Статті в журналах: "Data-Driven reduced order modeling"

1

Guo, Mengwu, and Jan S. Hesthaven. "Data-driven reduced order modeling for time-dependent problems." Computer Methods in Applied Mechanics and Engineering 345 (March 2019): 75–99. http://dx.doi.org/10.1016/j.cma.2018.10.029.

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Xie, X., M. Mohebujjaman, L. G. Rebholz, and T. Iliescu. "Data-Driven Filtered Reduced Order Modeling of Fluid Flows." SIAM Journal on Scientific Computing 40, no. 3 (January 2018): B834—B857. http://dx.doi.org/10.1137/17m1145136.

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3

Ivagnes, Anna, Giovanni Stabile, Andrea Mola, Traian Iliescu, and Gianluigi Rozza. "Hybrid data-driven closure strategies for reduced order modeling." Applied Mathematics and Computation 448 (July 2023): 127920. http://dx.doi.org/10.1016/j.amc.2023.127920.

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Borcea, Liliana, Josselin Garnier, Alexander V. Mamonov, and Jörn Zimmerling. "When Data Driven Reduced Order Modeling Meets Full Waveform Inversion." SIAM Review 66, no. 3 (May 2024): 501–32. http://dx.doi.org/10.1137/23m1552826.

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Peters, Nicholas, Christopher Silva, and John Ekaterinaris. "A data-driven reduced-order model for rotor optimization." Wind Energy Science 8, no. 7 (July 20, 2023): 1201–23. http://dx.doi.org/10.5194/wes-8-1201-2023.

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Abstract. For rotor design applications, such as wind turbine rotors or urban air mobility (UAM) rotorcraft and flying-car design, there is a significant challenge in quickly and accurately modeling rotors operating in complex, turbulent flow fields. One potential path for deriving reasonably accurate but low-cost rotor performance predictions is available through the application of data-driven surrogate modeling. In this study, an initial investigation is undertaken to apply a proper orthogonal decomposition (POD)-based reduced-order model (ROM) for predicting rotor distributed loads. The POD ROM was derived based on computational fluid dynamics (CFD) results and utilized to produce distributed-pressure predictions on rotor blades subjected to topology change due to variations in the twist and taper ratio. Rotor twist, θ, was varied between 0, 10, 20, and 30∘, while the taper ratio, λ, was varied as 1.0, 0.9, 0.8, and 0.7. For a demonstration of the approach, all rotors consisted of a single blade. The POD ROM was validated for three operation cases: a high-pitch or a high-thrust rotor in hover, a low-pitch or a low-thrust rotor in hover, and a rotor in forward flight at a low speed resembling wind turbine operation with wind shear. Results showed that reasonably accurate distributed-load predictions could be achieved and the resulting surrogate model can predict loads at a minimal computational cost. The computational cost for the hovering blade surface pressure prediction was reduced from 12 h on 440 cores required for CFD to a fraction of a second on a single core required for POD. For rotors in forward flight, cost was reduced from 20 h on 440 cores to less than a second on a single core. The POD ROM was used to carry out a design optimization of the rotor such that the figure of merit was maximized for hovering-rotor cases and the lift-to-drag effective ratio was maximized in forward flight.

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Zhang, Xinshuai, Tingwei Ji, Fangfang Xie, Changdong Zheng, and Yao Zheng. "Data-driven nonlinear reduced-order modeling of unsteady fluid–structure interactions." Physics of Fluids 34, no. 5 (May 2022): 053608. http://dx.doi.org/10.1063/5.0090394.

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A novel data-driven nonlinear reduced-order modeling framework is proposed for unsteady fluid–structure interactions (FSIs). In the proposed framework, a convolutional variational autoencoder model is developed to determine the coordinate transformation from a high-dimensional physical field into a reduced space. This enables the efficient extraction of nonlinear low-dimensional manifolds from the high-dimensional unsteady flow field of the FSIs. The sparse identification of a nonlinear dynamics (SINDy) algorithm is then used to identify the dynamical governing equations of the reduced space and the vibration responses. To investigate and validate the effectiveness of the proposed framework for modeling and predicting unsteady flow fields in FSI problems, the two-dimensional laminar vortex shedding of a fixed cylinder is considered. Furthermore, the proposed data-driven nonlinear reduced-order modeling framework is applied to the three-dimensional vortex-induced vibration of a flexible cylinder. Using the SINDy model to analyze the vibration responses, the dynamics of the flexible cylinder are found to be correlated with the flow wake patterns, revealing the underlying FSI mechanism. The present work is a significant step toward the establishment of machine learning-based nonlinear reduced-order models for complex flow phenomena, the discovery of underlying unsteady FSI physics, and real-time flow control.

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Baumann, Henry, Alexander Schaum, and Thomas Meurer. "Data-driven control-oriented reduced order modeling for open channel flows." IFAC-PapersOnLine 55, no. 26 (2022): 193–99. http://dx.doi.org/10.1016/j.ifacol.2022.10.399.

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German, Péter, Mauricio E. Tano, Carlo Fiorina, and Jean C. Ragusa. "Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media." Fluids 6, no. 8 (July 28, 2021): 266. http://dx.doi.org/10.3390/fluids6080266.

