Reduced Order Probabilistic Emulator of RAM‐SCB: Toward Non‐Linearity With Autoencoders

The rapid acquisition of high-fidelity flow field information is of great significance for engineering applications such as multi-field coupling. Current research in flow field modeling predominantly focuses on low Reynolds numbers and periodic flows, exhibiting weak generalization capabilities and notable issues with temporal inferring error accumulation. Therefore, we establish a reduced order model (ROM) based on Convolutional Auto-Encoder (CAE) and Long Short-Term Memory (LSTM) neural network and propose an unsteady flow field modeling method for the airfoil with a high Reynolds number and strong nonlinear characteristics. The attention mechanism and weak physical constraints are integrated into the model architecture to improve the modeling accuracy. A broadband excitation training strategy is proposed to overcome the error accumulation problem of long-term inferring. With only a small amount of latent codes, the relative error of the flow field reconstructed by CAE can be less than 5‰. By training LSTM with broadband excitation signals, stable dynamic evolution can be achieved in the time dimension. CAE-LSTM can accurately predict the forced response and complex limit cycle behavior of the airfoil in a wide range of amplitude and frequency under subsonic/transonic conditions. The relative errors of predicted variables and integral force are less than 1%. The fluid–structure interaction framework is built by coupling the ROM and motion equations of the structure. CAE-LSTM predicts the time series response of pitch displacement and moment coefficient at different reduced frequencies, which is in good agreement with computational fluid dynamics, and the simulation time savings exceed one order of magnitude.

The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) for parametrized PDEs to speed up the solution of the aforementioned problems can be problematic. This is primarily due to the strong variability characterizing the solution set and to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To enhance ROM efficiency, we proposed a new generation of non-intrusive, nonlinear ROMs, based on deep learning (DL) algorithms, such as convolutional, feedforward, and autoencoder neural networks. In the proposed DL-ROM, both the nonlinear solution manifold and the nonlinear reduced dynamics used to model the system evolution on that manifold can be learnt in a non-intrusive way thanks to DL algorithms trained on a set of FOM snapshots. DL-ROMs were shown to be able to accurately capture complex front propagation processes, both in physiological and pathological cardiac EP, very rapidly once neural networks were trained, however, at the expense of huge training costs. In this study, we show that performing a prior dimensionality reduction on FOM snapshots through randomized proper orthogonal decomposition (POD) enables to speed up training times and to decrease networks complexity. Accuracy and efficiency of this strategy, which we refer to as POD-DL-ROM, are assessed in the context of cardiac EP on an idealized left atrium (LA) geometry and considering snapshots arising from a NURBS (non-uniform rational B-splines)-based isogeometric analysis (IGA) discretization. Once the ROMs have been trained, POD-DL-ROMs can efficiently solve both physiological and pathological cardiac EP problems, for any new scenario, in real-time, even in extremely challenging contexts such as those featuring circuit re-entries, that are among the factors triggering cardiac arrhythmias.

In the present study, a nonlinear system identification approach based on a long short-term memory (LSTM) neural network is applied for the prediction of transonic buffet aerodynamics. The identification approach is applied as a reduced-order modeling (ROM) technique for an efficient computation of time-varying integral quantities such as aerodynamic force and moment coefficients. Therefore, the nonlinear identification procedure as well as the generalization of the ROM are presented. The training data set for the LSTM–ROM is provided by performing forced-motion unsteady Reynolds-averaged Navier–Stokes simulations. Subsequent to the training process, the ROM is applied for the computation of the aerodynamic integral quantities associated with transonic buffet. The performance of the trained ROM is demonstrated by computing the aerodynamic loads of the NACA0012 airfoil investigated at transonic freestream conditions. In contrast to previous studies considering only a pitching excitation, both the pitch and plunge degrees of freedom of the airfoil are individually and simultaneously excited by means of an user-defined training signal. Therefore, strong nonlinear effects are considered for the training of the ROM. By comparing the results with a full-order computational fluid dynamics solution, a good prediction capability of the presented ROM method is indicated. However, compared to the results of previous studies including only the airfoil pitching excitation, a slightly reduced prediction performance is shown.

