Reducing dimensionality is a key preprocessing step in many data analysis applications to address the negative effects of the curse of dimensionality and collinearity on model performance and computational complexity, to denoise the data or to reduce storage requirements. Moreover, in many applications it is desirable to reduce the input dimensions by choosing a subset of variables that best represents the entire set without any a priori information available. Unsupervised variable selection techniques provide a solution to this second problem. An autoencoder, if properly regularized, can solve both unsupervised dimensionality reduction and variable selection, but the training of large neural networks can be prohibitive in time sensitive applications. We present an approach called Recovery of Linear Components (RLC), which serves as a middle ground between linear and non-linear dimensionality reduction techniques, reducing autoencoder training times while enhancing performance over purely linear techniques. With the aid of synthetic and real world case studies, we show that the RLC, when compared with an autoencoder of similar complexity, shows higher accuracy, similar robustness to overfitting, and faster training times. Additionally, at the cost of a relatively small increase in computational complexity, RLC is shown to outperform the current state-of-the-art for a semiconductor manufacturing wafer measurement site optimization application.
Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoders
Institute for Fluid Dynamics and Ship Theory, Hamburg University of Technology（汉堡工业大学流体动力学与船舶理论研究所）；Institute of Mathematics, Hamburg University of Technology（汉堡工业大学数学研究所）
USACE Engineer Research Development Center（美国陆军工程兵团工程师研究与发展中心）；University of Genoa（热那亚大学）；University of Padua（帕多瓦大学）
Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as a non-intrusive method for propagating the latent-space dynamics in reduced order models. Here, we investigate employing deep autoencoders for discovering the reduced basis representation, the dynamics of which are then approximated by NODE. The ability of deep autoencoders to represent the latent-space is compared to the traditional proper orthogonal decom…
Compressed sensing techniques enable efficient acquisition and recovery of sparse, high-dimensional data signals via low-dimensional projections. In this work, we propose Uncertainty Autoencoders, a learning framework for unsupervised representation learning inspired by compressed sensing. We treat the low-dimensional projections as noisy latent representations of an autoencoder and directly learn both the acquisition (i.e., encoding) and amortized recovery (i.e., decoding) procedures. Our learning objective optimizes for a tractable variational lower bound to the mutual information between th…
In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the state space can most accurately be described by a \textit{nonlinear} manifold. Previous research has shown that deep learning can provide an efficient method for performing nonlinear dimension reduction, though they are dependent on the availability of training data and are often problem-specific \citep[see][]{carlberg_ca}. Here, we utilize randomized traini…
Imperial College London（伦敦帝国理工学院）；Jacobs（雅各布斯工程集团）
Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional space in which a high-dimensional system is approximated. Proper orthogonal decomposition (POD) and singular value decomposition (SVD) are often used for this purpose and yield an optimal linear subspace. Autoencoders provide a nonlinear alternative to POD/SVD, that may capture, more efficiently, features or patterns in the high-fidelity model results. Reduce…
Autoencoder-based reduced-order modeling (ROM) has recently attracted significant attention, owing to its ability to capture underlying nonlinear features. However, two critical drawbacks severely undermine its scalability to various physical applications: entangled and therefore uninterpretable latent variables (LVs) and the blindfold determination of latent space dimension. In this regard, this study proposes the physics-aware ROM using only interpretable and information-intensive LVs extracted by $β$-variational autoencoder, which are referred to as physics-aware LVs throughout this paper. …
Florida State University（佛罗里达州立大学）；University of South Carolina（南卡罗来纳大学）
The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite this, it is still unknown whether deep CAEs provide superior performance over established linear techniques or other network-based methods in all modeling scenarios. To elucidate this, the effect of autoencoder architecture on its associated ROM is studied through the comparison of deep CAEs against two alternatives: a simple fully connected autoencoder, and a novel graph convolutional autoencoder. Through benchmark e…
Seoul National University（首尔大学）；Samsung Electronics Co. Ltd.（三星电子株式会社）
In this paper, we propose Squeezed Convolutional Variational AutoEncoder (SCVAE) for anomaly detection in time series data for Edge Computing in Industrial Internet of Things (IIoT). The proposed model is applied to labeled time series data from UCI datasets for exact performance evaluation, and applied to real world data for indirect model performance comparison. In addition, by comparing the models before and after applying Fire Modules from SqueezeNet, we show that model size and inference times are reduced while similar levels of performance is maintained.
Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay, which precludes the realization of efficient reduced-order models based on linear subspace approximations. Among the possible solutions, there are purely data-driven methods that leverage autoencoders and their variants to learn a latent representation of the dynamical system, and then evolve it in time with another architecture. Despite their success in many applications where standard linear techniques fail, more has to be done to increase…
$β$-Variational autoencoders and transformers for reduced-order modelling of fluid flows
Universidad Carlos III de Madrid（马德里卡洛斯三世大学）；Spanish National Institute for Aerospace Technology (INTA)（西班牙国家航空航天技术研究院）；Illinois Institute of Technology（伊利诺伊理工学院）；KTH Royal Institute of Technology（瑞典皇家理工学院）
Harvard University（哈佛大学）；Sandia National Laboratories（桑迪亚国家实验室）；NexGen Analytics（奈克斯根分析公司）
Projection-based model order reduction on nonlinear manifolds has been recently proposed for problems with slowly decaying Kolmogorov n-width such as advection-dominated ones. These methods often use neural networks for manifold learning and showcase improved accuracy over traditional linear subspace-reduced order models. A disadvantage of the previously proposed methods is the potential high computational costs of training the networks on high-fidelity solution snapshots. In this work, we propose and analyze a novel method that overcomes this disadvantage by training a neural network only on …
In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mildly nonlinear measurements, that learns a structured representation from training data, and that efficiently computes a signal estimate. In particular, we apply a stacked denoising autoencoder (SDA), as an unsupervised feature learner. SDA enables us to capture statistical depend…
Learning Holographic Reduced Representations with Clifford Variational Autoencoders
Institute of Neuroinformatics（神经信息学研究所）；University of Zurich & ETH Zurich（苏黎世大学与苏黎世联邦理工学院）；National Research Council Canada（加拿大国家研究委员会）；University of Waterloo（滑铁卢大学）
Data Science Institute, Imperial College London（伦敦帝国理工学院数据科学研究所）；Universidad de Granada（格拉纳达大学）
We propose a new 'Bi-Reduced Space' approach to solving 3D Variational Data Assimilation using Convolutional Autoencoders. We prove that our approach has the same solution as previous methods but has significantly lower computational complexity; in other words, we reduce the computational cost without affecting the data assimilation accuracy. We tested the new method with data from a real-world application: a pollution model of a site in Elephant and Castle, London and found that we could reduce the size of the background covariance matrix representation by O(10^3) and, at the same time, incre…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage procedure for recovery of sparse solutions to Stochastic Optimization problem under assumption of smoothness and quadratic minoration on the expected objective. An interesting feature of the proposed algorithm is linear convergence of the approximate solution during the preliminary phase of the routine when the component of stochastic error in the gradient obser…
Virginia Tech（弗吉尼亚理工大学）；Computational Science Laboratory（计算科学实验室）
Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities.…
Deep learning models are state-of-the-art in compressive spectral imaging (CSI) recovery. These methods use a deep neural network (DNN) as an image generator to learn non-linear mapping from compressed measurements to the spectral image. For instance, the deep spectral prior approach uses a convolutional autoencoder network (CAE) in the optimization algorithm to recover the spectral image by using a non-linear representation. However, the CAE training is detached from the recovery problem, which does not guarantee optimal representation of the spectral images for the CSI problem. This work pro…
Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of freedom. Traditional ROM techniques such as proper orthogonal decomposition (POD) focus on linear projections of the dynamics onto a set of spectral features. In this paper we explore the construction of ROM using autoencoders (AE) that perform nonlinear projections of the system dynamics onto a low dimensional manifold learned from data. The approach uses convo…
Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena both in time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade with the primary goal to decompose complex flows to a set of features most important for future state prediction and control, typically using a dimensionality reduction technique. In this work, a novel data-driven technique based on the power of deep neural networks for reduced order modeling of the unsteady fluid flows is introduced. An autoencoder network i…
Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques
Cornell University（康奈尔大学）；Catholic University of the Sacred Heart（圣心天主教大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Sandia National Laboratories（桑迪亚国家实验室）
Obesity is a common issue in modern societies today that can lead to various diseases and significantly reduced quality of life. Currently, research has been conducted to investigate resting state EEG (electroencephalogram) signals with an aim to identify possible neurological characteristics associated with obesity. In this study, we propose a deep learning-based framework to extract the resting state EEG features for obese and lean subject classification. Specifically, a novel variational autoencoder framework is employed to extract subject-invariant features from the raw EEG signals, which …
University of Cambridge（剑桥大学）；Delft University of Technology（代尔夫特理工大学）；Imperial College London（帝国理工学院）；The Alan Turing Institute（艾伦·图灵研究所）
The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear decomposition of the turbulent state for a reduced-order representation of the dynamics. We divide the turbulent flow into a spatial problem and a temporal problem. First, we compute the latent space, which is the manifold onto which the turbulent dynamics live (i.e., it is a numerical approximation of the turbulent attractor). The latent space is found by a series of …
Machine Learning models are vulnerable to adversarial attacks that rely on perturbing the input data. This work proposes a novel strategy using Autoencoder Deep Neural Networks to defend a machine learning model against two gradient-based attacks: The Fast Gradient Sign attack and Fast Gradient attack. First we use an autoencoder to denoise the test data, which is trained with both clean and corrupted data. Then, we reduce the dimension of the denoised data using the hidden layer representation of another autoencoder. We perform this experiment for multiple values of the bound of adversarial p…
Reconstruction of neuromorphic dynamics from a single scalar time series using variational autoencoder and neural network map
Kotelnikov Institute of Radio-Engineering and Electronics of Russian Academy of Sciences, Saratov Branch（俄罗斯科学院科捷尔尼科夫无线电工程与电子研究所萨拉托夫分部）；HSE University（高等经济大学）
Learning Reduced Representations for Quantum Classifiers
Institute for Particle Physics and Astrophysics, ETH Zurich（粒子物理与天体物理研究所，苏黎世联邦理工学院）；Columbia University（哥伦比亚大学）；IBM Quantum, IBM Research – Zurich（IBM量子，IBM瑞士研究）；European Organization for Nuclear Research (CERN)（欧洲核子研究中心）；Institute for Quantum Electronics, ETH Zurich（量子电子研究所，苏黎世联邦理工学院）；Fraunhofer Institute for Applied Solid State Physics IAF（应用固态物理研究所（IAF））
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；University of Massachusetts（马萨诸塞大学）
Variational Autoencoders (VAEs) are a popular generative model, but one in which conditional inference can be challenging. If the decomposition into query and evidence variables is fixed, conditional VAEs provide an attractive solution. To support arbitrary queries, one is generally reduced to Markov Chain Monte Carlo sampling methods that can suffer from long mixing times. In this paper, we propose an idea we term cross-coding to approximate the distribution over the latent variables after conditioning on an evidence assignment to some subset of the variables. This allows generating query sam…
Convolutional autoencoders for the reconstruction of three-dimensional interfacial multiphase flows
Department of Mechanical Engineering, Stanford University（斯坦福大学机械工程系）；Department of Engineering Mechanics, KTH Royal Institute of Technology（皇家理工学院工程力学系）
Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning
Sandia National Laboratories（桑迪亚国家实验室）；Cornell University（康奈尔大学）；Catholic University of the Sacred Heart（圣心天主教大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
Data Science Institute（数据科学研究所）；Imperial College London（伦敦帝国理工学院）；Leonardo Centre, Imperial Business School（帝国理工商学院莱昂纳多中心）；Department of Earth Science & Engineering（地球科学与工程系）
This paper presents an approach to improve the forecast of computational fluid dynamics (CFD) simulations of urban air pollution 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 comp…