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This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

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Gruber, Anthony, Max Gunzburger, Lili Ju, and Zhu Wang. "A comparison of neural network architectures for data-driven reduced-order modeling." Computer Methods in Applied Mechanics and Engineering 393 (April 2022): 114764. http://dx.doi.org/10.1016/j.cma.2022.114764.

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10

Li, Mengnan, and Lijian Jiang. "Data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media." Journal of Computational Physics 474 (February 2023): 111799. http://dx.doi.org/10.1016/j.jcp.2022.111799.

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Mohebujjaman, M., L. G. Rebholz, and T. Iliescu. "Physically constrained data‐driven correction for reduced‐order modeling of fluid flows." International Journal for Numerical Methods in Fluids 89, no. 3 (October 15, 2018): 103–22. http://dx.doi.org/10.1002/fld.4684.

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12

Sun, Zhe, Lu-yu Sun, Li-xin Xu, Yu-long Hu, Gui-yong Zhang, and Zhi Zong. "A CFD-Based Data-Driven Reduced Order Modeling Method for Damaged Ship Motion in Waves." Journal of Marine Science and Engineering 11, no. 4 (March 23, 2023): 686. http://dx.doi.org/10.3390/jmse11040686.

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A simple CFD-based data-driven reduced order modeling method was proposed for the study of damaged ship motion in waves. It consists of low-order modeling of the whole concerned parameter range and high-order modeling for selected key scenarios identified with the help of low-order results. The difference between the low and high-order results for the whole parameter range, where the main trend of the physics behind the problem is expected to be captured, is then modeled by some commonly used machine learning or data regression methods based on the data from key scenarios which is chosen as Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) in this study. The final prediction is obtained by adding the results from the low-order model and the difference. The low and high-order modeling were conducted through computational fluid dynamics (CFD) simulations with coarse and refined meshes. Taking the roll Response Amplitude Operator (RAO) of a DTMB-5415 ship model with a damaged cabin as an example, the proposed physics-informed data-driven model was shown to have the same level of accuracy as pure high-order modeling, whilst the computational time can be reduced by 22~55% for the studied cases. This simple reduced order modeling approach is also expected to be applicable to other ship hydrodynamic problems.

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Pawar, Suraj, Shady E. Ahmed, Omer San, and Adil Rasheed. "Data-driven recovery of hidden physics in reduced order modeling of fluid flows." Physics of Fluids 32, no. 3 (March 1, 2020): 036602. http://dx.doi.org/10.1063/5.0002051.

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14

Yu, Mengjun, and Kun Li. "A data-driven reduced-order modeling approach for parameterized time-domain Maxwell's equations." Networks and Heterogeneous Media 19, no. 3 (2024): 1309–35. http://dx.doi.org/10.3934/nhm.2024056.

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<p>This paper proposed a data-driven non-intrusive model order reduction (NIMOR) approach for parameterized time-domain Maxwell's equations. The NIMOR method consisted of fully decoupled offline and online stages. Initially, the high-fidelity (HF) solutions for some training time and parameter sets were obtained by using a discontinuous Galerkin time-domain (DGTD) method. Subsequently, a two-step or nested proper orthogonal decomposition (POD) technique was used to generate the reduced basis (RB) functions and the corresponding projection coefficients within the RB space. The high-order dynamic mode decomposition (HODMD) method leveraged these corresponding coefficients to predict the projection coefficients at all training parameters over a time region beyond the training domain. Instead of direct regression and interpolating new parameters, the predicted projection coefficients were reorganized into a three-dimensional tensor, which was then decomposed into time- and parameter-dependent components through the canonical polyadic decomposition (CPD) method. Gaussian process regression (GPR) was then used to approximate the relationship between the time/parameter values and the above components. Finally, the reduced-order solutions at new time/parameter values were quickly obtained through a linear combination of the POD modes and the approximated projection coefficients. Numerical experiments were presented to evaluate the performance of the method in the case of plane wave scattering.</p>

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Besabe, Lander, Michele Girfoglio, Annalisa Quaini, and Gianluigi Rozza. "Data-driven reduced order modeling of a two-layer quasi-geostrophic ocean model." Results in Engineering 25 (March 2025): 103691. https://doi.org/10.1016/j.rineng.2024.103691.

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Fasel, Urban, Nicola Fonzi, Andrea Iannelli, and Steven L. Brunton. "FlexWing-ROM: A matlab framework for data-driven reduced-order modeling of flexible wings." Journal of Open Source Software 7, no. 80 (December 12, 2022): 4211. http://dx.doi.org/10.21105/joss.04211.

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Brewick, Patrick T., Sami F. Masri, Biagio Carboni, and Walter Lacarbonara. "Enabling reduced-order data-driven nonlinear identification and modeling through naïve elastic net regularization." International Journal of Non-Linear Mechanics 94 (September 2017): 46–58. http://dx.doi.org/10.1016/j.ijnonlinmec.2017.01.016.

