Articles de revues : « Data-driven model order reduction »

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Nagy, Peter, et Marco Fossati. « Adaptive Data-Driven Model Order Reduction for Unsteady Aerodynamics ». Fluids 7, n^o 4 (6 avril 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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Gosea, Ion Victor, et Athanasios C. Antoulas. « Data-driven model order reduction of quadratic-bilinear systems ». Numerical Linear Algebra with Applications 25, n^o 6 (22 juillet 2018) : e2200. http://dx.doi.org/10.1002/nla.2200.

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Shah, Aarohi, et Julian J. Rimoli. « Smart parts : Data-driven model order reduction for nonlinear mechanical assemblies ». Finite Elements in Analysis and Design 200 (mars 2022) : 103682. http://dx.doi.org/10.1016/j.finel.2021.103682.

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Sarna, Neeraj, et Peter Benner. « Data-Driven model order reduction for problems with parameter-dependent jump-discontinuities ». Computer Methods in Applied Mechanics and Engineering 387 (décembre 2021) : 114168. http://dx.doi.org/10.1016/j.cma.2021.114168.

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Pierquin, A., T. Henneron et S. Clenet. « Data-Driven Model-Order Reduction for Magnetostatic Problem Coupled With Circuit Equations ». IEEE Transactions on Magnetics 54, n^o 3 (mars 2018) : 1–4. http://dx.doi.org/10.1109/tmag.2017.2771358.

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Peng, Haijun, Ningning Song et Ziyun Kan. « Data-driven model order reduction with proper symplectic decomposition for flexible multibody system ». Nonlinear Dynamics 107, n^o 1 (6 novembre 2021) : 173–203. http://dx.doi.org/10.1007/s11071-021-06990-3.

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Kim, Hyejin, Haeseong Cho, Sihun Lee, SangJoon Shin et Haedeong Kim. « Development of an Efficient Nonlinear Structural Analysis Using Data-driven Model Order Reduction ». Transactions of the Korean Society for Noise and Vibration Engineering 31, n^o 6 (20 décembre 2021) : 604–13. http://dx.doi.org/10.5050/ksnve.2021.31.6.604.

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Gosea, I. V., M. Petreczky et A. C. Antoulas. « Data-Driven Model Order Reduction of Linear Switched Systems in the Loewner Framework ». SIAM Journal on Scientific Computing 40, n^o 2 (janvier 2018) : B572—B610. http://dx.doi.org/10.1137/17m1120233.

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Spinosa, Angelo Giuseppe, Arturo Buscarino, Luigi Fortuna, Matteo Iafrati et Giuseppe Mazzitelli. « Data-driven order reduction in Hammerstein–Wiener models of plasma dynamics ». Engineering Applications of Artificial Intelligence 100 (avril 2021) : 104180. http://dx.doi.org/10.1016/j.engappai.2021.104180.

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Casciati, Fabio, et Lucia Faravelli. « Sensor placement driven by a model order reduction (MOR) reasoning ». Smart Structures and Systems 13, n^o 3 (25 mars 2014) : 343–52. http://dx.doi.org/10.12989/sss.2014.13.3.343.

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Zhang, Yi, Yi-Fei Pu, Jin-Rong Hu, Yan Liu, Qing-Li Chen et Ji-Liu Zhou. « Efficient CT Metal Artifact Reduction Based on Fractional-Order Curvature Diffusion ». Computational and Mathematical Methods in Medicine 2011 (2011) : 1–9. http://dx.doi.org/10.1155/2011/173748.

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We propose a novel metal artifact reduction method based on a fractional-order curvature driven diffusion model for X-ray computed tomography. Our method treats projection data with metal regions as a damaged image and uses the fractional-order curvature-driven diffusion model to recover the lost information caused by the metal region. The numerical scheme for our method is also analyzed. We use the peak signal-to-noise ratio as a reference measure. The simulation results demonstrate that our method achieves better performance than existing projection interpolation methods, including linear interpolation and total variation.

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Buchfink, Patrick, Ashish Bhatt et Bernard Haasdonk. « Symplectic Model Order Reduction with Non-Orthonormal Bases ». Mathematical and Computational Applications 24, n^o 2 (21 avril 2019) : 43. http://dx.doi.org/10.3390/mca24020043.

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Parametric high-fidelity simulations are of interest for a wide range of applications. However, the restriction of computational resources renders such models to be inapplicable in a real-time context or in multi-query scenarios. Model order reduction (MOR) is used to tackle this issue. Recently, MOR is extended to preserve specific structures of the model throughout the reduction, e.g., structure-preserving MOR for Hamiltonian systems. This is referred to as symplectic MOR. It is based on the classical projection-based MOR and uses a symplectic reduced order basis (ROB). Such an ROB can be derived in a data-driven manner with the Proper Symplectic Decomposition (PSD) in the form of a minimization problem. Due to the strong nonlinearity of the minimization problem, it is unclear how to efficiently find a global optimum. In our paper, we show that current solution procedures almost exclusively yield suboptimal solutions by restricting to orthonormal ROBs. As a new methodological contribution, we propose a new method which eliminates this restriction by generating non-orthonormal ROBs. In the numerical experiments, we examine the different techniques for a classical linear elasticity problem and observe that the non-orthonormal technique proposed in this paper shows superior results with respect to the error introduced by the reduction.

