Machine Learning Approach to Model Order Reduction of Nonlinear Systems via Autoencoder and LSTM Networks

Simpson, Thomas; Dervilis, Nikolaos; Chatzi, Eleni

doi:10.1061/(asce)em.1943-7889.0001971

Cited by 43 publications

(26 citation statements)

References 48 publications

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“…The reduced order modelling method used herein is a purely data-driven approach, in the sense that it relies on response time histories of input and output data, which in this case stem from FOM simulations, but that would further be possible to retrieve via measurements. The method makes use of an autoencoder neural network, for the purpose of dimensionality reduction and an LSTM neural network for the learning of system dynamics [4]. The process is demonstrated in figure 3, where the training of the ROM initially involves the generation of input-output data using the FOM of the system of concern.…”

Section: Reduced Order Modelling Methodologymentioning

confidence: 99%

“…The network then predicts response of the system within the latent space, [ Z], and the predicted response of the full system is recovered by passing [ Z] through the decoder to recover the prediction in the physical space [ X]. The full methodology is extensively described and demonstrated in [4].…”

Section: Reduced Order Modelling Methodologymentioning

confidence: 99%

“…There has been considerable research interest in the leveraging of machine learning (ML) methods for delivery of efficient ROMs [1,2]. This involves training ML models from full order simulations and using the powerful capacity of ML to capture nonlinear relationships in data, such that these models can then be used to approximate the response of the full order model (FOM) under different inputs [3,4].…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we demonstrate exploitation of a recently developed nonlinear ROM framework [4]. The developed framework makes use of autoencoder neural networks for dimensionality reduction [12]; LSTM neural networks [13] are then used to model the dynamics of the system on the reduced basis.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Reduced Order Modelling of Soil Structure Interaction Effects via LSTM and Autoencoder Neural Networks

Simpson¹,

Dervilis²,

Couturier³

et al. 2022

Preprint

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In the field of structural health monitoring (SHM), inverse problems which require repeated analyses are common. With the increase in the use of nonlinear models, the development of nonlinear reduced order modelling techniques is of paramount interest. Of considerable research interest, is the use of flexible and scalable machine learning methods which can learn to approximate the behaviour of nonlinear dynamic systems using input and output data. One such nonlinear system of interest, in the context of wind turbine structures, is the soil structure interaction (SSI) problem. Soil demonstrates strongly nonlinear behaviour with regards to its restoring force and has been shown to considerably influence the dynamic response of wind turbine structures. In this work, we demonstrate the application of a recently developed nonlinear reduced order modelling method, which leverages Autoencoder and LSTM neural networks, to a nonlinear soil structure interaction problem of a wind turbine monopile subject to realistic loading at the seabed level. The accuracy and efficiency of the methodology is compared to full order simulations carried out using Abaqus. The ROM was shown to have good fidelity and a considerable reduction in computational time for the system considered.

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Section: Reduced Order Modelling Methodologymentioning

confidence: 99%

Section: Reduced Order Modelling Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Reduced Order Modelling of Soil Structure Interaction Effects via LSTM and Autoencoder Neural Networks

Simpson¹,

Dervilis²,

Couturier³

et al. 2022

Preprint

Self Cite

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“…In the framework proposed by Fresca et al [22], a further dimensionality reduction carried out on the FOM data through proper orthogonal decomposition (POD), yielding the so-called POD DL-ROM technique, also allows to speedup training times and to compress data dimensions, enhancing the construction of DL-ROMs. Neural networks have also been used to model simple structures by Simpson et al [62], with two main differences: the convolutional autoencoder uses Long Short-Term Memory (LSTM) networks; a statistical regression model is used instead of the DFNN. The adoption of LSTM cells is beneficial for the prediction of the time evolution beyond the training window, which is not targeted in the present contribution focusing on periodic responses.…”

Section: Introductionmentioning

confidence: 99%

Deep learning-based reduced order models for the real-time simulation of the nonlinear dynamics of microstructures

Fresca¹,

Gobat²,

Fedeli³

et al. 2021

Preprint

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We propose a non-intrusive Deep Learning-based Reduced Order Model (DL-ROM) capable of capturing the complex dynamics of mechanical systems showing inertia and geometric nonlinearities. In the first phase, a limited number of high fidelity snapshots are used to generate a POD-Galerkin ROM which is subsequently exploited to generate the data, covering the whole parameter range, used in the training phase of the DL-ROM. A convolutional autoencoder is employed to map the system response onto a lowdimensional representation and, in parallel, to model the reduced nonlinear trial manifold. The system dynamics on the manifold is described by means of a deep feedforward neural network that is trained together with the autoencoder. The strategy is benchmarked against high fidelity solutions on a clamped-clamped beam and on a real micromirror with softening response and multiplicity of solutions. By comparing the different computational costs, we discuss the impressive gain in performance and show that the DL-ROM truly represents a real-time tool which can be profitably and efficiently employed in complex system-level simulation procedures for design and optimisation purposes.

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Deep learning‐based reduced order models for the real‐time simulation of the nonlinear dynamics of microstructures

Fresca

Gobat

Fedeli

et al. 2022

Numerical Meth Engineering

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We propose a non‐intrusive deep learning‐based reduced order model (DL‐ROM) capable of capturing the complex dynamics of mechanical systems showing inertia and geometric nonlinearities. In the first phase, a limited number of high fidelity snapshots are used to generate a POD‐Galerkin ROM which is subsequently exploited to generate the data, covering the whole parameter range, used in the training phase of the DL‐ROM. A convolutional autoencoder is employed to map the system response onto a low‐dimensional representation and, in parallel, to model the reduced nonlinear trial manifold. The system dynamics on the manifold is described by means of a deep feedforward neural network that is trained together with the autoencoder. The strategy is benchmarked against high fidelity solutions on a clamped‐clamped beam and on a real micromirror with softening response and multiplicity of solutions. By comparing the different computational costs, we discuss the impressive gain in performance and show that the DL‐ROM truly represents a real‐time tool which can be profitably and efficiently employed in complex system‐level simulation procedures for design and optimization purposes.

show abstract

Machine Learning Approach to Model Order Reduction of Nonlinear Systems via Autoencoder and LSTM Networks

Cited by 43 publications

References 48 publications

Nonlinear Reduced Order Modelling of Soil Structure Interaction Effects via LSTM and Autoencoder Neural Networks

Nonlinear Reduced Order Modelling of Soil Structure Interaction Effects via LSTM and Autoencoder Neural Networks

Deep learning-based reduced order models for the real-time simulation of the nonlinear dynamics of microstructures

Deep learning‐based reduced order models for the real‐time simulation of the nonlinear dynamics of microstructures

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