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Sherman, Julie, Christian Sampson, Emmanuel Fleurantin, Zhimin Wu, and Christopher K. R. T. Jones. "A Data-Driven Study of the Drivers of Stratospheric Circulation via Reduced Order Modeling and Data Assimilation." Meteorology 3, no. 1 (December 19, 2023): 1–35. http://dx.doi.org/10.3390/meteorology3010001.

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Stratospheric dynamics are strongly affected by the absorption/emission of radiation in the Earth’s atmosphere and Rossby waves that propagate upward from the troposphere, perturbing the zonal flow. Reduced order models of stratospheric wave–zonal interactions, which parameterize these effects, have been used to study interannual variability in stratospheric zonal winds and sudden stratospheric warming (SSW) events. These models are most sensitive to two main parameters: Λ, forcing the mean radiative zonal wind gradient, and h, a perturbation parameter representing the effect of Rossby waves. We take one such reduced order model with 20 years of ECMWF atmospheric reanalysis data and estimate Λ and h using both a particle filter and an ensemble smoother to investigate if the highly-simplified model can accurately reproduce the averaged reanalysis data and which parameter properties may be required to do so. We find that by allowing additional complexity via an unparameterized Λ(t), the model output can closely match the reanalysis data while maintaining behavior consistent with the dynamical properties of the reduced-order model. Furthermore, our analysis shows physical signatures in the parameter estimates around known SSW events. This work provides a data-driven examination of these important parameters representing fundamental stratospheric processes through the lens and tractability of a reduced order model, shown to be physically representative of the relevant atmospheric dynamics.

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Nagy, Peter, and Marco Fossati. "Adaptive Data-Driven Model Order Reduction for Unsteady Aerodynamics." Fluids 7, no. 4 (April 6, 2022): 130. http://dx.doi.org/10.3390/fluids7040130.

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A data-driven adaptive reduced order modelling approach is presented for the reconstruction of impulsively started and vortex-dominated flows. A residual-based error metric is presented for the first time in the framework of the adaptive approach. The residual-based adaptive Reduced Order Modelling selects locally in time the most accurate reduced model approach on the basis of the lowest residual produced by substituting the reconstructed flow field into a finite volume discretisation of the Navier–Stokes equations. A study of such an error metric was performed to assess the performance of the resulting residual-based adaptive framework with respect to a single-ROM approach based on the classical proper orthogonal decomposition, as the number of modes is varied. Two- and three-dimensional unsteady flows were considered to demonstrate the key features of the method and its performance.

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Matveev, Konstantin I. "Reduced-order modeling of vortex-driven excitation of acoustic modes." Acoustics Research Letters Online 6, no. 1 (January 2005): 14–19. http://dx.doi.org/10.1121/1.1815253.

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Prakash, Aviral, and Yongjie Jessica Zhang. "Projection-based reduced order modeling and data-driven artificial viscosity closures for incompressible fluid flows." Computer Methods in Applied Mechanics and Engineering 425 (May 2024): 116930. http://dx.doi.org/10.1016/j.cma.2024.116930.

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Cillo, Pierfrancesco, Alexander Brauchler, Sebastian Gonzalez, Pascal Ziegler, Fabio Antonacci, Augusto Sarti, and Peter Eberhard. "Improving accuracy in parametric reduced-order models for classical guitars through data-driven discrepancy modeling." Acta Acustica 8 (2024): 59. http://dx.doi.org/10.1051/aacus/2024055.

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Recently developed high-fidelity finite element (FE) models represent a state-of-the-art approach for gaining a deeper understanding of the vibrational behavior of musical instruments. They can also be used as virtual prototypes. However, certain analyses, such as optimization or parameter identification, necessitate numerous model evaluations, resulting in long computation times when utilizing the FE model. Projection-based parametric model order reduction (PMOR) proves to be a powerful tool for enhancing the computational efficiency of FE models while retaining parameter dependencies. Despite their advantages, projection-based methods often require complete system matrices, which may have limited accessibility. Consequently, a systematic discrepancy is introduced in the reduced-order model compared to the original model. This contribution introduces a discrepancy modeling method designed to approximate the parameter-dependent effect of a radiating boundary condition in an FE model of a classical guitar that cannot be exported from the commercial FE software Abaqus. To achieve this, a projection-based reduced-order model is augmented by a data-driven model that captures the error in the approximation of eigenfrequencies and eigenmodes. Artificial neural networks account for the data-driven discrepancy models. This methodology offers significant computational savings and improved accuracy, making it highly suitable for far-reaching parametric studies and iterative processes. The combination of PMOR and neural networks demonstrate greater accuracy than using either approach alone. This paper extends our prior research presented in the proceedings of Forum Acusticum 2023, offering a more comprehensive examination and additional insights.

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23

Guang, Weilong, Peng Wang, Jinshuai Zhang, Linjuan Yuan, Yue Wang, Guang Feng, and Ran Tao. "Reduced Order Data-Driven Analysis of Cavitating Flow over Hydrofoil with Machine Learning." Journal of Marine Science and Engineering 12, no. 1 (January 12, 2024): 148. http://dx.doi.org/10.3390/jmse12010148.

