A Theory-guided Auto-Encoder (TgAE) framework is proposed for surrogate construction and is further used for uncertainty quantification and inverse modeling tasks. The framework is built based on the Auto-Encoder (or Encoder-Decoder) architecture of convolutional neural network (CNN) via a theory-guided training process. In order to achieve the theory-guided training, the governing equations of the studied problems can be discretized and the finite difference scheme of the equations can be embedded into the training of CNN. The residual of the discretized governing equations as well as the data mismatch constitute the loss function of the TgAE. The trained TgAE can be used to construct a surrogate that approximates the relationship between the model parameters and responses with limited labeled data. In order to test the performance of the TgAE, several subsurface flow cases are introduced. The results show the satisfactory accuracy of the TgAE surrogate and efficiency of uncertainty quantification tasks can be improved with the TgAE surrogate. The TgAE also shows good extrapolation ability for cases with different correlation lengths and variances. Furthermore, the parameter inversion task has been implemented with the TgAE surrogate and satisfactory results can be obtained.
We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet) architecture into image-to-image regression encoder-decoder network. Specifically, the aim is to exploit the benefits of CapsNet over convolution neural network (CNN) $-$ retaining pose and position information related to an entity to name a few. The performance of proposed approach is illustrated by solving an elliptic stochastic partial differential equatio…
We are interested in the development of surrogate models for uncertainty quantification and propagation in problems governed by stochastic PDEs using a deep convolutional encoder-decoder network in a similar fashion to approaches considered in deep learning for image-to-image regression tasks. Since normal neural networks are data intensive and cannot provide predictive uncertainty, we propose a Bayesian approach to convolutional neural nets. A recently introduced variational gradient descent algorithm based on Stein's method is scaled to deep convolutional networks to perform approximate Baye…
University of Notre Dame（圣母大学）；Nanjing University（南京大学）
Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of dimensionality, the saturation discontinuity due to capillarity effects, and the time-dependence of the multi-output responses. In this paper, we propose a deep convolutional encoder-decoder neural network methodology to tackle these issues. The surrogate modeling task is transformed to an image-to-image regression strategy. This approach extracts high-level coarse featu…
Peng Cheng Laboratory（鹏城实验室）；Southern University of Science and Technology（南方科技大学）；Peking University（北京大学）
We build surrogate models for dynamic 3D subsurface single-phase flow problems with multiple vertical producing wells. The surrogate model provides efficient pressure estimation of the entire formation at any timestep given a stochastic permeability field, arbitrary well locations and penetration lengths, and a timestep matrix as inputs. The well production rate or bottom hole pressure can then be determined based on Peaceman's formula. The original surrogate modeling task is transformed into an image-to-image regression problem using a convolutional encoder-decoder neural network architecture…
Graz University of Technology（格拉茨工业大学）；Graz Center for Computational Engineering（格拉茨计算工程中心）；University Medicine Essen（埃森大学医学院）；Norwegian University of Science and Technology (NTNU)（挪威科技大学）
Inhomogeneities in the aortic wall can lead to localized stress accumulations, possibly initiating dissection. In many cases, a dissection results from pathological changes such as fragmentation or loss of elastic fibers. But it has been shown that even the healthy aortic wall has an inherent heterogeneous microstructure. Some parts of the aorta are particularly susceptible to the development of inhomogeneities due to pathological changes, however, the distribution in the aortic wall and the spatial extent, such as size, shape, and type, are difficult to predict. Motivated by this observation,…
Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）
Neural networks are powerful surrogates for numerous forward processes. The inversion of such surrogates is extremely valuable in science and engineering. The most important property of a successful neural inverse method is the performance of its solutions when deployed in the real world, i.e., on the native forward process (and not only the learned surrogate). We propose Autoinverse, a highly automated approach for inverting neural network surrogates. Our main insight is to seek inverse solutions in the vicinity of reliable data which have been sampled form the forward process and used for tr…
AutoSurrogate: An LLM-Driven Multi-Agent Framework for Autonomous Construction of Deep Learning Surrogate Models in Subsurface Flow
School of Physics and Astronomy, The University of Edinburgh（物理与天文学学院，爱丁堡大学）；Institute of GeoEnergy Engineering, School of Energy, Geoscience, Infrastructure and Society, Heriot-Watt University（地球能源工程研究所，能源、地质科学、基础设施与社会学院，赫瑞斯泰大学）；Subsurface Energy Transition and Innovation Centre, Heriot-Watt University（地下能源转型与创新中心，赫瑞斯泰大学）
Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；Universiteit van Amsterdam（阿姆斯特丹大学）
In this work, we explore adversarial attacks on the Variational Autoencoders (VAE). We show how to modify data point to obtain a prescribed latent code (supervised attack) or just get a drastically different code (unsupervised attack). We examine the influence of model modifications ($β$-VAE, NVAE) on the robustness of VAEs and suggest metrics to quantify it.
