Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

Fukami, Kai; Murata, Takaaki; Zhang, Kai; Fukagata, Koji

doi:10.1017/jfm.2021.697

Cited by 51 publications

(17 citation statements)

References 69 publications

(72 reference statements)

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“…Furthermore, of particular interest here is how we can control a high-dimensional and nonlinear dynamical system by using the capability of AE demonstrated in the present study, which can promote efficient order reduction of data thanks to nonlinear operations inside neural networks. From this viewpoint, it is widely known that capturing appropriate coordinates capitalizing on such model order reduction techniques including AE considered in the present study is also important since being able to describe dynamics on a proper coordinate system enables us to apply a broad variety of modern control theory in a computationally efficient manner while keeping its interpretability and generaliziability [90]. To that end, there are several studies to enforce linearity in the latent space of AE [91,92], although their demonstrations are still limited to low-dimensional problems that are distanced from practical applications.…”

Section: Discussionmentioning

confidence: 99%

Model Order Reduction with Neural Networks: Application to Laminar and Turbulent Flows

et al. 2021

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We investigate the capability of neural network-based model order reduction, i.e., autoencoder (AE), for fluid flows. As an example model, an AE which comprises of convolutional neural networks and multi-layer perceptrons is considered in this study. The AE model is assessed with four canonical fluid flows, namely: (1) two-dimensional cylinder wake, (2) its transient process, (3) NOAA sea surface temperature, and (4) a cross-sectional field of turbulent channel flow, in terms of a number of latent modes, the choice of nonlinear activation functions, and the number of weights contained in the AE model. We find that the AE models are sensitive to the choice of the aforementioned parameters depending on the target flows. Finally, we foresee the extensional applications and perspectives of machine learning based order reduction for numerical and experimental studies in the fluid dynamics community.

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Section: Discussionmentioning

confidence: 99%

Model Order Reduction with Neural Networks: Application to Laminar and Turbulent Flows

et al. 2021

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“…Proper Orthogonal Decomposition (POD) is one such SVD-based method and has been applied successfully to many fields such as reactor physics [5], urban flows [6] and fluid-structure interaction [7]. However, since 2018 there has been an explosion of interest in using autoencoders for dimensionality reduction, see references 26, 28-44, 48-52 in [3] and others in [8]. Due to the nonlinear activation functions, these networks find a nonlinear map between the high-and lowdimensional spaces, whereas with SVD-based methods, the mapping is linear.…”

Section: Related Workmentioning

confidence: 99%

“…As with other SVD-based methods, DMD can struggle to capture symmetries and invariants in the flow fields [4], which is one reason why we opt for a combination of autoencoder (for dimensionality reduction) and adversarial network (for prediction). SINDy aims to find a sparse representation of a dynamical system relying on the assumption that, for many physical systems, only a small number of terms dominate the dynamical behaviour and has been applied to a number of fluid dynamics problems, including flow past a cylinder [8,38]. It can be difficult to compress accurately to a small number of variables, and SINDy was not used here, because we did not want to be restricted to using a small number of reduced variables.…”

Section: Related Workmentioning

confidence: 99%

Extending the Capabilities of Data-Driven Reduced-Order Models to Make Predictions for Unseen Scenarios: Applied to Flow Around Buildings

Heaney

Liu

et al. 2022

Front. Phys.

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We present a data-driven or non-intrusive reduced-order model (NIROM) which is capable of making predictions for a significantly larger domain than the one used to generate the snapshots or training data. This development relies on the combination of a novel way of sampling the training data (which frees the NIROM from its dependency on the original problem domain) and a domain decomposition approach (which partitions unseen geometries in a manner consistent with the sub-sampling approach). The method extends current capabilities of reduced-order models to generalise, i.e., to make predictions for unseen scenarios. The method is applied to a 2D test case which simulates the chaotic time-dependent flow of air past buildings at a moderate Reynolds number using a computational fluid dynamics (CFD) code. The procedure for 3D problems is similar, however, a 2D test case is considered sufficient here, as a proof-of-concept. The reduced-order model consists of a sampling technique to obtain the snapshots; a convolutional autoencoder for dimensionality reduction; an adversarial network for prediction; all set within a domain decomposition framework. The autoencoder is chosen for dimensionality reduction as it has been demonstrated in the literature that these networks can compress information more efficiently than traditional (linear) approaches based on singular value decomposition. In order to keep the predictions realistic, properties of adversarial networks are exploited. To demonstrate its ability to generalise, once trained, the method is applied to a larger domain which has a different arrangement of buildings. Statistical properties of the flows from the reduced-order model are compared with those from the CFD model in order to establish how realistic the predictions are.

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“…This balance relies on regularisation parameters and further cause a convex optimisation problem that is harder to solve. Furthermore, the user-selection of the regularisation parameters directly controls the model complexity and needs to be varied and adjusted from case to case [ 9 ]. The method proposed in this work tries to avoid the direct dependency of the model complexity on user selected parameters.…”

Section: Introductionmentioning

confidence: 99%

Towards robust data-driven reduced-order modelling for turbulent flows: application to vortex-induced vibrations

Schubert

Sieber

Oberleithner

et al. 2022

Theor. Comput. Fluid Dyn.

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This work presents a robust method that minimises the impact of user-selected parameter on the identification of generic models to study the coherent dynamics in turbulent flows. The objective is to gain insight into the flow dynamics from a data-driven reduced order model (ROM) that is developed from measurement data of the respective flow. For an efficient separation of the coherent dynamics, spectral proper orthogonal decomposition (SPOD) is used, projecting the flow field onto a low-dimensional subspace, so that the dominating dynamics can be represented with a minimal number of modes. A function library is defined using polynomial combinations of the temporal modal coefficients to describe the flow dynamics with a system of nonlinear ordinary differential equations. The most important library functions are identified in a two-stage cross-validation procedure (conservative and restrictive sparsification) and combined in the final model. In the first stage, the process uses a simple approximation of the derivative to match the model with the data. This stage delivers a reduced set of possible library function candidates for the model. In the second, more complex stage, the model of the entire flow is integrated over a short time and compared with the progression of the measured data. This restrictive stage allows a robust identification of nonlinearities and modal interactions in the data and their representation in the model. The method is demonstrated using data from particle image velocimetry (PIV) measurements of a circular cylinder undergoing vortex-induced vibration (VIV) at $$\mathrm{Re}=4000$$ Re = 4000 . It delivers a reduced order model that reproduces the average dynamics of the flow and reveals the interaction of coexisting flow dynamics by the model structure.

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Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

Cited by 51 publications

References 69 publications

Model Order Reduction with Neural Networks: Application to Laminar and Turbulent Flows

Model Order Reduction with Neural Networks: Application to Laminar and Turbulent Flows

Extending the Capabilities of Data-Driven Reduced-Order Models to Make Predictions for Unseen Scenarios: Applied to Flow Around Buildings

Towards robust data-driven reduced-order modelling for turbulent flows: application to vortex-induced vibrations

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