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Luo, Yushuang, Xiantao Li et Wenrui Hao. « Stability preserving data-driven models with latent dynamics ». Chaos : An Interdisciplinary Journal of Nonlinear Science 32, n^o 8 (août 2022) : 081103. http://dx.doi.org/10.1063/5.0096889.

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In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a given data set. We present a model framework where the stability of the coupled dynamics can be easily enforced. The model is implemented by recurrent cells and trained using backpropagation through time. Numerical examples using benchmark tests from order reduction problems demonstrate the stability of the model and the efficiency of the recurrent cell implementation. As applications, two fluid–structure interaction problems are considered to illustrate the accuracy and predictive capability of the model.

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Li, Yong, Jue Yang, Wei Long Liu et Cheng Lin Liao. « Multi-Level Model Reduction and Data-Driven Identification of the Lithium-Ion Battery ». Energies 13, n^o 15 (23 juillet 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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Deshmukh, Rohit, Jack J. McNamara, Zongxian Liang, J. Zico Kolter et Abhijit Gogulapati. « Model order reduction using sparse coding exemplified for the lid-driven cavity ». Journal of Fluid Mechanics 808 (27 octobre 2016) : 189–223. http://dx.doi.org/10.1017/jfm.2016.616.

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Basis identification is a critical step in the construction of accurate reduced-order models using Galerkin projection. This is particularly challenging in unsteady flow fields due to the presence of multi-scale phenomena that cannot be ignored and may not be captured using a small set of modes extracted using the ubiquitous proper orthogonal decomposition. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. Compared with proper orthogonal decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to identify a compact representation that spans all scales of the observed data. As such, the inherently multi-scale bases may improve reduced-order modelling of unsteady flow fields. The approach is examined for a canonical problem of an incompressible flow inside a two-dimensional lid-driven cavity. The results demonstrate that Galerkin reduction of the governing equations using sparse modes yields a significantly improved predictive model of the fluid dynamics.

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Song, Ningning, Haijun Peng et Ziyun Kan. « A hybrid data-driven model order reduction strategy for flexible multibody systems considering impact and friction ». Mechanism and Machine Theory 169 (mars 2022) : 104649. http://dx.doi.org/10.1016/j.mechmachtheory.2021.104649.

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Bao, Anqi, Eduardo Gildin, Abhinav Narasingam et Joseph S. Kwon. « Data-Driven Model Reduction for Coupled Flow and Geomechanics Based on DMD Methods ». Fluids 4, n^o 3 (19 juillet 2019) : 138. http://dx.doi.org/10.3390/fluids4030138.

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Learning reservoir flow dynamics is of primary importance in creating robust predictive models for reservoir management including hydraulic fracturing processes. Physics-based models are to a certain extent exact, but they entail heavy computational infrastructure for simulating a wide variety of parameters and production scenarios. Reduced-order models offer computational advantages without compromising solution accuracy, especially if they can assimilate large volumes of production data without having to reconstruct the original model (data-driven models). Dynamic mode decomposition (DMD) entails the extraction of relevant spatial structure (modes) based on data (snapshots) that can be used to predict the behavior of reservoir fluid flow in porous media. In this paper, we will further enhance the application of the DMD, by introducing sparse DMD and local DMD. The former is particularly useful when there is a limited number of sparse measurements as in the case of reservoir simulation, and the latter can improve the accuracy of developed DMD models when the process dynamics show a moving boundary behavior like hydraulic fracturing. For demonstration purposes, we first show the methodology applied to (flow only) single- and two-phase reservoir models using the SPE10 benchmark. Both online and offline processes will be used for evaluation. We observe that we only require a few DMD modes, which are determined by the sparse DMD structure, to capture the behavior of the reservoir models. Then, we applied the local DMDc for creating a proxy for application in a hydraulic fracturing process. We also assessed the trade-offs between problem size and computational time for each reservoir model. The novelty of our method is the application of sparse DMD and local DMDc, which is a data-driven technique for fast and accurate simulations.

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Ibañez, R., E. Abisset-Chavanne, E. Cueto, A. Ammar, J. L. Duval et F. Chinesta. « Some applications of compressed sensing in computational mechanics : model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction ». Computational Mechanics 64, n^o 5 (10 avril 2019) : 1259–71. http://dx.doi.org/10.1007/s00466-019-01703-5.

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German, Péter, Mauricio E. Tano, Carlo Fiorina et Jean C. Ragusa. « Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media ». Fluids 6, n^o 8 (28 juillet 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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Mendonça, Gonçalo, Frederico Afonso et Fernando Lau. « Model order reduction in aerodynamics : Review and applications ». Proceedings of the Institution of Mechanical Engineers, Part G : Journal of Aerospace Engineering 233, n^o 15 (11 juin 2019) : 5816–36. http://dx.doi.org/10.1177/0954410019853472.