Compared to conventional artificial neurons that produce dense and real-valued responses, biologically-inspired spiking neurons transmit sparse and binary information, which can also lead to energy-efficient implementations. Recent research has shown that spiking neural networks can be trained like standard recurrent neural networks using the surrogate gradient method. They have shown promising results on speech command recognition tasks. Using the same technique, we show that they are scalable to large vocabulary continuous speech recognition, where they are capable of replacing LSTMs in the …
University of British Columbia（不列颠哥伦比亚大学）；BC Children’s Hospital Research Institute（不列颠哥伦比亚儿童医院研究所）；Biocomplexity Institute（生物复杂性研究所）；Indiana University（印第安纳大学）；University of Virginia（弗吉尼亚大学）
Neural networks (NNs) have proven to be a viable alternative to traditional direct numerical algorithms, with the potential to accelerate computational time by several orders of magnitude. In the present paper we study the use of encoder-decoder convolutional neural network (CNN) as surrogates for steady-state diffusion solvers. The construction of such surrogates requires the selection of an appropriate task, network architecture, training set structure and size, loss function, and training algorithm hyperparameters. It is well known that each of these factors can have a significant impact on…
University of British Columbia（不列颠哥伦比亚大学）；Inverted AI Ltd.（Inverted AI有限公司）；University of Oxford（牛津大学）；Convergent Manufacturing Technologies Inc.（Convergent制造技术公司）；Mila（米拉）
We present a framework for automatically structuring and training fast, approximate, deep neural surrogates of stochastic simulators. Unlike traditional approaches to surrogate modeling, our surrogates retain the interpretable structure and control flow of the reference simulator. Our surrogates target stochastic simulators where the number of random variables itself can be stochastic and potentially unbounded. Our framework further enables an automatic replacement of the reference simulator with the surrogate when undertaking amortized inference. The fidelity and speed of our surrogates allow…
Medical Imaging Classification with Cold-Atom Reservoir Computing using Auto-Encoders and Surrogate-Driven Training
Instituto de Telecomunicações, Dept. of Electrical and Computer Engineering, University of Coimbra, Portugal（葡萄牙科英布拉大学电信研究所，电气与计算机工程系）；ISR - Institute of Systems and Robotics, Dept. of Electrical and Computer Engineering, University of Coimbra, Portugal（葡萄牙科英布拉大学系统与机器人研究所，电气与计算机工程系）；CFisUC, Department of Physics, University of Coimbra, Portugal（葡萄牙科英布拉大学物理系，CFisUC）
Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the optimization problem as a layer in the model training pipeline results in predictions of the unobserved parameters that lead to higher decision quality. Unfortunately, this process comes at a large computational cost because the optimization problem must be solved and differentiated through in each training iteration; furthermore, it may also sometimes fail to im…
University of Technology Sydney（悉尼科技大学）；USU Software AG（USU软件股份公司）
The evaluation of machine learning (ML) pipelines is essential during automatic ML pipeline composition and optimisation. The previous methods such as Bayesian-based and genetic-based optimisation, which are implemented in Auto-Weka, Auto-sklearn and TPOT, evaluate pipelines by executing them. Therefore, the pipeline composition and optimisation of these methods requires a tremendous amount of time that prevents them from exploring complex pipelines to find better predictive models. To further explore this research challenge, we have conducted experiments showing that many of the generated pip…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Cambridge（剑桥大学）
We study the role of latent space dimensionality in Wasserstein auto-encoders (WAEs). Through experimentation on synthetic and real datasets, we argue that random encoders should be preferred over deterministic encoders. We highlight the potential of WAEs for representation learning with promising results on a benchmark disentanglement task.