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Predicting the flow situation of cavitation owing to its high-dimensional nonlinearity has posed great challenges. To address these challenges, this study presents a novel reduced order modeling (ROM) method to accurately analyze and predict cavitation flow fields under different conditions. The proposed ROM decomposes the flow field into linearized low-order modes while maintaining its accuracy and effectively reducing its dimensionality. Specifically, this study focuses on predicting cavitation on the Clark-Y hydrofoil using a combination of numerical simulation, proper orthogonal decomposition (POD), and neural networks. By analyzing different cavitation conditions, the results revealed that the POD method effectively reduces the order of the cavity flow field while achieving excellent flow field reconstruction. Notably, the zeroth- and first-order modes are associated with attachment cavitation, while the second-, third- and fourth-order modes correspond to cavitation shedding. Additionally, the fifth- and sixth-order modes along the hydrofoil surface are associated with the backward jet flow. To predict the conditions of high-energy modes, the neural network proved to be more effective, exhibiting excellent performance in stable attached cavitation. However, for cloud cavitation, the accuracy of the neural network model requires further improvement. This study not only introduces a novel approach for predicting cavitation flow fields but also highlights new challenges that will require continuous attention in future research endeavors.

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Rahman, Sk, Adil Rasheed, and Omer San. "A Hybrid Analytics Paradigm Combining Physics-Based Modeling and Data-Driven Modeling to Accelerate Incompressible Flow Solvers." Fluids 3, no. 3 (July 18, 2018): 50. http://dx.doi.org/10.3390/fluids3030050.

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Numerical solution of the incompressible Navier–Stokes equations poses a significant computational challenge due to the solenoidal velocity field constraint. In most computational modeling frameworks, this divergence-free constraint requires the solution of a Poisson equation at every step of the underlying time integration algorithm, which constitutes the major component of the computational expense. In this study, we propose a hybrid analytics procedure combining a data-driven approach with a physics-based simulation technique to accelerate the computation of incompressible flows. In our approach, proper orthogonal basis functions are generated to be used in solving the Poisson equation in a reduced order space. Since the time integration of the advection–diffusion equation part of the physics-based model is computationally inexpensive in a typical incompressible flow solver, it is retained in the full order space to represent the dynamics more accurately. Encoder and decoder interface conditions are provided by incorporating the elliptic constraint along with the data exchange between the full order and reduced order spaces. We investigate the feasibility of the proposed method by solving the Taylor–Green vortex decaying problem, and it is found that a remarkable speed-up can be achieved while retaining a similar accuracy with respect to the full order model.

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Demou, Andreas D., and Nikos Savva. "Hybrid AI-Analytical Modeling of Droplet Dynamics on Inclined Heterogeneous Surfaces." Mathematics 12, no. 8 (April 15, 2024): 1188. http://dx.doi.org/10.3390/math12081188.

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This work presents a novel approach for the study of the movement of droplets on inclined surfaces under the influence of gravity and chemical heterogeneities. The developed numerical methodology uses data-driven modeling to extend the applicability limits of an analytically derived reduced-order model for the contact line velocity. More specifically, while the reduced-order model is able to capture the effects of the chemical heterogeneities to a satisfactory degree, it does not account for gravity. To alleviate this shortcoming, datasets generated from direct numerical simulations are used to train a data-driven model for the contact line velocity, which is based on the Fourier neural operator and corrects the reduced-order model predictions to match the reference solutions. This hybrid surrogate model, which comprises of both analytical and data-driven components, is then integrated in time to simulate the droplet movement, offering a speedup of five orders of magnitude compared to direct numerical simulations. The performance of this hybrid model is quantified and assessed in different wetting scenarios, by considering various inclination angles and values for the Bond number, demonstrating the accuracy of the predictions as long as the adopted parameters lie within the ranges considered in the training dataset.

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26

Ma, Zhan, and Wenxiao Pan. "Data-driven nonintrusive reduced order modeling for dynamical systems with moving boundaries using Gaussian process regression." Computer Methods in Applied Mechanics and Engineering 373 (January 2021): 113495. http://dx.doi.org/10.1016/j.cma.2020.113495.

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Zhang, Hu, Chang Xu, Shangshang Wei, Zhiwen Deng, and Zhixiong Jiao. "Sparsity Promoting Dynamic Mode Decomposition for Data-Driven Modeling of Wind Turbine Wake." Journal of Physics: Conference Series 2474, no. 1 (April 1, 2023): 012028. http://dx.doi.org/10.1088/1742-6596/2474/1/012028.

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Abstract High-fidelity numerical simulation is suitable for analyzing the complex unsteady flow field dynamics of wind turbines. For a better understanding of these flow characteristics, the dynamic mode decomposition method can be used to carry out a reduced-order model study on the wakefield of wind turbines based on large-eddy simulations (LES) numerical simulation. In this paper, we abstract material dynamic information from the wakefield of the wind turbine by applying the sparsity-promoting dynamic mode decomposition (SPDMD) method, and the decomposition results are contrasted with the standard dynamic mode decomposition (DMD) method. Indicated that both mode decomposition methods can abstract the dynamic characteristics of wake and reveal the development and variation law of wind turbine wake. However, the frequency and spatial structure of the selected modes are different. For the purpose of demonstrating the extraction impact of the DMD/SPDMD method on the wakefield of wind turbines, DMD/SPDMD reduced-order models are established respectively. The result indicated that the relatively limited number of SPDMD modes is adequate to validly rehabilitate the wakefield of the unabridged wind turbine while standard DMD methods prerequisite more decomposition modes. Therefore, compared with the standard DMD method, the SPDMD method has strong robustness in mode selection, eliminates the feature information that contributes weakly to the flow, and has a smaller performance loss in the reconstruction of the wakefield of the wind turbine. The consumption of computing resources is greatly reduced.

