The coupling of deep reinforcement learning to numerical flow control problems has recently received a considerable attention, leading to groundbreaking results and opening new perspectives for the domain. Due to the usually high computational cost of fluid dynamics solvers, the use of parallel environments during the learning process represents an essential ingredient to attain efficient control in a reasonable time. Yet, most of the deep reinforcement learning literature for flow control relies on on-policy algorithms, for which the massively parallel transition collection may break theoretical assumptions and lead to suboptimal control models. To overcome this issue, we propose a parallelism pattern relying on partial-trajectory buffers terminated by a return bootstrapping step, allowing a flexible use of parallel environments while preserving the on-policiness of the updates. This approach is illustrated on a CPU-intensive continuous flow control problem from the literature.
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Deep learning (DL) enables the development of computer models that are capable of learning, visualizing, optimizing, refining, and predicting data. In recent years, DL has been applied in a range of fields, including audio-visual data processing, agriculture, transportation prediction, natural language, biomedicine, disaster management, bioinformatics, drug design, genomics, face recognition, and ecology. To explore the current state of deep learning, it is necessary to investigate the latest developments and applications of deep learning in these disciplines. However, the literature is lacking in exploring the applications of deep learning in all potential sectors. This paper thus extensively investigates the potential applications of deep learning across all major fields of study as well as the associated benefits and challenges. As evidenced in the literature, DL exhibits accuracy in prediction and analysis, makes it a powerful computational tool, and has the ability to articulate itself and optimize, making it effective in processing data with no prior training. Given its independence from training data, deep learning necessitates massive amounts of data for effective analysis and processing, much like data volume. To handle the challenge of compiling huge amounts of medical, scientific, healthcare, and environmental data for use in deep learning, gated architectures like LSTMs and GRUs can be utilized. For multimodal learning, shared neurons in the neural network for all activities and specialized neurons for particular tasks are necessary.
Multiscale constitutive framework of 1D blood flow modeling: Asymptotic limits and numerical methods
In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is presented and discussed. By analyzing the asymptotic limits of the proposed model, it is shown that different types of blood propagation phenomena in arteries and veins can be described through an appropriate choice of scaling parameters, which are related to distinct characterizations of the fluid-structure interaction mechanism (whether elastic or viscoelastic) that exist between vessel walls and blood flow. In these asymptotic limits, well-known blood flow models from the literature are recovered. Additionally, by analyzing the perturbation of the local elastic equilibrium of the system, a new viscoelastic blood flow model is derived. The proposed approach is highly flexible and suitable for studying the human cardiovascular system, which is composed of vessels with high morphological and mechanical variability. The resulting multiscale hyperbolic model of blood flow is solved using an asymptotic-preserving Implicit-Explicit Runge-Kutta Finite Volume method, which ensures the consistency of the numerical scheme with the different asymptotic limits of the mathematical model without affecting the choice of the time step by restrictions related to the smallness of the scaling parameters. Several numerical tests confirm the validity of the proposed methodology, including a case study investigating the hemodynamics of a thoracic aorta in the presence of a stent.
There is growing interest in Bayesian clinical trial designs with informative prior distributions, e.g. for extrapolation of adult data to pediatrics, or use of external controls. While the classical type I error is commonly used to evaluate such designs, it cannot be strictly controlled and it is acknowledged that other metrics may be more appropriate. We focus on two common situations - borrowing control data or information on the treatment contrast - and discuss several fully probabilistic metrics to evaluate the risk of false positive conclusions. Each metric requires specification of a design prior, which can differ from the analysis prior and permits understanding of the behaviour of a Bayesian design under scenarios where the analysis prior differs from the true data generation process. The metrics include the average type I error and the pre-posterior probability of a false positive result. We show that, when borrowing control data, the average type I error is asymptotically (in certain cases strictly) controlled when the analysis and design prior coincide. We illustrate use of these Bayesian metrics with real applications, and discuss how they could facilitate discussions between sponsors, regulators and other stakeholders about the appropriateness of Bayesian borrowing designs for pivotal studies.
Within the applications of spatial point processes, it is increasingly becoming common that events are labeled by marks, prompting an exploration beyond the spatial distribution of events by incorporating the marks in the undertaken analysis. In this paper, we first consider marked spatial point processes in $\R^2$, where marks are either integer-valued, real-valued, or object-valued, and review the state-of-the-art to analyze the spatial structure and type of interaction/correlation between marks. More specifically, we review cross/dot-type summary characteristics, mark-weighted summary characteristics, various mark correlation functions, and frequency domain approaches. Second, we propose novel cross/dot-type higher-order summary characteristics, mark-weighted summary characteristics, and mark correlation functions for marked point processes on linear networks. Through a simulation study, we show that ignoring the underlying network gives rise to erroneous conclusions about the interaction/correlation between marks. Finally, we consider two applications: the locations of two types of butterflies in Melbourne, Australia, and the locations of public trees along the street network of Vancouver, Canada, where trees are labeled by their diameters at breast height.