What do auto-encoders learn about the underlying data generating distribution? Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of data. This paper clarifies some of these previous observations by showing that minimizing a particular form of regularized reconstruction error yields a reconstruction function that locally characterizes the shape of the data generating density. We show that the auto-encoder captures the score (derivative of the log-density with respect to the input). It contradicts previous interpretations of reconstructi…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Google Brain（谷歌大脑）
We propose the Wasserstein Auto-Encoder (WAE)---a new algorithm for building a generative model of the data distribution. WAE minimizes a penalized form of the Wasserstein distance between the model distribution and the target distribution, which leads to a different regularizer than the one used by the Variational Auto-Encoder (VAE). This regularizer encourages the encoded training distribution to match the prior. We compare our algorithm with several other techniques and show that it is a generalization of adversarial auto-encoders (AAE). Our experiments show that WAE shares many of the prop…
Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of the unknown data generating density. This paper contributes to the mathematical understanding of this phenomenon and helps define better justified sampling algorithms for deep learning based on auto-encoder variants. We consider an MCMC where each step samples from a Gaussian whose mean and covariance matrix depend on the previous state, defines through its asymptotic distribution a target density. First, we show that good choices (in the sense of consistency) for these mean and cova…
Can phenotypic activity be predicted without experimental readouts?
AI Laboratory for Molecular Engineering (AIME)（AI分子工程实验室（AIME））；Chalmers University of Technology（查尔姆斯理工大学）；University of Gothenburg（哥德堡大学）；Science for Life Laboratory (SciLifeLab)（生命科学实验室（SciLifeLab））
University of Amsterdam（阿姆斯特丹大学）；Canadian Institute for Advanced Research (CIFAR)（加拿大高级研究院）
We introduce the variational graph auto-encoder (VGAE), a framework for unsupervised learning on graph-structured data based on the variational auto-encoder (VAE). This model makes use of latent variables and is capable of learning interpretable latent representations for undirected graphs. We demonstrate this model using a graph convolutional network (GCN) encoder and a simple inner product decoder. Our model achieves competitive results on a link prediction task in citation networks. In contrast to most existing models for unsupervised learning on graph-structured data and link prediction, o…
Given a convolutional dictionary underlying a set of observed signals, can a carefully designed auto-encoder recover the dictionary in the presence of noise? We introduce an auto-encoder architecture, termed constrained recurrent sparse auto-encoder (CRsAE), that answers this question in the affirmative. Given an input signal and an approximate dictionary, the encoder finds a sparse approximation using FISTA. The decoder reconstructs the signal by applying the dictionary to the output of the encoder. The encoder and decoder in CRsAE parallel the sparse-coding and dictionary update steps in opt…
Hong Kong University of Science and Technology（香港科技大学）；Amazon（亚马逊）
The (variational) graph auto-encoder and its variants have been popularly used for representation learning on graph-structured data. While the encoder is often a powerful graph convolutional network, the decoder reconstructs the graph structure by only considering two nodes at a time, thus ignoring possible interactions among edges. On the other hand, structured prediction, which considers the whole graph simultaneously, is computationally expensive. In this paper, we utilize the well-known triadic closure property which is exhibited in many real-world networks. We propose the triad decoder, w…
Seoul National University（首尔大学）；Samsung SDS（三星SDS）；Samsung Research（三星研究院）
In this paper, we propose a novel structure for a cross-modal data association, which is inspired by the recent research on the associative learning structure of the brain. We formulate the cross-modal association in Bayesian inference framework realized by a deep neural network with multiple variational auto-encoders and variational associators. The variational associators transfer the latent spaces between auto-encoders that represent different modalities. The proposed structure successfully associates even heterogeneous modal data and easily incorporates the additional modality to the entir…
