A filtered density function (FDF) model based on deep neural network (DNN), termed DNN-FDF, is introduced for large eddy simulation (LES) of turbulent flows involving conserved scalar transport. The primary objectives of this study are to develop the DNN-FDF models and evaluate their predictive capability in accounting for various filtered moments, including that of non-linear source terms. A systematic approach is proposed to select DNN training sample size and architecture via learning curves to minimize bias and variance. Two DNN-FDF models are developed, one utilizing FDF data from Direct Numerical Simulations (DNS) of constant-density temporal mixing layer, and the other from zero-dimensional pairwise mixing stirred reactor simulations. The latter is particularly intended for cases where generating DNS data is computationally infeasible. DNN-FDF models are applied for LES of a variable-density temporal mixing layer. The accuracy and consistency of both DNN-FDF models are established by comparing their predicted filtered scalar moments with those of conventional LES, where moment transport equations are directly solved. The DNN-FDF models are shown to outperform a widely used presumed-FDF model, especially for multi-modal FDFs and higher variance values. Results are further assessed against DNS and the transported FDF method. The latter couples LES with Monte Carlo for mixture fraction FDF computation. Most importantly, the study shows that DNN-FDF models can accurately filter highly non-linear functions within variable-density flows, highlighting their potential for turbulent reacting flow simulations. Overall, the DNN-FDF approach is shown to offer an accurate yet computationally economical approach for describing turbulent scalar transport.
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By composing graphical models with deep learning architectures, we learn generative models with the strengths of both frameworks. The structured variational autoencoder (SVAE) inherits structure and interpretability from graphical models, and flexible likelihoods for high-dimensional data from deep learning, but poses substantial optimization challenges. We propose novel algorithms for learning SVAEs, and are the first to demonstrate the SVAE's ability to handle multimodal uncertainty when data is missing by incorporating discrete latent variables. Our memory-efficient implicit differentiation scheme makes the SVAE tractable to learn via gradient descent, while demonstrating robustness to incomplete optimization. To more rapidly learn accurate graphical model parameters, we derive a method for computing natural gradients without manual derivations, which avoids biases found in prior work. These optimization innovations enable the first comparisons of the SVAE to state-of-the-art time series models, where the SVAE performs competitively while learning interpretable and structured discrete data representations.
Geospatial Tessellation in the Agent-In-Cell Model: A Framework for Agent-Based Modeling of Pandemic
Agent-based simulation, a powerful tool for analyzing complex systems, faces challenges when integrating geographic elements due to increased computational demands. This study introduces a series of 'agent-in-the-cell' Agent-Based Models to simulate COVID spread in a city, utilizing geographical features and real-world mobility data from Safegraph. We depart from traditional aggregated transmission probabilities, focusing on direct person-to-person contact probabilities, informed by physics-based transmission studies. Our approach addresses computational complexities through innovative strategies. Agents, termed 'meta-agents', are linked to specific home cells in a city's tessellation. We explore various tessellations and agent densities, finding that Voronoi Diagram tessellations, based on specific street network locations, outperform Census Block Group tessellations in preserving dynamics. Additionally, a hybrid tessellation combining Voronoi Diagrams and Census Block Groups proves effective with fewer meta-agents, maintaining an accurate representation of city dynamics. Our analysis covers diverse city sizes in the U.S., offering insights into agent count reduction effects, sensitivity metrics, and city-specific factors. We benchmark our model against an existing ABM, focusing on runtime and reduced agent count implications. Key optimizations include meta-agent usage, advanced tessellation methods, and parallelization techniques. This study's findings contribute to the field of agent-based modeling, especially in scenarios requiring geographic specificity and high computational efficiency.
A mixture of multivariate Poisson-log normal factor analyzers is introduced by imposing constraints on the covariance matrix, which resulted in flexible models for clustering purposes. In particular, a class of eight parsimonious mixture models based on the mixtures of factor analyzers model are introduced. Variational Gaussian approximation is used for parameter estimation, and information criteria are used for model selection. The proposed models are explored in the context of clustering discrete data arising from RNA sequencing studies. Using real and simulated data, the models are shown to give favourable clustering performance. The GitHub R package for this work is available at //github.com/anjalisilva/mixMPLNFA and is released under the open-source MIT license.
