scholarly journals Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 757 ◽  
Author(s):  
Xuping Xie ◽  
Guannan Zhang ◽  
Clayton G. Webster
Keyword(s):  
Differential Operators ◽  
Nonlinear Dynamical Systems ◽  
Dimensional Space ◽  
Fluid Dynamic ◽  
Data Driven ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Highly Nonlinear ◽  
Low Dimensional

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.

scholarly journals Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network

2019 ◽  
Author(s):  
Xuping Xie ◽  
Guannan Zhang ◽  
Clayton G. Webster
Keyword(s):  
Differential Operators ◽  
Nonlinear Dynamical Systems ◽  
Dimensional Space ◽  
Fluid Dynamic ◽  
Data Driven ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Highly Nonlinear ◽  
Low Dimensional

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

scholarly journals Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Zhe Bai ◽  
Liqian Peng
Keyword(s):  
Machine Learning ◽  
Nonlinear Dynamical Systems ◽  
Reduced Order Models ◽  
Simulation Code ◽  
Nonlinear Dynamical ◽  
Reduced Order ◽  
Nonlinear Model Reduction ◽  
Regression Techniques ◽  
Low Dimensional ◽  
Modern Machine

AbstractAlthough projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters; this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $$10^3{\times }$$ 10 3 × in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs. The domain of applications include both parabolic and hyperbolic PDEs, regardless of the dimension of full-order models (FOMs).

Reduced Order Model for Unsteady Fluid Flows via Recurrent Neural Networks

2019 ◽  
Author(s):  
Sandeep B. Reddy ◽  
Allan Ross Magee ◽  
Rajeev K. Jaiman ◽  
J. Liu ◽  
W. Xu ◽  
...  
Keyword(s):  
Neural Networks ◽  
Reynolds Number ◽  
Flow Field ◽  
Unsteady Flow ◽  
Recurrent Neural Networks ◽  
Reduced Order Model ◽  
Data Driven ◽  
Order Model ◽  
Reduced Order ◽  
Low Dimensional

Abstract In this paper, we present a data-driven approach to construct a reduced-order model (ROM) for the unsteady flow field and fluid-structure interaction. This proposed approach relies on (i) a projection of the high-dimensional data from the Navier-Stokes equations to a low-dimensional subspace using the proper orthogonal decomposition (POD) and (ii) integration of the low-dimensional model with the recurrent neural networks. For the hybrid ROM formulation, we consider long short term memory networks with encoder-decoder architecture, which is a special variant of recurrent neural networks. The mathematical structure of recurrent neural networks embodies a non-linear state space form of the underlying dynamical behavior. This particular attribute of an RNN makes it suitable for non-linear unsteady flow problems. In the proposed hybrid RNN method, the spatial and temporal features of the unsteady flow system are captured separately. Time-invariant modes obtained by low-order projection embodies the spatial features of the flow field, while the temporal behavior of the corresponding modal coefficients is learned via recurrent neural networks. The effectiveness of the proposed method is first demonstrated on a canonical problem of flow past a cylinder at low Reynolds number. With regard to a practical marine/offshore engineering demonstration, we have applied and examined the reliability of the proposed data-driven framework for the predictions of vortex-induced vibrations of a flexible offshore riser at high Reynolds number.

scholarly journals Non-intrusive Nonlinear Model Reduction via Machine Learning Approximations to Low-dimensional Operators

2021 ◽  
Author(s):  
Zhe Bai ◽  
Liqian Peng
Keyword(s):  
Machine Learning ◽  
Nonlinear Dynamical Systems ◽  
Reduced Order Models ◽  
Simulation Code ◽  
Nonlinear Dynamical ◽  
Reduced Order ◽  
Nonlinear Model Reduction ◽  
Regression Techniques ◽  
Low Dimensional ◽  
Modern Machine

Abstract Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters; this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $10^3\times$ in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs.