We present two instances, L-GAE and L-VGAE, of the variational graph auto-encoding family (VGAE) based on separating feature propagation operations from graph convolution layers typically found in graph learning methods to a single linear matrix computation made prior to input in standard auto-encoder architectures. This decoupling enables the independent and fixed design of the auto-encoder without requiring additional GCN layers for every desired increase in the size of a node's local receptive field. Fixing the auto-encoder enables a fairer assessment on the size of a nodes receptive field …
Peking University（北京大学）；Peng Cheng Laboratory（鹏城实验室）；The University of Illinois at Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）
The increasing amount of data in astronomy provides great challenges for machine learning research. Previously, supervised learning methods achieved satisfactory recognition accuracy for the star-galaxy classification task, based on manually labeled data set. In this work, we propose a novel unsupervised approach for the star-galaxy recognition task, namely Cascade Variational Auto-Encoder (CasVAE). Our empirical results show our method outperforms the baseline model in both accuracy and stability.
The pipeline optimization problem in machine learning requires simultaneous optimization of pipeline structures and parameter adaptation of their elements. Having an elegant way to express these structures can help lessen the complexity in the management and analysis of their performances together with the different choices of optimization strategies. With these issues in mind, we created the AutoMLPipeline (AMLP) toolkit which facilitates the creation and evaluation of complex machine learning pipeline structures using simple expressions. We use AMLP to find optimal pipeline signatures, datam…
College of Electronics and Information Engineering, Tongji University（同济大学电子与信息工程学院）
Auto-encoder is a special kind of neural network based on reconstruction. De-noising auto-encoder (DAE) is an improved auto-encoder which is robust to the input by corrupting the original data first and then reconstructing the original input by minimizing the reconstruction error function. And contractive auto-encoder (CAE) is another kind of improved auto-encoder to learn robust feature by introducing the Frobenius norm of the Jacobean matrix of the learned feature with respect to the original input. In this paper, we combine de-noising auto-encoder and contractive auto- encoder, and propose …
Pennsylvania State University（宾夕法尼亚州立大学）；Institute of Computational and Data Sciences（计算与数据科学研究所）
River bathymetry is critical for many aspects of water resources management. We propose and demonstrate a bathymetry inversion method using a deep-learning-based surrogate for shallow water equations solvers. The surrogate uses the convolutional autoencoder with a shared-encoder, separate-decoder architecture. It encodes the input bathymetry and decodes to separate outputs for flow-field variables. A gradient-based optimizer is used to perform bathymetry inversion with the trained surrogate. Two physically-based constraints on both bed elevation value and slope have to be added as inversion lo…
Auto-encoders have emerged as a successful framework for unsupervised learning. However, conventional auto-encoders are incapable of utilizing explicit relations in structured data. To take advantage of relations in graph-structured data, several graph auto-encoders have recently been proposed, but they neglect to reconstruct either the graph structure or node attributes. In this paper, we present the graph attention auto-encoder (GATE), a neural network architecture for unsupervised representation learning on graph-structured data. Our architecture is able to reconstruct graph-structured inpu…
Courant Institute of Mathematical Science（库朗数学科学研究所）；New York University（纽约大学）
We introduce a simple new regularizer for auto-encoders whose hidden-unit activation functions contain at least one zero-gradient (saturated) region. This regularizer explicitly encourages activations in the saturated region(s) of the corresponding activation function. We call these Saturating Auto-Encoders (SATAE). We show that the saturation regularizer explicitly limits the SATAE's ability to reconstruct inputs which are not near the data manifold. Furthermore, we show that a wide variety of features can be learned when different activation functions are used. Finally, connections are estab…
Cyber-Physical Systems Group, Vienna University of Technology（维也纳工业大学网络物理系统组）