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The need of the aerospace industry, at national or European level, of faster yet reliable computational fluid dynamics models is the main drive for the application of model reduction techniques. This need is linked to the time cost of high-fidelity models, rendering them inefficient for applications like multi-disciplinary optimization. With the goal of testing and applying model reduction to computational fluid dynamics models applicable to lifting surfaces, a bibliographical research covering reduction of nonlinear, dynamic, or steady models was conducted. This established the prevalence of projection and least mean squares methods, which rely on solutions of the original high-fidelity model and their proper orthogonal decomposition to work. Other complementary techniques such as adaptive sampling, greedy sampling, and hybrid models are also presented and discussed. These projection and least mean squares methods are then tested on simple and documented benchmarks to estimate the error and speed-up of the reduced order models thus generated. Dynamic, steady, nonlinear, and multiparametric problems were reduced, with the simplest version of these methods showing the most promise. These methods were later applied to single parameter problems, namely the lid-driven cavity with incompressible Navier–Stokes equations and varying Reynolds number, and the elliptic airfoil at varying angles of attack for compressible Euler flow. An analysis of the performance of these methods is given at the end of this article, highlighting the computational speed-up obtained with these techniques, and the challenges presented by multiparametric problems and problems showing point singularities in their domain.

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Taddei, Tommaso. « A Registration Method for Model Order Reduction : Data Compression and Geometry Reduction ». SIAM Journal on Scientific Computing 42, n^o 2 (janvier 2020) : A997—A1027. http://dx.doi.org/10.1137/19m1271270.

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Morsy, Ahmed Amr, Mariella Kast et Paolo Tiso. « A frequency-domain reduced order model for joints by hyper-reduction and model-driven sampling ». Mechanical Systems and Signal Processing 185 (février 2023) : 109744. http://dx.doi.org/10.1016/j.ymssp.2022.109744.

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Akram, Namra, Mehboob Alam, Rashida Hussain, Asghar Ali, Shah Muhammad, Rahila Malik et Anwar Ul Haq. « Passivity Preserving Model Order Reduction Using the Reduce Norm Method ». Electronics 9, n^o 6 (9 juin 2020) : 964. http://dx.doi.org/10.3390/electronics9060964.

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Modeling and design of on-chip interconnect, the interconnection between the components is becoming the fundamental roadblock in achieving high-speed integrated circuits. The scaling of interconnect in nanometer regime had shifted the paradime from device-dominated to interconnect-dominated design methodology. Driven by the expanding complexity of on-chip interconnects, a passivity preserving model order reduction (MOR) is essential for designing and estimating the performance for reliable operation of the integrated circuit. In this work, we developed a new frequency selective reduce norm spectral zero (RNSZ) projection method, which dynamically selects interpolation points using spectral zeros of the system. The proposed reduce-norm scheme can guarantee stability and passivity, while creating the reduced models, which are fairly accurate across selected narrow range of frequencies. The reduced order results indicate preservation of passivity and greater accuracy than the other model order reduction methods.

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Xie, Xuping, Guannan Zhang et Clayton G. Webster. « Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network ». Mathematics 7, n^o 8 (19 août 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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Demo, Nicola, Marco Tezzele, Andrea Mola et Gianluigi Rozza. « Hull Shape Design Optimization with Parameter Space and Model Reductions, and Self-Learning Mesh Morphing ». Journal of Marine Science and Engineering 9, n^o 2 (11 février 2021) : 185. http://dx.doi.org/10.3390/jmse9020185.

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In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.

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Bittner, Brian, Ross L. Hatton et Shai Revzen. « Data-driven geometric system identification for shape-underactuated dissipative systems ». Bioinspiration & ; Biomimetics 17, n^o 2 (24 janvier 2022) : 026004. http://dx.doi.org/10.1088/1748-3190/ac3b9c.

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Abstract Modeling system dynamics becomes challenging when the properties of individual system components cannot be directly measured, and often requires identification of properties from observed motion. In this paper, we show that systems whose movement is highly dissipative have features which provide an opportunity to more easily identify models and more quickly optimize motions than would be possible with general techniques. Geometric mechanics provides means for reduction of the dynamics by environmental homogeneity, while the dissipative nature minimizes the role of second order (inertial) features in the dynamics. Here we extend the tools of geometric system identification to ‘shape-underactuated dissipative systems (SUDS)’—systems whose motions are more dissipative than inertial, but whose actuation is restricted to a subset of the body shape coordinates. Many animal motions are SUDS, including micro-swimmers such as nematodes and flagellated bacteria, and granular locomotors such as snakes and lizards. Many soft robots are also SUDS, particularly robots that incorporate highly damped series elastic actuators to reduce the rigidity of their interactions with their environments during locomotion and manipulation. We motivate the use of SUDS models, and validate their ability to predict motion of a variety of simulated viscous swimming platforms. For a large class of SUDS, we show how the shape velocity actuation inputs can be directly converted into torque inputs, suggesting that systems with soft pneumatic or dielectric elastomer actuators can be modeled with the tools presented. Based on fundamental assumptions in the physics, we show how our model complexity scales linearly with the number of passive shape coordinates. This scaling offers a large reduction on the number of trials needed to identify the system model from experimental data, and may reduce overfitting. The sample efficiency of our method suggests its use in modeling, control, and optimization in robotics, and as a tool for the study of organismal motion in friction dominated regimes.

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Zhong, Jiaqi, et Shan Liang. « A Data-Driven Based Spatiotemporal Model Reduction for Microwave Heating Process with the Mixed Boundary Conditions ». Processes 9, n^o 5 (9 mai 2021) : 827. http://dx.doi.org/10.3390/pr9050827.

