetry fields. The dynamics of the precessing vortex core is quantitatively characterized using dynamic mode decomposition. The governing equations of the FOM are projected onto a low-dimensional linear manifold to construct a reduced-order model (ROM). A discretely-consistent least squares projection is used to guarantee global stability. The ROM provides an accurate reconstruction of the combustion dynamics within the training region, but faces a significant challenge in future state predictions. This limitation is mainly due to the increased projection error, which in turn is a direct consequence of the highly chaotic nature of the flow field, involving a wide range of dispersed coherent structures. This shortcoming is overcome using an adaptive basis method which yields accurate predictions of dynamics beyond the training region consistent with the FOM. Formal projection-based ROMs have not been applied to a problem of this scale and complexity, and achieving accurate and efficient ROMs is a grand challenge problem. A production-ready ROM method will significantly decrease the computational cost of the flame dynamics as well as the portability of this prediction to smaller-scale computers.

Mode transformation and interaction in vortex-induced vibration of laminar flow past a circular cylinder

An investigation of the mode transformation and interaction underlying the behavior of vortex-induced vibration (VIV) of a flow past a circular cylinder elastically mounted on a linear spring is conducted using a high-fidelity full-order model (FOM) based on computational fluid dynamics (CFD), a reduced-order model (ROM), and a dynamic mode decomposition (DMD) of the velocity. A reduced-order model for the fluid dynamics is obtained using the eigensystem realization algorithm (ERA), which is subsequently coupled to a linear structural equation to provide a state space model for the coupled VIV system, in order to provide a simplified computationally inexpensive mathematical representation of the system. This methodology is used to study the dynamics of laminar flows past an elastically mounted circular cylinder with Reynolds number Re ranging from 20 to 180, inclusive. The results of the simulations conducted using FOM/CFD and ROM/ERA, in conjunction with the power spectral analysis and DMD, are used to identify the characteristic natural frequencies and the growth/decay of various modes (including the complex interactions between the myriad wake modes and the structural mode) of the VIV system as a function of the Reynolds number and the reduced natural frequency Fs (or, equivalently, the reduced velocity Ur). A detailed analysis of the distribution of the eigenvalues of the transfer (or, system) matrix of the reduced VIV system shows that the frequency range of the lock-in can be partitioned into resonance and flutter lock-in regimes. The resonance lock-in (lower branch of the VIV response) dominates the fluid-structure interaction. Furthermore, it is shown that when the structural natural frequency is close to one of the eigenfrequencies associated with the wake modes, resonance lock-in (rather than flutter lock-in) will be the primary mechanism governing the VIV response even though the real part of the eigenvalues associated with structural mode is positive. With increasing Reynolds number, the instability of each wake mode is enhanced resulting in a transformation of the wake modes interacting with the structural mode. It is suggested herein that the weakened interaction between the wake modes and the structural mode at Re = 180 (associated with the greater separation between the root loci of the modes) results in the premature termination of the resonance lock-in at Fs=0.155 with increasing Ur. The DMD and power spectral analysis of the time series of the transverse displacement and lift coefficient are used to support the results obtained from ROM/ERA and, more specifically, to provide a clear demonstration of the balanced interaction between the wake modes and the structural mode. This result is used to explain the beating phenomenon, which occurs in the initial branch and the significant lag time that arises between the initial branch and the occurrence of a fully developed response in the lower branch.