This paper studies an intelligent ultimate technique for health-monitoring and prognostic of common rotary machine components, particularly bearings. During a run-to-failure experiment, rich unsupervised features from vibration sensory data are extracted by a trained sparse auto-encoder. Then, the correlation of the extracted attributes of the initial samples (presumably healthy at the beginning of the test) with the succeeding samples is calculated and passed through a moving-average filter. The normalized output is named auto-encoder correlation-based (AEC) rate which stands for an informati…
VAE-DNN: Energy-Efficient Trainable-by-Parts Surrogate Model For Parametric Partial Differential Equations
School of Water Conservancy and Transportation（水利与交通学院）；Zhengzhou University（郑州大学）；Department of Civil and Environmental Engineering（土木与环境工程系）；University of Illinois Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）
A rekindled the interest in auto-encoder algorithms has been spurred by recent work on deep learning. Current efforts have been directed towards effective training of auto-encoder architectures with a large number of coding units. Here, we propose a learning algorithm for auto-encoders based on a rate-distortion objective that minimizes the mutual information between the inputs and the outputs of the auto-encoder subject to a fidelity constraint. The goal is to learn a representation that is minimally committed to the input data, but that is rich enough to reconstruct the inputs up to certain …
Multi-view learning is a learning problem that utilizes the various representations of an object to mine valuable knowledge and improve the performance of learning algorithm, and one of the significant directions of multi-view learning is sub-space learning. As we known, auto-encoder is a method of deep learning, which can learn the latent feature of raw data by reconstructing the input, and based on this, we propose a novel algorithm called Auto-encoder based Co-training Multi-View Learning (ACMVL), which utilizes both complementarity and consistency and finds a joint latent feature represent…
We propose Information Theoretic-Learning (ITL) divergence measures for variational regularization of neural networks. We also explore ITL-regularized autoencoders as an alternative to variational autoencoding bayes, adversarial autoencoders and generative adversarial networks for randomly generating sample data without explicitly defining a partition function. This paper also formalizes, generative moment matching networks under the ITL framework.
Montreal Institute for Learning Algorithms（蒙特利尔学习算法研究所）；University of Montreal（蒙特利尔大学）；HEC Montreal（蒙特利尔高等商学院）
We discuss necessary and sufficient conditions for an auto-encoder to define a conservative vector field, in which case it is associated with an energy function akin to the unnormalized log-probability of the data. We show that the conditions for conservativeness are more general than for encoder and decoder weights to be the same ("tied weights"), and that they also depend on the form of the hidden unit activation function, but that contractive training criteria, such as denoising, will enforce these conditions locally. Based on these observations, we show how we can use auto-encoders to extr…
Huazhong University of Science & Technology（华中科技大学）；China Three Gorges University（三峡大学）；Wuhan Polytechnic University（武汉轻工大学）；Wuhan University（武汉大学）；University of Edinburgh（爱丁堡大学）
Auto-encoders are often used as building blocks of deep network classifier to learn feature extractors, but task-irrelevant information in the input data may lead to bad extractors and result in poor generalization performance of the network. In this paper,via dropping the task-irrelevant input variables the performance of auto-encoders can be obviously improved .Specifically, an importance-based variable selection method is proposed to aim at finding the task-irrelevant input variables and dropping them.It firstly estimates importance of each variable,and then drops the variables with importa…
This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element approaches involve the spatiotemporal discretization of the PDE and the solution of the corresponding linear system of equations at each time step. Instead, the proposed method utilizes a convolutional autoencoder in conjunction with a feed forward neural network to establish a low-cost and accurate mapping from the problem's parametric space to its solution space. …
Auto-encoder models that preserve similarities in the data are a popular tool in representation learning. In this paper we introduce several auto-encoder models that preserve local distances when mapping from the data space to the latent space. We use a local distance preserving loss that is based on the continuous k-nearest neighbours graph which is known to capture topological features at all scales simultaneously. To improve training performance, we formulate learning as a constraint optimisation problem with local distance preservation as the main objective and reconstruction accuracy as a…