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In this paper, a data-driven based spatiotemporal model reduction approach is proposed for predicting the temperature distribution and developing the computation speeds in the microwave heating process. Due to the mixed boundary conditions, it is difficult for the traditional spectral method to directly obtain the analytical eigenfunctions. Motivated by the time/space separation theory, we first propose a general framework of spatiotemporal model reduction, which can effectively develop the computation speeds in the numerical analysis of multi-physical fields. Subsequently, the empirical eigenfunctions are generated by applying the Karhunen–Loève theory to decompose the snapshots. Then, the partial differential Equation (PDE) model is discretized into a class of recursive equations and transformed as the reduced-order ordinary differential Equation (ODE) model. Finally, the effectiveness and superiority of the proposed approach is demonstrated by a comparison study with a traditional method on the microwave heating Debye medium.

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Boubehziz, Toufik, Carlos Quesada-Granja, Claire Dupont, Pierre Villon, Florian De Vuyst et Anne-Virginie Salsac. « A Data-Driven Space-Time-Parameter Reduced-Order Model with Manifold Learning for Coupled Problems : Application to Deformable Capsules Flowing in Microchannels ». Entropy 23, n^o 9 (9 septembre 2021) : 1193. http://dx.doi.org/10.3390/e23091193.

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An innovative data-driven model-order reduction technique is proposed to model dilute micrometric or nanometric suspensions of microcapsules, i.e., microdrops protected in a thin hyperelastic membrane, which are used in Healthcare as innovative drug vehicles. We consider a microcapsule flowing in a similar-size microfluidic channel and vary systematically the governing parameter, namely the capillary number, ratio of the viscous to elastic forces, and the confinement ratio, ratio of the capsule to tube size. The resulting space-time-parameter problem is solved using two global POD reduced bases, determined in the offline stage for the space and parameter variables, respectively. A suitable low-order spatial reduced basis is then computed in the online stage for any new parameter instance. The time evolution of the capsule dynamics is achieved by identifying the nonlinear low-order manifold of the reduced variables; for that, a point cloud of reduced data is computed and a diffuse approximation method is used. Numerical comparisons between the full-order fluid-structure interaction model and the reduced-order one confirm both accuracy and stability of the reduction technique over the whole admissible parameter domain. We believe that such an approach can be applied to a broad range of coupled problems especially involving quasistatic models of structural mechanics.

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Hou, Hui, Hao Geng, Yong Huang, Hao Wu, Xixiu Wu et Shiwen Yu. « Damage Probability Assessment of Transmission Line-Tower System Under Typhoon Disaster, Based on Model-Driven and Data-Driven Views ». Energies 12, n^o 8 (16 avril 2019) : 1447. http://dx.doi.org/10.3390/en12081447.

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Under the typhoon disaster, the power grid often has serious accidents caused by falling power towers and breaking lines. It is of great significance to analyze and predict the damage probability of a transmission line-tower system for disaster prevention and reduction. However, some problems existing in current models, such as complicated calculation, few factors, and so on, affect the accuracy of the prediction. Therefore, a damage probability assessment method of a transmission line-tower system under a typhoon disaster is proposed. Firstly, considering the actual wind load and the design wind load, physical models for calculating the damage probability of the transmission line and power tower are established, respectively based on model-driven thought. Then, the damage probability of the transmission line-tower system is obtained, combining the transmission line and power tower damage probability. Secondly, in order to improve prediction accuracy, this paper analyzes the historical sample data containing multiple influencing factors, such as geographic information, meteorological information, and power grid information, and then obtains the correction coefficient based on data-driven thought. Thirdly, the comprehensive damage probability of the transmission line-tower system is calculated considering the results of model-driven and data-driven thought. Ultimately, the proposed method is verified to be effective, taking typhoon ‘Mangkhut’ in 2018 as a case study.

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Rahman, Sk, Omer San et Adil Rasheed. « A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence ». Fluids 3, n^o 4 (31 octobre 2018) : 86. http://dx.doi.org/10.3390/fluids3040086.

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We put forth a robust reduced-order modeling approach for near real-time prediction of mesoscale flows. In our hybrid-modeling framework, we combine physics-based projection methods with neural network closures to account for truncated modes. We introduce a weighting parameter between the Galerkin projection and extreme learning machine models and explore its effectiveness, accuracy and generalizability. To illustrate the success of the proposed modeling paradigm, we predict both the mean flow pattern and the time series response of a single-layer quasi-geostrophic ocean model, which is a simplified prototype for wind-driven general circulation models. We demonstrate that our approach yields significant improvements over both the standard Galerkin projection and fully non-intrusive neural network methods with a negligible computational overhead.

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Li, Zhengyuan, Jie Chen, Yanmei Meng, Jihong Zhu, Jiqin Li, Yue Zhang et Chengfeng Li. « Multi-Objective Optimization of Sugarcane Milling System Operations Based on a Deep Data-Driven Model ». Foods 11, n^o 23 (28 novembre 2022) : 3845. http://dx.doi.org/10.3390/foods11233845.

