We present a new data-driven model to reconstruct nonlinear flow from spatially sparse observations. The model is a version of a conditional variational auto-encoder (CVAE), which allows for probabilistic reconstruction and thus uncertainty quantification of the prediction. We show that in our model, conditioning on the measurements from the complete flow data leads to a CVAE where only the decoder depends on the measurements. For this reason we call the model as Semi-Conditional Variational Autoencoder (SCVAE). The method, reconstructions and associated uncertainty estimates are illustrated on the velocity data from simulations of 2D flow around a cylinder and bottom currents from the Bergen Ocean Model. The reconstruction errors are compared to those of the Gappy Proper Orthogonal Decomposition (GPOD) method.
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…
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…
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…
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…
Peking University（北京大学）；Southern University of Science and Technology（南方科技大学）
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 dat…
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,…
Despite numerous studies of deep autoencoders (AEs) for unsupervised anomaly detection, AEs still lack a way to express uncertainty in their predictions, crucial for ensuring safe and trustworthy machine learning systems in high-stake applications. Therefore, in this work, the formulation of Bayesian autoencoders (BAEs) is adopted to quantify the total anomaly uncertainty, comprising epistemic and aleatoric uncertainties. To evaluate the quality of uncertainty, we consider the task of classifying anomalies with the additional option of rejecting predictions of high uncertainty. In addition, we…
We propose the first Bayesian encoder for metric learning. Rather than relying on neural amortization as done in prior works, we learn a distribution over the network weights with the Laplace Approximation. We actualize this by first proving that the contrastive loss is a valid log-posterior. We then propose three methods that ensure a positive definite Hessian. Lastly, we present a novel decomposition of the Generalized Gauss-Newton approximation. Empirically, we show that our Laplacian Metric Learner (LAM) estimates well-calibrated uncertainties, reliably detects out-of-distribution examples…
IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learning
Shanghai Normal University（上海师范大学）；Shanghai Jiaotong University（上海交通大学）；Tongji University（同济大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
Deep neural network controllers for autonomous driving have recently benefited from significant performance improvements, and have begun deployment in the real world. Prior to their widespread adoption, safety guarantees are needed on the controller behaviour that properly take account of the uncertainty within the model as well as sensor noise. Bayesian neural networks, which assume a prior over the weights, have been shown capable of producing such uncertainty measures, but properties surrounding their safety have not yet been quantified for use in autonomous driving scenarios. In this paper…
University of Colorado Boulder（科罗拉多大学博尔德分校）；The Charles Stark Draper Laboratory, Inc.（查尔斯·斯塔克·德雷珀实验室公司）
For safe and reliable deployment in the real world, autonomous agents must elicit appropriate levels of trust from human users. One method to build trust is to have agents assess and communicate their own competencies for performing given tasks. Competency depends on the uncertainties affecting the agent, making accurate uncertainty quantification vital for competency assessment. In this work, we show how ensembles of deep generative models can be used to quantify the agent's aleatoric and epistemic uncertainties when forecasting task outcomes as part of competency assessment.
Argonne National Laboratory（阿贡国家实验室）；Université Paris-Saclay（巴黎萨克雷大学）
Deep neural networks are powerful predictors for a variety of tasks. However, they do not capture uncertainty directly. Using neural network ensembles to quantify uncertainty is competitive with approaches based on Bayesian neural networks while benefiting from better computational scalability. However, building ensembles of neural networks is a challenging task because, in addition to choosing the right neural architecture or hyperparameters for each member of the ensemble, there is an added cost of training each model. We propose AutoDEUQ, an automated approach for generating an ensemble of …
A new data-driven method for operator learning of stochastic differential equations(SDE) is proposed in this paper. The central goal is to solve forward and inverse stochastic problems more effectively using limited data. Deep operator network(DeepONet) has been proposed recently for operator learning. Compared to other neural networks to learn functions, it aims at the problem of learning nonlinear operators. However, it can be challenging by using the original model to learn nonlinear operators for high-dimensional stochastic problems. We propose a new multi-resolution autoencoder DeepONet m…
A key factor for ensuring safety in Autonomous Vehicles (AVs) is to avoid any abnormal behaviors under undesirable and unpredicted circumstances. As AVs increasingly rely on Deep Neural Networks (DNNs) to perform safety-critical tasks, different methods for uncertainty quantification have recently been proposed to measure the inevitable source of errors in data and models. However, uncertainty quantification in DNNs is still a challenging task. These methods require a higher computational load, a higher memory footprint, and introduce extra latency, which can be prohibitive in safety-critical …
A rise in popularity of Deep Neural Networks (DNNs), attributed to more powerful GPUs and widely available datasets, has seen them being increasingly used within safety-critical domains. One such domain, self-driving, has benefited from significant performance improvements, with millions of miles having been driven with no human intervention. Despite this, crashes and erroneous behaviours still occur, in part due to the complexity of verifying the correctness of DNNs and a lack of safety guarantees. In this paper, we demonstrate how quantitative measures of uncertainty can be extracted in real…
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.