Towards aerodynamic surrogate modeling based on $β$-variational autoencoders
Theoretical and Computational Aerodynamics Branch, Spanish National Institute for Aerospace Technology (INTA)（西班牙航空航天技术国家研究所理论与计算空气动力学分支）；Subdirectorate General of Terrestrial Systems, Spanish National Institute for Aerospace Technology (INTA)（西班牙航空航天技术国家研究所陆地系统总处）；Department of Aerospace Engineering, Universidad Carlos III de Madrid（马德里卡洛斯三世大学航空航天工程系）
Clustering is essential to many tasks in pattern recognition and computer vision. With the advent of deep learning, there is an increasing interest in learning deep unsupervised representations for clustering analysis. Many works on this domain rely on variants of auto-encoders and use the encoder outputs as representations/features for clustering. In this paper, we show that an l2 normalization constraint on these representations during auto-encoder training, makes the representations more separable and compact in the Euclidean space after training. This greatly improves the clustering accura…
Auto-encoders are perhaps the best-known non-probabilistic methods for representation learning. They are conceptually simple and easy to train. Recent theoretical work has shed light on their ability to capture manifold structure, and drawn connections to density modelling. This has motivated researchers to seek ways of auto-encoder scoring, which has furthered their use in classification. Gated auto-encoders (GAEs) are an interesting and flexible extension of auto-encoders which can learn transformations among different images or pixel covariances within images. However, they have been much l…
Harvard University（哈佛大学）；Massachusetts Institute of Technology（麻省理工学院）
State-of-the-art approaches for clustering high-dimensional data utilize deep auto-encoder architectures. Many of these networks require a large number of parameters and suffer from a lack of interpretability, due to the black-box nature of the auto-encoders. We introduce Mixture Model Auto-Encoders (MixMate), a novel architecture that clusters data by performing inference on a generative model. Derived from the perspective of sparse dictionary learning and mixture models, MixMate comprises several auto-encoders, each tasked with reconstructing data in a distinct cluster, while enforcing spars…
We discuss the similarities and differences between training an auto-encoder to minimize the reconstruction error, and training the same auto-encoder to compress the data via a generative model. Minimizing a codelength for the data using an auto-encoder is equivalent to minimizing the reconstruction error plus some correcting terms which have an interpretation as either a denoising or contractive property of the decoding function. These terms are related but not identical to those used in denoising or contractive auto-encoders [Vincent et al. 2010, Rifai et al. 2011]. In particular, the codele…
The development of a deep (stacked) convolutional auto-encoder in the Caffe deep learning framework is presented in this paper. We describe simple principles which we used to create this model in Caffe. The proposed model of convolutional auto-encoder does not have pooling/unpooling layers yet. The results of our experimental research show comparable accuracy of dimensionality reduction in comparison with a classic auto-encoder on the example of MNIST dataset.
McGill University（麦吉尔大学）；National Institute of Informatics（国立信息学研究所）
This paper proposes a deep denoising auto-encoder technique to extract better acoustic features for speech synthesis. The technique allows us to automatically extract low-dimensional features from high dimensional spectral features in a non-linear, data-driven, unsupervised way. We compared the new stochastic feature extractor with conventional mel-cepstral analysis in analysis-by-synthesis and text-to-speech experiments. Our results confirm that the proposed method increases the quality of synthetic speech in both experiments.
Université Paris Dauphine - PSL Research University（巴黎第九大学-巴黎文理研究大学）；CEREMADE（CEREMADE（巴黎第九大学应用数学研究中心））
The quality of generative models (such as Generative adversarial networks and Variational Auto-Encoders) depends heavily on the choice of a good probability distance. However some popular metrics like the Wasserstein or the Sliced Wasserstein distances, the Jensen-Shannon divergence, the Kullback-Leibler divergence, lack convenient properties such as (geodesic) convexity, fast evaluation and so on. To address these shortcomings, we introduce a class of distances that have built-in convexity. We investigate the relationship with some known paradigms (sliced distances - a synonym for Radon dista…