In this paper, efficient alternating direction implicit (ADI) schemes are proposed to solve three-dimensional heat equations with irregular boundaries and interfaces. Starting from the well-known Douglas-Gunn ADI scheme, a modified ADI scheme is constructed to mitigate the issue of accuracy loss in solving problems with time-dependent boundary conditions. The unconditional stability of the new ADI scheme is also rigorously proven with the Fourier analysis. Then, by combining the ADI schemes with a 1D kernel-free boundary integral (KFBI) method, KFBI-ADI schemes are developed to solve the heat equation with irregular boundaries. In 1D sub-problems of the KFBI-ADI schemes, the KFBI discretization takes advantage of the Cartesian grid and preserves the structure of the coefficient matrix so that the fast Thomas algorithm can be applied to solve the linear system efficiently. Second-order accuracy and unconditional stability of the KFBI-ADI schemes are verified through several numerical tests for both the heat equation and a reaction-diffusion equation. For the Stefan problem, which is a free boundary problem of the heat equation, a level set method is incorporated into the ADI method to capture the time-dependent interface. Numerical examples for simulating 3D dendritic solidification phenomenons are also presented.
In unsupervised scenarios, deep contrastive multi-view clustering (DCMVC) is becoming a hot research spot, which aims to mine the potential relationships between different views. Most existing DCMVC algorithms focus on exploring the consistency information for the deep semantic features, while ignoring the diverse information on shallow features. To fill this gap, we propose a novel multi-view clustering network termed CodingNet to explore the diverse and consistent information simultaneously in this paper. Specifically, instead of utilizing the conventional auto-encoder, we design an asymmetric structure network to extract shallow and deep features separately. Then, by aligning the similarity matrix on the shallow feature to the zero matrix, we ensure the diversity for the shallow features, thus offering a better description of multi-view data. Moreover, we propose a dual contrastive mechanism that maintains consistency for deep features at both view-feature and pseudo-label levels. Our framework's efficacy is validated through extensive experiments on six widely used benchmark datasets, outperforming most state-of-the-art multi-view clustering algorithms.
Devising deep latent variable models for multi-modal data has been a long-standing theme in machine learning research. Multi-modal Variational Autoencoders (VAEs) have been a popular generative model class that learns latent representations which jointly explain multiple modalities. Various objective functions for such models have been suggested, often motivated as lower bounds on the multi-modal data log-likelihood or from information-theoretic considerations. In order to encode latent variables from different modality subsets, Product-of-Experts (PoE) or Mixture-of-Experts (MoE) aggregation schemes have been routinely used and shown to yield different trade-offs, for instance, regarding their generative quality or consistency across multiple modalities. In this work, we consider a variational bound that can tightly lower bound the data log-likelihood. We develop more flexible aggregation schemes that generalise PoE or MoE approaches by combining encoded features from different modalities based on permutation-invariant neural networks. Our numerical experiments illustrate trade-offs for multi-modal variational bounds and various aggregation schemes. We show that tighter variational bounds and more flexible aggregation models can become beneficial when one wants to approximate the true joint distribution over observed modalities and latent variables in identifiable models.
Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the temporal dependence structure of Hawkes processes is generally a computationally expensive task, all the more with Bayesian estimation methods. In particular, for generalised nonlinear Hawkes processes, Monte-Carlo Markov Chain methods applied to compute the doubly intractable posterior distribution are not scalable to high-dimensional processes in practice. Recently, efficient algorithms targeting a mean-field variational approximation of the posterior distribution have been proposed. In this work, we first unify existing variational Bayes approaches under a general nonparametric inference framework, and analyse the asymptotic properties of these methods under easily verifiable conditions on the prior, the variational class, and the nonlinear model. Secondly, we propose a novel sparsity-inducing procedure, and derive an adaptive mean-field variational algorithm for the popular sigmoid Hawkes processes. Our algorithm is parallelisable and therefore computationally efficient in high-dimensional setting. Through an extensive set of numerical simulations, we also demonstrate that our procedure is able to adapt to the dimensionality of the parameter of the Hawkes process, and is partially robust to some type of model mis-specification.
We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.
Machine-learning models have demonstrated great success in learning complex patterns that enable them to make predictions about unobserved data. In addition to using models for prediction, the ability to interpret what a model has learned is receiving an increasing amount of attention. However, this increased focus has led to considerable confusion about the notion of interpretability. In particular, it is unclear how the wide array of proposed interpretation methods are related, and what common concepts can be used to evaluate them. We aim to address these concerns by defining interpretability in the context of machine learning and introducing the Predictive, Descriptive, Relevant (PDR) framework for discussing interpretations. The PDR framework provides three overarching desiderata for evaluation: predictive accuracy, descriptive accuracy and relevancy, with relevancy judged relative to a human audience. Moreover, to help manage the deluge of interpretation methods, we introduce a categorization of existing techniques into model-based and post-hoc categories, with sub-groups including sparsity, modularity and simulatability. To demonstrate how practitioners can use the PDR framework to evaluate and understand interpretations, we provide numerous real-world examples. These examples highlight the often under-appreciated role played by human audiences in discussions of interpretability. Finally, based on our framework, we discuss limitations of existing methods and directions for future work. We hope that this work will provide a common vocabulary that will make it easier for both practitioners and researchers to discuss and choose from the full range of interpretation methods.
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