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The extraction of sugarcane juice is the first step of sugar production. The optimal values of process indicators and the set values of operating parameters in this process are still determined by workers’ experience, preventing adaptive adjustment of the production process. To address this issue, a multi-objective optimization framework based on a deep data-driven model is proposed to optimize the operation of sugarcane milling systems. First, the sugarcane milling process is abstracted as the interaction of material flow, energy flow, and information flow (MF–EF–IF) by introducing synergetic theory, and each flow’s order parameters and state parameters are obtained. Subsequently, the state parameters of the subsystems are taken as inputs, and the order parameters—including the grinding capacity, electric consumption per ton of sugarcane, and sucrose extraction—are produced as outputs. A collaborative optimization model of the MF–EF–IF of the milling system is established by using a deep kernel extreme learning machine (DK-ELM). The established milling system model is applied for an improved multi-objective chicken swarm optimization (IMOCSO) algorithm to obtain the optimal values of the order parameters. Finally, the milling process is described as a Markov decision process (MDP) with the optimal values of the order parameters as the control objectives, and an improved deep deterministic policy gradient (DDPG) algorithm is employed to achieve the adaptive optimization of the operating parameters under different working conditions of the milling system. Computational experiments indicate that enhanced performance is achieved, with an increase of 3.2 t per hour in grinding capacity, a reduction of 660 W per ton in sugarcane electric consumption, and an increase of 0.03% in the sucrose extraction.

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Sengupta, P., et S. Chakraborty. « Model reduction technique for Bayesian model updating of structural parameters using simulated modal data ». Proceedings of the 12th Structural Engineering Convention, SEC 2022 : Themes 1-2 1, n^o 1 (19 décembre 2022) : 1403–12. http://dx.doi.org/10.38208/acp.v1.670.

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An attempt has been made to study the effectiveness of model reduction technique for Bayesian approach of model updating with incomplete modal data sets. The inverse problems in system identification require the solution of a family of plausible values of model parameters based on available data. Specifically, an iterative model reduction algorithm is proposed based on a non-linear optimization method to solve the transformation parameter such that no prior choices of response parameters are required. The modal ordinates synthesized at the unmeasured degrees of freedom (DOF) from the reduced order model are used for a better estimate of likelihood functions. The reduced-order model is subsequently implemented for updating of unknown structural parameters. The present study also synthesizes the mode shape ordinates at unmeasured DOF from the reduced order model. The efficiency of the proposed model reduction algorithm is further studied by adding noises of varying percentages to the measured modal data sets. The proposed methodology is illustrated numerically to update the stiffness parameters of an eight-story shear building model considering simulated datasets contaminated by Gaussian error as evidence. The capability of the proposed model reduction algorithm coupled with Markov Chain Monte Carlo (MCMC) algorithm is compared with the case where only MCMC algorithm is used to investigate their effectiveness in updating model parameters. The numerical study focuses on the effect of reduced number of measurements for various measurement configurations in estimating the variation of errors in determining the modal data. Subsequently, its effects in reducing the uncertainty of model updating parameters are investigated. The effectiveness of the proposed model reduction algorithm is tested for number of modes equal to the number of master DOFs and gradually decrease of mode numbers from the number of master DOFs.

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Sledge, Isaac, et José Príncipe. « Reduction of Markov Chains Using a Value-of-Information-Based Approach ». Entropy 21, n^o 4 (30 mars 2019) : 349. http://dx.doi.org/10.3390/e21040349.

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In this paper, we propose an approach to obtain reduced-order models of Markov chains. Our approach is composed of two information-theoretic processes. The first is a means of comparing pairs of stationary chains on different state spaces, which is done via the negative, modified Kullback–Leibler divergence defined on a model joint space. Model reduction is achieved by solving a value-of-information criterion with respect to this divergence. Optimizing the criterion leads to a probabilistic partitioning of the states in the high-order Markov chain. A single free parameter that emerges through the optimization process dictates both the partition uncertainty and the number of state groups. We provide a data-driven means of choosing the `optimal’ value of this free parameter, which sidesteps needing to a priori know the number of state groups in an arbitrary chain.

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Lu, Xiaoxin, Julien Yvonnet, Leonidas Papadopoulos, Ioannis Kalogeris et Vissarion Papadopoulos. « A Stochastic FE2 Data-Driven Method for Nonlinear Multiscale Modeling ». Materials 14, n^o 11 (27 mai 2021) : 2875. http://dx.doi.org/10.3390/ma14112875.

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A stochastic data-driven multilevel finite-element (FE2) method is introduced for random nonlinear multiscale calculations. A hybrid neural-network–interpolation (NN–I) scheme is proposed to construct a surrogate model of the macroscopic nonlinear constitutive law from representative-volume-element calculations, whose results are used as input data. Then, a FE2 method replacing the nonlinear multiscale calculations by the NN–I is developed. The NN–I scheme improved the accuracy of the neural-network surrogate model when insufficient data were available. Due to the achieved reduction in computational time, which was several orders of magnitude less than that to direct FE2, the use of such a machine-learning method is demonstrated for performing Monte Carlo simulations in nonlinear heterogeneous structures and propagating uncertainties in this context, and the identification of probabilistic models at the macroscale on some quantities of interest. Applications to nonlinear electric conduction in graphene–polymer composites are presented.