Universitat Politècnica de Catalunya – BarcelonaTech（加泰罗尼亚理工大学）；SEAT（西雅特公司）
Uncertainty Quantification (UQ) is a key discipline for computational modeling of complex systems, enhancing reliability of engineering simulations. In crashworthiness, having an accurate assessment of the behavior of the model uncertainty allows reducing the number of prototypes and associated costs. Carrying out UQ in this framework is especially challenging because it requires highly expensive simulations. In this context, surrogate models (metamodels) allow drastically reducing the computational cost of Monte Carlo process. Different techniques to describe the metamodel are considered, Ord…
Deep learning has emerged as a technique of choice for rapid feature extraction across imaging disciplines, allowing rapid conversion of the data streams to spatial or spatiotemporal arrays of features of interest. However, applications of deep learning in experimental domains are often limited by the out-of-distribution drift between the experiments, where the network trained for one set of imaging conditions becomes sub-optimal for different ones. This limitation is particularly stringent in the quest to have an automated experiment setting, where retraining or transfer learning becomes impr…
University of Notre Dame（圣母大学）；Technical University of Munich（慕尼黑工业大学）；University of Pennsylvania（宾夕法尼亚大学）
Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training. The construction of such emulators is by definition a small data problem which poses challenges to deep learning approaches that have been developed to operate in the big data regime. Even in cases where such models have been shown to have good predictive capability in high dimensions, they fail to address constraints in the data implied by the PDE model. This paper provides a methodology that incorporates the…
Interpretable Time Series Autoregression for Periodicity Quantification
Department of Urban Studies and Planning, Massachusetts Institute of Technology（城市研究与规划系，麻省理工学院）；Questrom School of Business, Boston University（questrom商学院，波士顿大学）；Department of Mathematics at the University of California, San Diego（加州大学圣地亚哥分校数学系）
Machine learning models are vulnerable to adversarial examples. Iterative adversarial training has shown promising results against strong white-box attacks. However, adversarial training is very expensive, and every time a model needs to be protected, such expensive training scheme needs to be performed. In this paper, we propose to apply iterative adversarial training scheme to an external auto-encoder, which once trained can be used to protect other models directly. We empirically show that our model outperforms other purifying-based methods against white-box attacks, and transfers well to d…
Autonomous Uncertainty Quantification for Computational Point-of-care Sensors
Electrical & Computer Engineering Department（电气与计算机工程系）；Bioengineering Department（生物工程系）；California NanoSystems Institute (CNSI)（加州纳米系统研究所）；Department of Surgery（外科医学系）；University of California, Los Angeles（加州大学洛杉矶分校）
Risk-aware Classification via Uncertainty Quantification
Amazon Alexa AI（亚马逊Alexa人工智能）；DEVCOM Army Research Laboratory（DEVCOM陆军研究实验室）；University College London（伦敦大学学院）；Fordham University（福特汉姆大学）；University of Brescia（布雷西亚大学）；Cardiff University（卡迪夫大学）
Queen Mary University of London（伦敦玛丽女王大学）；Alan Turing Institute（艾伦·图灵研究所）；Aarhus University（奥胡斯大学）；University of Bristol（布里斯托大学）；University of Lübeck（吕贝克大学）；German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心（DFKI））；KU Leuven（鲁汶大学）
Background: Black-box skepticism is one of the main hindrances impeding deep-learning-based automatic sleep scoring from being used in clinical environments. Methods: Towards interpretability, this work proposes a sequence-to-sequence sleep-staging model, namely SleepTransformer. It is based on the transformer backbone and offers interpretability of the model's decisions at both the epoch and sequence level. We further propose a simple yet efficient method to quantify uncertainty in the model's decisions. The method, which is based on entropy, can serve as a metric for deferring low-confidence…
Automated HER2 scoring with uncertainty quantification using lensfree holography and deep learning
Electrical and Computer Engineering Department, University of California, Los Angeles, CA, 90095, USA（加州大学洛杉矶分校电气与计算机工程系）；Bioengineering Department, University of California, Los Angeles, CA, 90095, USA（加州大学洛杉矶分校生物工程系）；California NanoSystems Institute (CNSI), University of California, Los Angeles, CA, 90095, USA（加州大学洛杉矶分校加州纳米系统研究所）；Department of Computer Science, University of California, Los Angeles, CA, 90095, USA（加州大学洛杉矶分校计算机科学系）