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Nguyen, Franck, Selim M. Barhli, Daniel Pino Muñoz, and David Ryckelynck. "Computer Vision with Error Estimation for Reduced Order Modeling of Macroscopic Mechanical Tests." Complexity 2018 (December 2, 2018): 1–10. http://dx.doi.org/10.1155/2018/3791543.

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In this paper, computer vision enables recommending a reduced order model for fast stress prediction according to various possible loading environments. This approach is applied on a macroscopic part by using a digital image of a mechanical test. We propose a hybrid approach that simultaneously exploits a data-driven model and a physics-based model, in mechanics of materials. During a machine learning stage, a classification of possible reduced order models is obtained through a clustering of loading environments by using simulation data. The recognition of the suitable reduced order model is performed via a convolutional neural network (CNN) applied to a digital image of the mechanical test. The CNN recommend a convenient mechanical model available in a dictionary of reduced order models. The output of the convolutional neural network being a model, an error estimator, is proposed to assess the accuracy of this output. This article details simple algorithmic choices that allowed a realistic mechanical modeling via computer vision.

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Li, Shijie, Anh-Tu Nguyen, Thierry-Marie Guerra, and Alexandre Kruszewski. "Reduced-order model based dynamic tracking for soft manipulators: Data-driven LPV modeling, control design and experimental results." Control Engineering Practice 138 (September 2023): 105618. http://dx.doi.org/10.1016/j.conengprac.2023.105618.

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Xie, Xuping, Guannan Zhang, and Clayton G. Webster. "Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network." Mathematics 7, no. 8 (August 19, 2019): 757. http://dx.doi.org/10.3390/math7080757.

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In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams–Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches.

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Csala, Hunor, Scott T. M. Dawson, and Amirhossein Arzani. "Comparing different nonlinear dimensionality reduction techniques for data-driven unsteady fluid flow modeling." Physics of Fluids 34, no. 11 (November 2022): 117119. http://dx.doi.org/10.1063/5.0127284.

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Computational fluid dynamics (CFD) is known for producing high-dimensional spatiotemporal data. Recent advances in machine learning (ML) have introduced a myriad of techniques for extracting physical information from CFD. Identifying an optimal set of coordinates for representing the data in a low-dimensional embedding is a crucial first step toward data-driven reduced-order modeling and other ML tasks. This is usually done via principal component analysis (PCA), which gives an optimal linear approximation. However, fluid flows are often complex and have nonlinear structures, which cannot be discovered or efficiently represented by PCA. Several unsupervised ML algorithms have been developed in other branches of science for nonlinear dimensionality reduction (NDR), but have not been extensively used for fluid flows. Here, four manifold learning and two deep learning (autoencoder)-based NDR methods are investigated and compared to PCA. These are tested on two canonical fluid flow problems (laminar and turbulent) and two biomedical flows in brain aneurysms. The data reconstruction capabilities of these methods are compared, and the challenges are discussed. The temporal vs spatial arrangement of data and its influence on NDR mode extraction is investigated. Finally, the modes are qualitatively compared. The results suggest that using NDR methods would be beneficial for building more efficient reduced-order models of fluid flows. All NDR techniques resulted in smaller reconstruction errors for spatial reduction. Temporal reduction was a harder task; nevertheless, it resulted in physically interpretable modes. Our work is one of the first comprehensive comparisons of various NDR methods in unsteady flows.

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Karasözen, Bülent, Süleyman Yıldız, and Murat Uzunca. "Intrusive and data-driven reduced order modelling of the rotating thermal shallow water equation." Applied Mathematics and Computation 421 (May 2022): 126924. http://dx.doi.org/10.1016/j.amc.2022.126924.

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Ahmed, Shady E., Omer San, Kursat Kara, Rami Younis, and Adil Rasheed. "Multifidelity computing for coupling full and reduced order models." PLOS ONE 16, no. 2 (February 11, 2021): e0246092. http://dx.doi.org/10.1371/journal.pone.0246092.

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Hybrid physics-machine learning models are increasingly being used in simulations of transport processes. Many complex multiphysics systems relevant to scientific and engineering applications include multiple spatiotemporal scales and comprise a multifidelity problem sharing an interface between various formulations or heterogeneous computational entities. To this end, we present a robust hybrid analysis and modeling approach combining a physics-based full order model (FOM) and a data-driven reduced order model (ROM) to form the building blocks of an integrated approach among mixed fidelity descriptions toward predictive digital twin technologies. At the interface, we introduce a long short-term memory network to bridge these high and low-fidelity models in various forms of interfacial error correction or prolongation. The proposed interface learning approaches are tested as a new way to address ROM-FOM coupling problems solving nonlinear advection-diffusion flow situations with a bifidelity setup that captures the essence of a broad class of transport processes.