Three-dimensional deep learning-based reduced order model for unsteady flow dynamics with variable Reynolds number

In this article, we present a deep learning-based reduced order model (DL-ROM) for predicting the fluid forces and unsteady vortex shedding patterns. We consider the flow past a sphere to examine the accuracy of our DL-ROM predictions. The proposed DL-ROM methodology relies on a three-dimensional convolutional recurrent autoencoder network (3D CRAN) to extract the low-dimensional flow features from the full-order snapshots in an unsupervised manner. The low-dimensional features are evolved in time using a long short-term memory-based recurrent neural network and reconstructed back to the full-order as flow voxels. These flow voxels are introduced as static and uniform query probes in the point cloud domain to reduce the unstructured mesh complexity while providing convenience in the 3D CRAN training. We introduce a novel procedure to recover the interface description and the instantaneous force quantities from these 3D flow voxels. To evaluate the 3D flow reconstruction and inference, the 3D CRAN methodology is first applied to an external flow past a static sphere at the single Reynolds number of Re = 300. We provide an assessment of the computing requirements in terms of the memory usage, training, and testing cost of the 3D CRAN framework. Subsequently, variable Re-based flow information is infused in one 3D CRAN to learn a symmetry-breaking flow regime (280 ≤ Re ≤ 460) for the flow past a sphere. Effects of transfer learning are analyzed for training this complex 3D flow regime on a relatively smaller time series dataset. The 3D CRAN framework learns the flow regime nearly 20 times faster than the parallel full-order model and predicts this flow regime in time with a reasonable accuracy. Based on the predicted flow fields, the network demonstrates an R2 accuracy of 98.58% for the drag and 76.43% for the lift over the sphere in this flow regime. The proposed framework aligns with the development of a digital twin for 3D unsteady flow field and instantaneous force predictions with variable Re-based effects.

Towards real time assessment of earthfill dams via Model Order Reduction

The use of Internet of Things (IoT) technologies is becoming a preferred solution for the assessment of tailings dams safety. Real-time sensor monitoring proves to be a key tool for reducing the risk related to these ever-evolving earth-fill structures, that exhibit a high rate of sudden and hazardous failures. In order to optimally exploit real-time embankment monitoring, one major hindrance has to be overcome: the creation of a supporting numerical model for stability analysis, with rapid-enough response to perform data assimilation in real time. A model should be built, such that its response can be obtained faster than the physical evolution of the analyzed phenomenon. In this work, Reduced Order Modeling (ROM) is used to boost computational efficiency in solving the coupled hydro-mechanical system of equations governing the problem. The Reduced Basis method is applied to the coupled hydro-mechanical equations that govern the groundwater flow, that are made non-linear as a result of considering an unsaturated soil. The resulting model’s performance is assessed by solving a 2D and a 3D problem relevant to tailings dams safety. The ROM technique achieves a speedup of 3 to 15 times with respect to the full-order model (FOM) while maintaining high levels of accuracy.

Fast active thermal cloaking through PDE-constrained optimization and reduced-order modelling

In this paper, we show how to efficiently achieve thermal cloaking from a computational standpoint in several virtual scenarios by controlling a distribution of active heat sources. We frame this problem in the setting of PDE-constrained optimization, where the reference field is the solution of the time-dependent heat equation in the absence of the object to cloak. The optimal control problem then aims at actuating the space–time control field so that the thermal field outside the obstacle is indistinguishable from the reference field. In particular, we consider multiple scenarios where material’s thermal diffusivity, source intensity and obstacle’s temperature are allowed to vary within a user-defined range. To tackle the thermal cloaking problem in a rapid and reliable way, we rely on a parametrized reduced order model built through the reduced basis method, thus entailing huge computational speedups compared with a high-fidelity, full-order model exploiting the finite-element method while dealing both with complex target shapes and disconnected control domains.