Data-Driven Reduced Order Modeling of Flows Around Two-Dimensional Bluff Bodies of Various Shapes

2019 ◽  
Author(s):  
Kazuto Hasegawa ◽  
Kai Fukami ◽  
Takaaki Murata ◽  
Koji Fukagata
Keyword(s):  
Number Fields ◽  
Flow Fields ◽  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Data Driven ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Order Model ◽  
Reduced Order ◽  
Low Dimensional

Abstract We propose a reduced order model for predicting unsteady flows using a data-driven method. As preliminary tests, we use two-dimensional unsteady flow around bluff bodies with different shapes as the training datasets obtained by direct numerical simulation (DNS). Our machine-learned architecture consists of two parts: Convolutional Neural Network-based AutoEncoder (CNN-AE) and Long Short Term Memory (LSTM), respectively. First, CNN-AE is used to map into a low-dimensional space from the flow field data. Then, LSTM is employed to predict the temporal evolution of the low-dimensional data generated by CNN-AE. Proposed machine-learned reduced order model is applied to two-dimensional circular cylinder flows at various Reynolds numbers and flows around bluff bodies of various shapes. The flow fields reconstructed by the machine-learned architecture show reasonable agreement with the reference DNS data. Furthermore, it can be seen that our machine-learned reduced order model can successfully map the high-dimensional flow data into low-dimensional field and predict the flow fields against unknown Reynolds number fields and shapes of bluff body. As concluding remarks, we discuss the extension study of machine-learned reduced order modeling for various applications in experimental and computational fluid dynamics.

scholarly journals Fully Parameterized Reduced Order Models Using Hyper-Dual Numbers and Component Mode Synthesis

2015 ◽  
Author(s):  
Matthew S. Bonney ◽  
Daniel C. Kammer ◽  
Matthew R. W. Brake
Keyword(s):  
Truncation Error ◽  
Sampling Methods ◽  
Latin Hypercube Sampling ◽  
Component Mode Synthesis ◽  
Reduced Order Models ◽  
Dual Numbers ◽  
Order Model ◽  
Full System ◽  
Reduced Order ◽  
Computational Burden

The uncertainty of a system is usually quantified with the use of sampling methods such as Monte-Carlo or Latin hypercube sampling. These sampling methods require many computations of the model and may include re-meshing. The re-solving and re-meshing of the model is a very large computational burden. One way to greatly reduce this computational burden is to use a parameterized reduced order model. This is a model that contains the sensitivities of the desired results with respect to changing parameters such as Young’s modulus. The typical method of computing these sensitivities is the use of finite difference technique that gives an approximation that is subject to truncation error and subtractive cancellation due to the precision of the computer. One way of eliminating this error is to use hyperdual numbers, which are able to generate exact sensitivities that are not subject to the precision of the computer. This paper uses the concept of hyper-dual numbers to parameterize a system that is composed of two substructures in the form of Craig-Bampton substructure representations, and combine them using component mode synthesis. The synthesis transformations using other techniques require the use of a nominal transformation while this approach allows for exact transformations when a perturbation is applied. This paper presents this technique for a planar motion frame and compares the use and accuracy of the approach against the true full system. This work lays the groundwork for performing component mode synthesis using hyper-dual numbers.

Dynamic Analysis of a Protein-Ligand Molecular Chain Attached to an Atomic Force Microscope

2004 ◽  
Vol 126 (4) ◽  
pp. 496-513 ◽  
Author(s):  
Deman Tang ◽  
Earl H. Dowell
Keyword(s):  
Nonlinear Systems ◽  
Atomic Force Microscope ◽  
Reduced Order Model ◽  
Molecular Chain ◽  
Static Equilibrium ◽  
Reduced Order Models ◽  
Base Excitation ◽  
Order Model ◽  
Reduced Order ◽  
Atomic Force

Dynamic numerical simulation of a protein-ligand molecular chain connected to a moving atomic force microscope (AFM) has been studied. A sinusoidal base excitation of the cantilevered beam of the AFM is considered in some detail. A comparison between results for a single molecule and those for multiple molecules has been made. For a small number of molecules, multiple stable static equilibrium positions are observed and chaotic behavior may be generated via a period-doubling cascade for harmonic base excitation of the AFM. For many molecules in the chain, only a single static equilibrium position exists. To enable these calculations, reduced-order (dynamic) models are constructed for fully linear, combined linear/nonlinear and fully nonlinear systems. Several distinct reduced-order models have been developed that offer the option of increased computational efficiency at the price of greater effort to construct the particular reduced-order model. The agreement between the original and reduced-order models (ROM) is very good even when only one mode is included in the ROM for either the fully linear or combined linear/nonlinear systems provided the excitation frequency is lower than the fundamental natural frequency of the linear system. The computational advantage of the reduced-order model is clear from the results presented.

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