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Csala, Hunor, Scott T. M. Dawson et Amirhossein Arzani. « Comparing different nonlinear dimensionality reduction techniques for data-driven unsteady fluid flow modeling ». Physics of Fluids 34, n^o 11 (novembre 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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Loiseau, Jean-Christophe, et Steven L. Brunton. « Constrained sparse Galerkin regression ». Journal of Fluid Mechanics 838 (10 janvier 2018) : 42–67. http://dx.doi.org/10.1017/jfm.2017.823.

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The sparse identification of nonlinear dynamics (SINDy) is a recently proposed data-driven modelling framework that uses sparse regression techniques to identify nonlinear low-order models. With the goal of low-order models of a fluid flow, we combine this approach with dimensionality reduction techniques (e.g. proper orthogonal decomposition) and extend it to enforce physical constraints in the regression, e.g. energy-preserving quadratic nonlinearities. The resulting models, hereafter referred to as Galerkin regression models, incorporate many beneficial aspects of Galerkin projection, but without the need for a high-fidelity solver to project the Navier–Stokes equations. Instead, the most parsimonious nonlinear model is determined that is consistent with observed measurement data and satisfies necessary constraints. Galerkin regression models also readily generalize to include higher-order nonlinear terms that model the effect of truncated modes. The effectiveness of such an approach is demonstrated on two canonical flow configurations: the two-dimensional flow past a circular cylinder and the shear-driven cavity flow. For both cases, the accuracy of the identified models compare favourably against reduced-order models obtained from a standard Galerkin projection procedure. Finally, the entire code base for our constrained sparse Galerkin regression algorithm is freely available online.

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Chamorro, Harold R., Alvaro D. Orjuela-Cañón, David Ganger, Mattias Persson, Francisco Gonzalez-Longatt, Lazaro Alvarado-Barrios, Vijay K. Sood et Wilmar Martinez. « Data-Driven Trajectory Prediction of Grid Power Frequency Based on Neural Models ». Electronics 10, n^o 2 (12 janvier 2021) : 151. http://dx.doi.org/10.3390/electronics10020151.

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Frequency in power systems is a real-time information that shows the balance between generation and demand. Good system frequency observation is vital for system security and protection. This paper analyses the system frequency response following disturbances and proposes a data-driven approach for predicting it by using machine learning techniques like Nonlinear Auto-regressive (NAR) Neural Networks (NN) and Long Short Term Memory (LSTM) networks from simulated and measured Phasor Measurement Unit (PMU) data. The proposed method uses a horizon-window that reconstructs the frequency input time-series data in order to predict the frequency features such as Nadir. Simulated scenarios are based on the gradual inertia reduction by including non-synchronous generation into the Nordic 32 test system, whereas the PMU collected data is taken from different locations in the Nordic Power System (NPS). Several horizon-windows are experimented in order to observe an adequate margin of prediction. Scenarios considering noisy signals are also evaluated in order to provide a robustness index of predictability. Results show the proper performance of the method and the adequate level of prediction based on the Root Mean Squared Error (RMSE) index.

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Lučin, Ivana, Bože Lučin, Zoran Čarija et Ante Sikirica. « Data-Driven Leak Localization in Urban Water Distribution Networks Using Big Data for Random Forest Classifier ». Mathematics 9, n^o 6 (22 mars 2021) : 672. http://dx.doi.org/10.3390/math9060672.

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In the present paper, a Random Forest classifier is used to detect leak locations on two different sized water distribution networks with sparse sensor placement. A great number of leak scenarios were simulated with Monte Carlo determined leak parameters (leak location and emitter coefficient). In order to account for demand variations that occur on a daily basis and to obtain a larger dataset, scenarios were simulated with random base demand increments or reductions for each network node. Classifier accuracy was assessed for different sensor layouts and numbers of sensors. Multiple prediction models were constructed for differently sized leakage and demand range variations in order to investigate model accuracy under various conditions. Results indicate that the prediction model provides the greatest accuracy for the largest leaks, with the smallest variation in base demand (62% accuracy for greater- and 82% for smaller-sized networks, for the largest considered leak size and a base demand variation of ±2.5%). However, even for small leaks and the greatest base demand variations, the prediction model provided considerable accuracy, especially when localizing the sources of leaks when the true leak node and neighbor nodes were considered (for a smaller-sized network and a base demand of variation ±20% the model accuracy increased from 44% to 89% when top five nodes with greatest probability were considered, and for a greater-sized network with a base demand variation of ±10% the accuracy increased from 36% to 77%).

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Rubio, P.-B., F. Louf et L. Chamoin. « Bayesian data assimilation with Transport Map sampling and PGD model order reduction ». Journal of Physics : Conference Series 1476 (mars 2020) : 012004. http://dx.doi.org/10.1088/1742-6596/1476/1/012004.

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González, David, Alberto Badías, Icíar Alfaro, Francisco Chinesta et Elías Cueto. « Model order reduction for real-time data assimilation through Extended Kalman Filters ». Computer Methods in Applied Mechanics and Engineering 326 (novembre 2017) : 679–93. http://dx.doi.org/10.1016/j.cma.2017.08.041.

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Stefanoiu, Dan, et Janetta Culita. « Joint Stochastic Spline and Autoregressive Identification Aiming Order Reduction Based on Noisy Sensor Data ». Sensors 20, n^o 18 (4 septembre 2020) : 5038. http://dx.doi.org/10.3390/s20185038.