Accurately reconstructing and predicting the global temperature field of turbine blades is of significant importance in the field of aero-engines. The complexities in geometries and operation conditions of the blades further complicate these problems, because temperatures can only be acquired from sparse and noisy measurements. Proper orthogonal decomposition (POD) and deep neural network auto-encoder (AE) are two typical reduced-order models to reconstruct the global temperature fields from sparse data points, and they are further combined with long short-term memory (LSTM) networks for prediction. In contrast with the linear modes of POD, the nonlinear features of AE may lead to advantages in reconstructing and predicting of temperature fields. A systematic comparison between the two methods is seldom studied in existing research, particularly regarding their noise resistance and time-series prediction capabilities. Therefore, a detailed study is conducted in this paper. The two-dimensional cross section of Mark II blades is used as an example; this work compares the performance of POD–LSTM and AE–LSTM in reconstructing and predicting the global temperature field of turbine blades based on sparse and noisy measurement data under transient operating conditions. The results indicate that both reduced-order prediction models achieved low mean absolute percentage errors (MAPEs) and high computational efficiency for reconstruction and prediction. With 12 sparse data points, the reconstruction error of two methods is comparable. Compared to the POD method, reduction coefficients of the AE method are more robust and have a uniform energy distribution, so AE exhibits superior noise resistance and time-series prediction capabilities.

Dimensionality reduction through convolutional autoencoders for fracture patterns prediction

Capabilities of Auto-encoders and Principal Component Analysis of the reduction of microstructural images; Application on the acceleration of Phase-Field simulations

Non-linear analysis is of increasing importance in wind energy engineering as a result of their exposure in extreme conditions and the ever-increasing size and slenderness of wind turbines. Whilst modern computing capabilities facilitate execution of complex analyses, certain applications which require multiple or real-time analyses remain a challenge, motivating adoption of accelerated computing schemes, such as reduced order modelling (ROM) methods. Soil structure interaction (SSI) simulations fall in this class of problems, with the non-linear restoring force significantly affecting the dynamic behaviour of the turbine. In this work, we propose a ROM approach to the SSI problem using a recently developed ROM methodology. We exploit a data-driven non-linear ROM methodology coupling an autoencoder with long short-term memory (LSTM) neural networks. The ROM is trained to emulate a steel monopile foundation constrained by non-linear soil and subject to forces and moments at the top of the foundation, which represent the equivalent loading of an operating turbine under wind and wave forcing. The ROM well approximates the time domain and frequency domain response of the Full Order Model (FOM) over a range of different wind and wave loading regimes, whilst reducing the computational toll by a factor of 300. We further propose an error metric for capturing isolated failure instances of the ROM.

Neural networks are employed to model reactive ion etching (RIE) using optical emission spectroscopy (OES) data. While OES is an excellent tool for monitoring plasma emission intensity, a primary issue with its use is the large dimensionality of the spectroscopic data. To alleviate this concern, principal component analysis (PCA) and autoencoder neural networks (AENNs) are implemented as mechanisms for feature extraction to reduce the dimensionality of the OES data. OES data are generated from a 2/sup 4/ factorial experiment designed to characterize RIE process variation during the etching of benzocyclobutene (BCB) in a SF/sub 6//O/sub 2/ plasma, with controllable input factors consisting of the two gas flows, RF power, and chamber pressure. The OES data, consisting of 226 wavelengths sampled every 20 s, are compressed into five principal components using PCA and seven features using AENNs. Each method is subsequently used to establish multilayer perceptron neural networks trained using error back-propagation to model etch rate, uniformity, selectivity, and anisotropy. The neural network models of the etch responses using both methods show excellent agreement, with root-mean-squared errors as low as 0.215% between model predictions and measured data.