In inverse problems, uncertainty quantification (UQ) deals with a probabilistic description of the solution nonuniqueness and data noise sensitivity. Setting seismic imaging into a Bayesian framework allows for a principled way of studying uncertainty by solving for the model posterior distribution. Imaging, however, typically constitutes only the first stage of a sequential workflow, and UQ becomes even more relevant when applied to subsequent tasks that are highly sensitive to the inversion outcome. In this paper, we focus on how UQ trickles down to horizon tracking for the determination of …
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…
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.
Duke University（杜克大学）；University of Minnesota（明尼苏达大学）
It has been conjectured that the Fisher divergence is more robust to model uncertainty than the conventional Kullback-Leibler (KL) divergence. This motivates the design of a new class of robust generative auto-encoders (AE) referred to as Fisher auto-encoders. Our approach is to design Fisher AEs by minimizing the Fisher divergence between the intractable joint distribution of observed data and latent variables, with that of the postulated/modeled joint distribution. In contrast to KL-based variational AEs (VAEs), the Fisher AE can exactly quantify the distance between the true and the model-b…
We propose a new structure for the variational auto-encoders (VAEs) prior, with the weakly informative multivariate Student's t-distribution. In the proposed model all distribution parameters are trained, thereby allowing for a more robust approximation of the underlying data distribution. We used Fashion-MNIST data in two experiments to compare the proposed VAEs with the standard Gaussian priors. Both experiments showed a better reconstruction of the images with VAEs using Student's t-prior distribution.
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…
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…
In this paper we propose a model that combines the strengths of RNNs and SGVB: the Variational Recurrent Auto-Encoder (VRAE). Such a model can be used for efficient, large scale unsupervised learning on time series data, mapping the time series data to a latent vector representation. The model is generative, such that data can be generated from samples of the latent space. An important contribution of this work is that the model can make use of unlabeled data in order to facilitate supervised training of RNNs by initialising the weights and network state.
Non-adversarial generative models such as variational auto-encoder (VAE), Wasserstein auto-encoders with maximum mean discrepancy (WAE-MMD), sliced-Wasserstein auto-encoder (SWAE) are relatively easy to train and have less mode collapse compared to Wasserstein auto-encoder with generative adversarial network (WAE-GAN). However, they are not very accurate in approximating the target distribution in the latent space because they don't have a discriminator to detect the minor difference between real and fake. To this end, we develop a novel non-adversarial framework called Tessellated Wasserstein…
Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, compressed sensing and sparse coding assume a data generating process, where the observed data is generated from some true latent signal source, and try to recover the corresponding signal from measurements. Looking at auto-encoders from this \textit{signal recovery perspective} enables us to have a more coherent view of these techniques. In this paper, in particular, we show …
Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the interpretability of the features. We study the problem of constructing optimal sparse linear auto-encoders. Two natural questions in such a setting are: i) Given a level of sparsity, what is the best approximation to PCA that can be achieved? ii) Are there low-order polynomial-time algorithms which can asymptotically achieve this optimal tradeoff between the sparsity and …
In this paper, we propose a new volume-preserving flow and show that it performs similarly to the linear general normalizing flow. The idea is to enrich a linear Inverse Autoregressive Flow by introducing multiple lower-triangular matrices with ones on the diagonal and combining them using a convex combination. In the experimental studies on MNIST and Histopathology data we show that the proposed approach outperforms other volume-preserving flows and is competitive with current state-of-the-art linear normalizing flow.