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This article introduces the spline approximation concept, in the context of system identification, aiming to obtain useful autoregressive models of reduced order. Models with a small number of poles are extremely useful in real time control applications, since the corresponding regulators are easier to design and implement. The main goal here is to compare the identification models complexity when using two types of experimental data: raw (affected by noises mainly produced by sensors) and smoothed. The smoothing of raw data is performed through a least squares optimal stochastic cubic spline model. The consecutive data points necessary to build each polynomial of spline model are adaptively selected, depending on the raw data behavior. In order to estimate the best identification model (of ARMAX class), two optimization strategies are considered: a two-step one (which provides first an optimal useful model and then an optimal noise model) and a global one (which builds the optimal useful and noise models at once). The criteria to optimize rely on the signal-to-noise ratio, estimated both for identification and validation data. Since the optimization criteria usually are irregular in nature, a metaheuristic (namely the advanced hill climbing algorithm) is employed to search for the model optimal structure. The case study described in the end of the article is concerned with a real plant with nonlinear behavior, which provides noisy acquired data. The simulation results prove that, when using smoothed data, the optimal useful models have significantly less poles than when using raw data, which justifies building cubic spline approximation models prior to autoregressive identification.

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Daescu, D. N., et I. M. Navon. « A Dual-Weighted Approach to Order Reduction in 4DVAR Data Assimilation ». Monthly Weather Review 136, n^o 3 (1 mars 2008) : 1026–41. http://dx.doi.org/10.1175/2007mwr2102.1.

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Abstract Strategies to achieve order reduction in four-dimensional variational data assimilation (4DVAR) search for an optimal low-rank state subspace for the analysis update. A common feature of the reduction methods proposed in atmospheric and oceanographic studies is that the identification of the basis functions relies on the model dynamics only, without properly accounting for the specific details of the data assimilation system (DAS). In this study a general framework of the proper orthogonal decomposition (POD) method is considered and a cost-effective approach is proposed to incorporate DAS information into the order-reduction procedure. The sensitivities of the cost functional in 4DVAR data assimilation with respect to the time-varying model state are obtained from a backward integration of the adjoint model. This information is further used to define appropriate weights and to implement a dual-weighted proper orthogonal decomposition (DWPOD) method for order reduction. The use of a weighted ensemble data mean and weighted snapshots using the adjoint DAS is a novel element in reduced-order 4DVAR data assimilation. Numerical results are presented with a global shallow-water model based on the Lin–Rood flux-form semi-Lagrangian scheme. A simplified 4DVAR DAS is considered in the twin-experiment framework with initial conditions specified from the 40-yr ECMWF Re-Analysis (ERA-40) datasets. A comparative analysis with the standard POD method shows that the reduced DWPOD basis may provide an increased efficiency in representing an a priori specified forecast aspect and as a tool to perform reduced-order optimal control. This approach represents a first step toward the development of an order-reduction methodology that combines in an optimal fashion the model dynamics and the characteristics of the 4DVAR DAS.

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Jiang, Jing-Wei, Yang Yang, Tong-Wei Ren, Fei Wang et Wei-Xi Huang. « Evolutionary Optimisation for Reduction of the Low-Frequency Discrete-Spectrum Force of Marine Propeller Based on a Data-Driven Surrogate Model ». Journal of Marine Science and Engineering 9, n^o 1 (25 décembre 2020) : 18. http://dx.doi.org/10.3390/jmse9010018.

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For practical problems with non-convex, large-scale and highly constrained characteristics, evolutionary optimisation algorithms are widely used. However, advanced data-driven methods have yet to be comprehensively applied in related fields. In this study, a surrogate model combined with the Non-dominated Sorting Genetic Algorithm II-Differential Evolution (NSGA-II-DE) is applied to reduce the low-frequency Discrete-Spectrum (DS) force of propeller noise. Reduction of this force has drawn a lot of attention as it is the primary signal used in the sonar-based detection and identification of ships. In the present study, a surrogate model is proposed based on a trained Back-Propagation (BP) fully connected neural network, which improves the optimisation efficiency. The neural network is designed by analysing the depth and width of the hidden layers. The results indicate that a four-layer neural network with 64, 128, 256 and 64 nodes in each layer, respectively, exhibits the highest prediction accuracy. The prediction errors for the first order of DST, second order of DST and the thrust coefficient are only 0.21%, 5.71% and 0.01%, respectively. Data-Driven Evolutionary Optimisation (DDEO) is applied to a standard high-skew propeller to reduce DST. DDEO and a Traditional Evolutionary Optimisation Method (TEOM) obtain the same optimisation results, while the time cost of DDEO is only 0.68% that of the TEOM. Thus, the proposed DDEO is applicable to complex engineering problems in various fields.

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Prével, Arthur, Vinca Rivière, Jean-Claude Darcheville, Gonzalo P. Urcelay et Ralph R. Miller. « Excitatory second-order conditioning using a backward first-order conditioned stimulus : A challenge for prediction error reduction ». Quarterly Journal of Experimental Psychology 72, n^o 6 (21 août 2018) : 1453–65. http://dx.doi.org/10.1177/1747021818793376.