An iterative algorithm for POD basis adaptation in solving parametric convection–diffusion equations

In this paper, we develop an iterative algorithm for proper orthogonal decomposition (POD) basis adaptation in solving linear parametric PDEs. Specifically, we consider the convection–diffusion equations with diffusivity as a parameter. To construct POD basis functions for the convection–diffusion equation with a small diffusivity, we need a fine-grid solver to obtain accurate solution snapshots, which leads to a large amount of computation and memory costs. Meanwhile, a coarse-grid solver is sufficient for obtaining accurate solution snapshots for the convection–diffusion equation with a large diffusivity. We aim to adapt the POD basis functions extracted from the solution snapshots of a large diffusivity for the construction of a reduced-order model at a small diffusivity without resorting to a fine-grid solver. Our POD basis adaptation method exploits the implicit dependence of solutions on diffusivity. The POD basis functions are adapted through an iterative algorithm, where the full-order model simulation at a large diffusivity and the POD-based reduced-order model simulation at a small diffusivity are implemented, alternatively. We also provide convergence analysis for our POD basis adaptation method. The algorithm and convergence analysis can be generalized to other types of linear parametric PDEs without any difficulty. Finally, we present numerical results to demonstrate the performance and accuracy of the proposed method.

Intrusive and data-driven reduced order modelling of the rotating thermal shallow water equation

In this paper, we investigate projection-based intrusive and data-driven model order reduction in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form. Discretization of the RTSWE in space with centered finite differences leads to Hamiltonian system of ordinary differential equations with linear and quadratic terms. The full-order model (FOM) is obtained by applying linearly implicit Kahan’s method in time. Applying proper orthogonal decomposition with Galerkin projection (POD-G), we construct the intrusive reduced-order model (ROM). We apply operator inference (OpInf) with re-projection as data-driven ROM. In the parametric case, we make use of the parameter dependency at the level of the PDE without interpolating between the reduced operators. The least-squares problem of the OpInf is regularized with the minimum norm solution. Both ROMs behave similarly and are able to accurately predict the in the test and training data and capture system behaviour in the prediction phase with several orders of magnitude in computational speed-up over the FOM. The preservation of system physics such as the conserved quantities of the RTSWE by both ROMs enable that the models fit better to data and stable solutions are obtained in long-term predictions which are robust to parameter changes.

A novel model reduction technique for mistuned blisks based on proper orthogonal decomposition in frequency domain

Aiming at the problem of dynamic model reduction of mistuned blisks, this study proposes a model reduction method based on the proper orthogonal decomposition (POD) in the frequency domain and establishes the reduced-order model (ROM). The mistuning amount of blisk is characterized as generalized mistuned load, and then a mistuned load interpolation algorithm is introduced to solve the forced vibration response. POD ROM is used to analyze the modal characteristics and vibration response characteristics of a mistuned blisk with 20 sectors, and the results are compared with the full-order model (FOM) and the subset nominal mode (SNM) reduced model. The results show that the model reduction method proposed in this paper can improve the calculation efficiency while ensuring calculation accuracy. In the aspect of modal characteristics of the mistuned blisk, its calculation accuracy is better than the SNM model reduction method, the calculation error of natural frequency is less than 0.05%, and the spatial distribution characteristics of mistuned modes are closer to the results of FOM. In terms of response characteristics, the forced response accuracy is affected by the integration time step and relaxation factor, and the steady-state amplitude error in the time domain can be controlled below 5%.

Nonintrusive Model Order Reduction for Cross-Diffusion Systems

In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tensor form resulting from finite-difference discretization of the differential operators by taking the advantage of Kronecker structure. The matrix/tensor differential equations are integrated in time with the implicit-explicit (IMEX) Euler method. The reduced bases, relying on a finite sample set of parameter values, are constructed in form of a two-level approach by applying higher-order singular value decomposition (HOSVD) to the space-time snapshots in tensor form, which leads to a large amount of computational and memory savings. The nonintrusive reduced approximations for an arbitrary parameter value are obtained through tensor product of the reduced basis by the parameter dependent core tensor that contains the reduced coefficients. The reduced coefficients for new parameter values are computed using radial basis function (RBF) interpolation. The efficiency of the proposed method is illustrated through numerical experiments for two-dimensional Schnakenberg and three-dimensional Brusselator cross-diffusion equations. The spatiotemporal patterns are accurately predicted by the reduced-order models with speed-up factors of orders two and three over the full-order models.