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34

Derouiche, Khouloud, Sevan Garois, Victor Champaney, Monzer Daoud, Khalil Traidi, and Francisco Chinesta. "Data-Driven Modeling for Multiphysics Parametrized Problems-Application to Induction Hardening Process." Metals 11, no. 5 (April 29, 2021): 738. http://dx.doi.org/10.3390/met11050738.

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Data-driven modeling provides an efficient approach to compute approximate solutions for complex multiphysics parametrized problems such as induction hardening (IH) process. Basically, some physical quantities of interest (QoI) related to the IH process will be evaluated under real-time constraint, without any explicit knowledge of the physical behavior of the system. Hence, computationally expensive finite element models will be replaced by a parametric solution, called metamodel. Two data-driven models for temporal evolution of temperature and austenite phase transformation, during induction heating, were first developed by using the proper orthogonal decomposition based reduced-order model followed by a nonlinear regression method for temperature field and a classification combined with regression for austenite evolution. Then, data-driven and hybrid models were created to predict hardness, after quenching. It is shown that the results of artificial intelligence models are promising and provide good approximations in the low-data limit case.

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35

Antil, Harbir, Matthias Heinkenschloss, Ronald H. W. Hoppe, Christopher Linsenmann, and Achim Wixforth. "Reduced order modeling based shape optimization of surface acoustic wave driven microfluidic biochips." Mathematics and Computers in Simulation 82, no. 10 (June 2012): 1986–2003. http://dx.doi.org/10.1016/j.matcom.2010.10.027.

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36

Riva, Stefano, Carolina Introini, Enrico Zio, and Antonio Cammi. "Impact of Malfunctioning Sensors on Data-Driven Reduced Order Modelling: Application to Molten Salt Reactors." EPJ Web of Conferences 302 (2024): 17003. http://dx.doi.org/10.1051/epjconf/202430217003.

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Over the years, the development of Data-Driven Reduced Order Modelling (DDROM) techniques has paved the way for novel approaches to combine the physical knowledge built in high-fidelity simulations with the physical observations from experimental measurements. On the one hand, these approaches allow updating and correcting the background information obtained from the physical model; on the other hand, they allow overcoming the sparsity of observations for a global state estimation. For these reasons, these approaches are of interest for applications where one of the two sources of information is incomplete: for example, for applications related to Circulating Fuel Reactors, such as the Molten Salt Fast Reactor. These reactors are characterised by a hostile and harsh environment and by the absence of solid structures inside the core, making the monitoring of the quantities of interest inside the core a challenging task. Many works of literature on DDROM assume that experimental data represent the truth, and although extensive research has been done on noisy sensors, few works of literature analyse what happens to the state estimation when one or more sensors malfunction. Then, the robust and reliable application of DDROM techniques, requires first investigating how their performance is affected by malfunctioning sensors. This work aims to investigate this aspect in the context of modelling and simulating the system response during an accidental transient occurring in a Molten Salt Fast Reactor, considering the impact of failed sensors on the performance of Data-Driven Reduced Order Modelling techniques. Quite importantly, this work also proposes a strategy based on Supervised Learning to compensate for the failed sensors.

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Pulikkathodi, Afsal, Elisabeth Lacazedieu, Ludovic Chamoin, Juan Pedro Berro Ramirez, Laurent Rota, and Malek Zarroug. "A neural network-based data-driven local modeling of spotwelded plates under impact." Mechanics & Industry 24 (2023): 34. http://dx.doi.org/10.1051/meca/2023029.

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Solving large structural problems with multiple complex localized behaviors is extremely challenging. To address this difficulty, both intrusive and non-intrusive Domain Decomposition Methods (DDM) have been developed in the past, where the refined model (local) is solved separately in its own space and time scales. In this work, the Finite Element Method (FEM) at the local scale is replaced with a data-driven Reduced Order Model (ROM) to further decrease computational time. The reduced model aims to create a low-cost, accurate and efficient mapping from interface velocities to interface forces and enable the prediction of their time evolution. The present work proposes a modeling technique based on the Physics-Guided Architecture of Neural Networks (PGANNs), which incorporates physical variables other than input/output variables into the neural network architecture. We develop this approach on a 2D plate with a hole as well as a 3D case with spot-welded plates undergoing fast deformation, representing nonlinear elastoplasticity problems. Neural networks are trained using simulation data generated by explicit dynamic FEM solvers. The PGANN results are in good agreement with the FEM solutions for both test cases, including those in the training dataset as well as the unseen dataset, given the loading type is present in the training set.

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38

Azaïez, M., T. Chacón Rebollo, M. Gómez Mármol, E. Perracchione, A. Rincón Casado, and J. M. Vega. "Data-driven reduced order modeling based on tensor decompositions and its application to air-wall heat transfer in buildings." SeMA Journal 78, no. 2 (June 2021): 213–32. http://dx.doi.org/10.1007/s40324-021-00252-3.