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Prével and colleagues reported excitatory learning with a backward conditioned stimulus (CS) in a conditioned reinforcement preparation. Their results add to existing evidence of backward CSs sometimes being excitatory and were viewed as challenging the view that learning is driven by prediction error reduction, which assumes that only predictive (i.e., forward) relationships are learned. The results instead were consistent with the assumptions of both Miller’s Temporal Coding Hypothesis and Wagner’s Sometimes Opponent Processes (SOP) model. The present experiment extended the conditioned reinforcement preparation developed by Prével et al. to a backward second-order conditioning preparation, with the aim of discriminating between these two accounts. We tested whether a second-order CS can serve as an effective conditioned reinforcer, even when the first-order CS with which it was paired is a backward CS that elicits no responding. Evidence of conditioned reinforcement was found, despite no conditioned response (CR) being elicited by the first-order backward CS. The evidence of second-order conditioning in the absence of excitatory conditioning to the first-order CS is interpreted as a challenge to SOP. In contrast, the present results are consistent with the Temporal Coding Hypothesis and constitute a conceptual replication in humans of previous reports of excitatory second-order conditioning in rodents with a backward CS. The proposal is made that learning is driven by “discrepancy” with prior experience as opposed to “ prediction error.”

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Raia, Maria Raluca, Mircea Ruba, Raul Octavian Nemes et Claudia Martis. « Artificial Neural Network and Data Dimensionality Reduction Based on Machine Learning Methods for PMSM Model Order Reduction ». IEEE Access 9 (2021) : 102345–54. http://dx.doi.org/10.1109/access.2021.3095668.

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Szalai, Robert. « Invariant spectral foliations with applications to model order reduction and synthesis ». Nonlinear Dynamics 101, n^o 4 (31 août 2020) : 2645–69. http://dx.doi.org/10.1007/s11071-020-05891-1.

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Abstract The paper introduces a technique that decomposes the dynamics of a nonlinear system about an equilibrium into low-order components, which then can be used to reconstruct the full dynamics. This is a nonlinear analogue of linear modal analysis. The dynamics is decomposed using Invariant Spectral Foliation (ISF), which is defined as the smoothest invariant foliation about an equilibrium and hence unique under general conditions. The conjugate dynamics of an ISF can be used as a reduced order model. An ISF can be fitted to vibration data without carrying out a model identification first. The theory is illustrated on a analytic example and on free-vibration data of a clamped-clamped beam.

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Wen, Bin, Zheng Li et Nicholas Zabaras. « Thermal Response Variability of Random Polycrystalline Microstructures ». Communications in Computational Physics 10, n^o 3 (septembre 2011) : 607–34. http://dx.doi.org/10.4208/cicp.200510.061210a.

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AbstractA data-driven model reduction strategy is presented for the representation of random polycrystal microstructures. Given a set of microstructure snapshots that satisfy certain statistical constraints such as given low-order moments of the grain size distribution, using a non-linear manifold learning approach, we identify the intrinsic low-dimensionality of the microstructure manifold. In addition to grain size, a linear dimensionality reduction technique (Karhunun-Loéve Expansion) is used to reduce the texture representation. The space of viable microstructures is mapped to a low-dimensional region thus facilitating the analysis and design of polycrystal microstructures. This methodology allows us to sample microstructure features in the reduced-order space thus making it a highly efficient, low-dimensional surrogate for representing microstructures (grain size and texture). We demonstrate the model reduction approach by computing the variability of homogenized thermal properties using sparse grid collocation in the reduced-order space that describes the grain size and orientation variability.

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Gosea, Ion Victor. « Exact and Inexact Lifting Transformations of Nonlinear Dynamical Systems : Transfer Functions, Equivalence, and Complexity Reduction ». Applied Sciences 12, n^o 5 (23 février 2022) : 2333. http://dx.doi.org/10.3390/app12052333.

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In this work, we deal with the problem of approximating and equivalently formulating generic nonlinear systems by means of specific classes thereof. Bilinear and quadratic-bilinear systems accomplish precisely this goal. Hence, by means of exact and inexact lifting transformations, we are able to reformulate the original nonlinear dynamics into a different, more simplified format. Additionally, we study the problem of complexity/model reduction of large-scale lifted models of nonlinear systems from data. The method under consideration is the Loewner framework, an established data-driven approach that requires samples of input–output mappings. The latter are known as generalized transfer functions, which are appropriately defined for both bilinear and quadratic-bilinear systems. We show connections between these mappings as well as between the matrices of reduced-order models. Finally, we illustrate the theoretical discussion with two numerical examples.

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Abbasi, Mohammad Hossein, Laura Iapichino, Wil Schilders et Nathan van de Wouw. « A data-based stability-preserving model order reduction method for hyperbolic partial differential equations ». Nonlinear Dynamics 107, n^o 4 (10 janvier 2022) : 3729–48. http://dx.doi.org/10.1007/s11071-021-07094-8.

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Neggers, Jan, Olivier Allix, François Hild et Stéphane Roux. « Big Data in Experimental Mechanics and Model Order Reduction : Today’s Challenges and Tomorrow’s Opportunities ». Archives of Computational Methods in Engineering 25, n^o 1 (28 juillet 2017) : 143–64. http://dx.doi.org/10.1007/s11831-017-9234-3.

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