Fluid-Structure interaction in a collapsible channel with a flexible wall segment which deforms under the fluid dynamic loads arising from the flow within the channel is considered by using a reduced order model based on the method of principal component analysis developed for unsteady aerodynamic pressures and the structural dynamic state variables by using a series of discrete time results. A computational fluid dynamics approach, based on the finite volume solver is used to solve the discretized Navier-Stokes equations. The structural model of the flexible wall is based on the membrane equation and the membrane tension is varied to study the effects of the structural modeling parameters on the instabilities that arise due to fluid-structu re interaction. It is well known in aeroelasticit y, that fluid-structural coupling based on lagging the fluid dynamics code with the structural dynamics solver can produce spurious numerical phenomena. On the other hand, tightly coupled aeroelastic solvers can be difficult to implement due to numerical ill-conditioning. Using a series of discrete time results, a reduced order model is developed for the unsteady aerodynamic pressure and the structural dynamic state variables based on the method of principal component analysis. This reduced order model now serves as a de-coupler for the fluidstructure interaction. The effects of varying the tension and the inertia of the membrane on the unsteady fluid dynamics are investigated using the reduced order model. The principal component analysis captures the fluid dynamic damping at every time instant in the system dynamics and this knowledge is used to detect the onset of instabilities. A regularization technique is also used to improve the conditioning of the matrices involved in the reduced-order fluid-structure interaction model.

In the present study, a hybrid deep learning reduced-order model (ROM) is applied for the prediction of wing buffet pressure distributions on a civil aircraft configuration. The hybrid model is compound of a convolutional variational neural network autoencoder (CNN-VAR-AE) and a long short-term memory (LSTM) neural network. The CNN-VAR-AE is used for the reduction of the high-dimensional flow field data, whereas the LSTM is applied to predict the temporal evolution of the pressure distributions. For training the neural network, experimental buffet data obtained by unsteady pressure sensitive paint measurement (iPSP), is applied. As a test case, the Airbus XRF-1 configuration is selected, considering two different experimental setups. The first setup is defined by a wind tunnel model with a clean wing, whereas the second setup includes an ultra high bypass ratio engine nacelle on each wing. Both configurations have been tested in the European Transonic Windtunnel, considering several transonic buffet conditions. Finalizing the training of the hybrid neural networks, the trained models are applied for the prediction of buffet flow conditions which are not included in the training data set. A comparison of the experimental results and the pressure distributions predicted by the hybrid ROMs indicate a precise prediction performance. Considering both aircraft configurations, the main buffet flow features are captured by the hybrid ROMs.

Application of a long short-term memory neural network for modeling transonic buffet aerodynamics

Kinetic equations are crucial for modeling non-equilibrium phenomena, but their computational complexity is a challenge. This paper presents a data-driven approach using reduced order models (ROM) to efficiently model non-equilibrium flows in kinetic equations by comparing two ROM approaches: proper orthogonal decomposition (POD) and autoencoder neural networks (AE). While AE initially demonstrate higher accuracy, POD’s precision improves as more modes are considered. Notably, our work recognizes that the classical POD model order reduction approach, although capable of accurately representing the non-linear solution manifold of the kinetic equation, may not provide a parsimonious model of the data due to the inherently non-linear nature of the data manifold. We demonstrate how AEs are used in finding the intrinsic dimension of a system and to allow correlating the intrinsic quantities with macroscopic quantities that have a physical interpretation.

LSTMED: An uneven dynamic process monitoring method based on LSTM and Autoencoder neural network

This paper presents a general workflow to generate and improve the forecast of model surrogates of computational fluid dynamics simulations using deep learning, and most specifically adversarial training. This adversarial approach aims to reduce the divergence of the forecasts from the underlying physical model. Our two-step method integrates a Principal Components Analysis (PCA) based adversarial autoencoder (PC-AAE) with adversarial Long short-term memory (LSTM) networks. Once the reduced-order model (ROM) of the CFD solution is obtained via PCA, an adversarial autoencoder is used on the principal components time series. Subsequentially, a LSTM is adversarially trained on the latent space produced by the PC-AAE to make forecasts. Here we show, that the application of adversarial training improves the rollout of the latent space predictions. Our workflow is applied to three different case studies including two models of urban air pollution in London.

A remote photoplethysmography (rPPG) analysis can extract vital signs from the source video, including heart rate estimation. One of the problems of heart rate estimation is periodic noise embedded in the source video. It is difficult for an rPPG analysis to discriminate between vital signal information and noise, increasing prediction error. To alleviate this problem, this paper used principal component analysis (PCA) to extract rPPG signals from the input video before forwarding the signal to Long Short Term Memory (LSTM) to estimate heart rate. The experimental results show that, among discrete Fourier Transform method, neural networks, and neural network with LSTM, the proposed method accomplished a much lower MAEP at 15.05, 13.90, and 17.90 in the cases of overall, with no periodic noise, and with periodic noise, respectively.