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39

Bai, Feng, and Yi Wang. "Reduced-Order Modeling Based on Hybrid Snapshot Simulation." International Journal of Computational Methods 18, no. 01 (June 26, 2020): 2050029. http://dx.doi.org/10.1142/s0219876220500292.

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This paper presents a hybrid snapshot simulation methodology to accelerate the generation of high-quality data for proper orthogonal decomposition (POD) and reduced-order model (ROM) development. The entire span of the snapshot simulation is divided into multiple intervals, each simulated by either high-fidelity full-order model (FOM) or fast local ROM. The simulation then alternates between FOM and local ROM to accelerate snapshot data generation while maintaining the data fidelity and representation. Model switch is determined on-the-fly by evaluating several criteria that monitor the dominance of leading POD modes and ROM trajectory. The incremental singular value decomposition (iSVD) is employed to continuously update ROMs for enhanced accuracy and utilization. A global ROM broadly applicable to various online simulation is immediately available at the end of the simulation. The hybrid snapshot simulation demonstrates excellent accuracy ([Formula: see text] error) and 2.09–2.6[Formula: see text]X speedup relative to its traditional counterpart. The constructed ROMs also preserve salient accuracy ([Formula: see text] error). The results prove feasibility of the proposed method for robust and efficient snapshot data generation and ROM development.

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40

Zapata Usandivaras, José Felix, Annafederica Urbano, Michael Bauerheim, and Bénédicte Cuenot. "Data Driven Models for the Design of Rocket Injector Elements." Aerospace 9, no. 10 (October 12, 2022): 594. http://dx.doi.org/10.3390/aerospace9100594.

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Improving the predictive capabilities of reduced-order models for the design of injector and chamber elements of rocket engines could greatly improve the quality of early rocket chamber designs. In the present work, we propose an innovative methodology that uses high-fidelity numerical simulations of turbulent reactive flows and artificial intelligence for the generation of surrogate models. The surrogate models that were generated and analyzed are deep learning networks trained on a dataset of 100 large eddy simulations of a single-shear coaxial injector chamber. The design of experiments was created considering three design parameters: chamber diameter, recess length, and oxidizer–fuel ratio. The paper presents the methodology developed for training and optimizing the data-driven models. Fully connected neural networks (FCNNs) and U-Nets were utilized as surrogate-modeling technology. Eventually, the surrogate models for the global quantity, average, and root mean square fields were used in order to analyze the impact of the length of the post’s recess on the performances obtained and the behavior of the flow.

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41

Li, Yong, Jue Yang, Wei Long Liu, and Cheng Lin Liao. "Multi-Level Model Reduction and Data-Driven Identification of the Lithium-Ion Battery." Energies 13, no. 15 (July 23, 2020): 3791. http://dx.doi.org/10.3390/en13153791.

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The lithium-ion battery is a complicated non-linear system with multi electrochemical processes including mass and charge conservations as well as electrochemical kinetics. The calculation process of the electrochemical model depends on an in-depth understanding of the physicochemical characteristics and parameters, which can be costly and time-consuming. We investigated the electrochemical modeling, reduction, and identification methods of the lithium-ion battery from the electrode-level to the system-level. A reduced 9th order linear model was proposed using electrode-level physicochemical modeling and the cell-level mathematical reduction method. The data-driven predictor-based subspace identification algorithm was presented for the estimation of lithium-ion battery model in the system-level. The effectiveness of the proposed modeling and identification methods was validated in an experimental study based on LiFePO4 cells. The accuracy and dynamic characteristics of the identified model were found to be much more likely related to the operating State of Charge (SOC) range. Experimental results showed that the proposed methods perform well with high precision and good robustness in the SOC range of 90% to 10%, and the tracking error increases significantly within higher (100–90%) or lower (10–0%) SOC ranges. Moreover, to achieve an optimal balance between high-precision and low complexity, statistical analysis revealed that the 6th, 3rd, and 5th order battery model is the optimal choice in the SOC range of 90% to 100%, 90% to 10%, and 10% to 0%, respectively.

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42

Guo, Mengwu, Shane A. McQuarrie, and Karen E. Willcox. "Bayesian operator inference for data-driven reduced-order modeling." Computer Methods in Applied Mechanics and Engineering, July 2022, 115336. http://dx.doi.org/10.1016/j.cma.2022.115336.

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43

Ma, Zhengxiao, Jian Yu, and Ruoye Xiao. "Data-driven reduced order modeling for parametrized time-dependent flow problems." Physics of Fluids, June 22, 2022. http://dx.doi.org/10.1063/5.0098122.

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This paper proposes a non-intrusive reduced basis (RB) method based on dynamic mode decomposition (DMD) for parameterized time-dependent flows. In the offline stage, the reduced basis functions are extracted by a two-step proper orthogonal decomposition (POD) algorithm. Then, a novel hybrid DMD regression model that combines windowed DMD and optimized DMD is introduced for the temporal evolution of the RB coefficients. To improve the stability of this method for complex non-linear problems, we introduce a threshold value to modify the DMD eigenvalues and eigenvectors. Moreover, the interpolation of the coefficients in parameter space is conducted by an artificial neural network (ANN) or random forest (RF) algorithm. The prediction of the RB solution at a new time/parameter value can be recovered at a low computational cost in the online stage, which is completely decoupled from the high-fidelity dimension. We demonstrate the performance of the proposed model with two cases: (i) laminar flow past a two-dimensional cylinder and (ii) turbulent flow around a three-dimensional SD7003 airfoil. The results show reasonable efficiency and robustness of this novel reduced-order model.

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44

Shi, Jianye, Kiran Manjunatha, Felix Vogt, and Stefanie Reese. "Data-driven reduced order surrogate modeling for coronary in-stent restenosis." Computer Methods and Programs in Biomedicine, October 2024, 108466. http://dx.doi.org/10.1016/j.cmpb.2024.108466.

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45

Geier, Charlotte, Merten Stender, and Norbert Hoffmann. "Data-driven reduced order modeling for mechanical oscillators using Koopman approaches." Frontiers in Applied Mathematics and Statistics 9 (April 28, 2023). http://dx.doi.org/10.3389/fams.2023.1124602.

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Data-driven reduced order modeling methods that aim at extracting physically meaningful governing equations directly from measurement data are facing a growing interest in recent years. The HAVOK-algorithm is a Koopman-based method that distills a forced, low-dimensional state-space model for a given dynamical system from a univariate measurement time series. This article studies the potential of HAVOK for application to mechanical oscillators by investigating which information of the underlying system can be extracted from the state-space model generated by HAVOK. Extensive parameter studies are performed to point out the strengths and pitfalls of the algorithm and ultimately yield recommendations for choosing tuning parameters. The application of the algorithm to real-world friction brake system measurements concludes this study.

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Snyder, William, Jeffrey A. McGuire, Changhong Mou, David A. Dillard, Traian Iliescu, and Raffaella De Vita. "Data‐Driven Variational Multiscale Reduced Order Modeling of Vaginal Tissue Inflation." International Journal for Numerical Methods in Biomedical Engineering, November 4, 2022. http://dx.doi.org/10.1002/cnm.3660.

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Ivagnes, Anna, Giovanni Stabile, Andrea Mola, Traian Iliescu, and Gianluigi Rozza. "Pressure Data-Driven Variational Multiscale Reduced Order Models." Journal of Computational Physics, January 2023, 111904. http://dx.doi.org/10.1016/j.jcp.2022.111904.

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48

Gosea, Ion Victor, Serkan Gugercin, and Steffen W. R. Werner. "Structured barycentric forms for interpolation-based data-driven reduced modeling of second-order systems." Advances in Computational Mathematics 50, no. 2 (April 2024). http://dx.doi.org/10.1007/s10444-024-10118-7.

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AbstractAn essential tool in data-driven modeling of dynamical systems from frequency response measurements is the barycentric form of the underlying rational transfer function. In this work, we propose structured barycentric forms for modeling dynamical systems with second-order time derivatives using their frequency domain input-output data. By imposing a set of interpolation conditions, the systems’ transfer functions are rewritten in different barycentric forms using different parametrizations. Loewner-like algorithms are developed for the explicit computation of second-order systems from data based on the developed barycentric forms. Numerical experiments show the performance of these new structured data-driven modeling methods compared to other interpolation-based data-driven modeling techniques from the literature.

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Borcea, Liliana, Josselin Garnier, Alexander V. Mamonov, and Jörn Zimmerling. "Waveform inversion via reduced order modeling." GEOPHYSICS, November 24, 2022, 1–91. http://dx.doi.org/10.1190/geo2022-0070.1.

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We introduce a novel approach to waveform inversion, based on a data driven reduced order model (ROM) of the wave operator. The presentation is for the acoustic wave equation, but the approach can be extended to elastic or electromagnetic waves. The data are time resolved measurements of the pressure wave gathered by an acquisition system which probes the unknown medium with pulses and measures the generated waves. We propose to solve the inverse problem of velocity estimation by minimizing the square misfit between the ROM computed from the recorded data and the ROM computed from the modeled data, at the current guess of the velocity. We give the step by step computation of the ROM, which depends nonlinearly on the data and yet can be obtained from them in a non-iterative fashion, using efficient methods from linear algebra. We also explain how to make the ROM robust to data inaccuracy. The ROM computation requires the full array response matrix gathered with co-located sources and receivers. However, we show that the computation can deal with an approximation of this matrix, obtained from towed-streamer data using interpolation and reciprocity on-the-fly.While the full-waveform inversion approach of nonlinear least-squares data fitting is challenging without low frequency information, due to multiple minima of the data fit objective function, we show that the ROM misfit objective function has a better behavior, even for a poor initial guess. We also show by an explicit computation of the objective functions in a simple setting that the ROM misfit objective function has convexity properties, whereas the least squares data fit objective function displays multiple local minima.

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Duan, Junming, and Jan S. Hesthaven. "Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems." Journal of Computational Physics, November 2023, 112621. http://dx.doi.org/10.1016/j.jcp.2023.112621.

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