This paper considers the secure aggregation problem for federated learning under an information theoretic cryptographic formulation, where distributed training nodes (referred to as users) train models based on their own local data and a curious-but-honest server aggregates the trained models without retrieving other information about users' local data. Secure aggregation generally contains two phases, namely key sharing phase and model aggregation phase. Due to the common effect of user dropouts in federated learning, the model aggregation phase should contain two rounds, where in the first round the users transmit masked models and, in the second round, according to the identity of surviving users after the first round, these surviving users transmit some further messages to help the server decrypt the sum of users' trained models. The objective of the considered information theoretic formulation is to characterize the capacity region of the communication rates in the two rounds from the users to the server in the model aggregation phase, assuming that key sharing has already been performed offline in prior. In this context, Zhao and Sun completely characterized the capacity region under the assumption that the keys can be arbitrary random variables. More recently, an additional constraint, known as "uncoded groupwise keys," has been introduced. This constraint entails the presence of multiple independent keys within the system, with each key being shared by precisely S users. The capacity region for the information-theoretic secure aggregation problem with uncoded groupwise keys was established in our recent work subject to the condition S > K - U, where K is the number of total users and U is the designed minimum number of surviving users. In this paper we fully characterize of the the capacity region for this problem by proposing a new converse bound and an achievable scheme.
Axiomatization and expressibility problems for Milner's process semantics (1984) of regular expressions modulo bisimilarity have turned out to be difficult for the full class of expressions with deadlock 0 and empty step~1. We report on a phenomenon that arises from the added presence of 1 when 0 is available, and that brings a crucial reason for this difficulty into focus. To wit, while interpretations of 1-free regular expressions are closed under bisimulation collapse, this is not the case for the interpretations of arbitrary regular expressions. Process graph interpretations of 1-free regular expressions satisfy the loop existence and elimination property LEE, which is preserved under bisimulation collapse. These features of LEE were applied for showing that an equational proof system for 1-free regular expressions modulo bisimilarity is complete, and that it is decidable in polynomial time whether a process graph is bisimilar to the interpretation of a 1-free regular expression. While interpretations of regular expressions do not satisfy the property LEE in general, we show that LEE can be recovered by refined interpretations as graphs with 1-transitions refined interpretations with 1-transitions (which are similar to silent steps for automata). This suggests that LEE can be expedient also for the general axiomatization and expressibility problems. But a new phenomenon emerges that needs to be addressed: the property of a process graph `to can be refined into a process graph with 1-transitions and with LEE' is not preserved under bisimulation collapse. We provide a 10-vertex graph with two 1-transitions that satisfies LEE, and in which a pair of bisimilar vertices cannot be collapsed on to each other while preserving the refinement property. This implies that the image of the process interpretation of regular expressions is not closed under bisimulation collapse.
The current body of research on terahertz (THz) wireless communications predominantly focuses on its application for single-user backhaul/fronthaul connectivity at sub-THz frequencies. First, we develop a generalized statistical model for signal propagation at THz frequencies encompassing physical layer impairments, including random path-loss with Gamma distribution for the molecular absorption coefficient, short-term fading characterized by the $\alpha$-$\eta$-$\kappa$-$\mu$ distribution, antenna misalignment errors, and transceiver hardware impairments. Next, we propose random access protocols for a cell-free wireless network, ensuring successful transmission for multiple users with limited delay and energy loss, exploiting the combined effect of random atmospheric absorption, non-linearity of fading, hardware impairments, and antenna misalignment errors. We consider two schemes: a fixed transmission probability (FTP) scheme where the transmission probability (TP) of each user is updated at the beginning of the data transmission and an adaptive transmission probability (ATP) scheme where the TP is updated with each successful reception of the data. We analyze the performance of both protocols using delay, energy consumption, and outage probability with scaling laws for the transmission of a data frame consisting of a single packet from users at a predefined quality of service (QoS).
We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with non-linear serial dependence through the introduction of appropriate latent variables. Alternatively, our models can be viewed as Bayesian hierarchical models with conditionally independent Poisson distributed observations. Inference about the important lags and their complex interactions is achieved via MCMC. When the observed counts are large, we deal with the resulting computational complexity of Bayesian inference via a two-step inferential strategy based on an initial analysis of a training set of the data. Our methodology is illustrated using simulation experiments and analysis of real-world data.
Fast inverse kinematics (IK) is a central component in robotic motion planning. For complex robots, IK methods are often based on root search and non-linear optimization algorithms. These algorithms can be massively sped up using a neural network to predict a good initial guess, which can then be refined in a few numerical iterations. Besides previous work on learning-based IK, we present a learning approach for the fundamentally more complex problem of IK with collision avoidance. We do this in diverse and previously unseen environments. From a detailed analysis of the IK learning problem, we derive a network and unsupervised learning architecture that removes the need for a sample data generation step. Using the trained network's prediction as an initial guess for a two-stage Jacobian-based solver allows for fast and accurate computation of the collision-free IK. For the humanoid robot, Agile Justin (19 DoF), the collision-free IK is solved in less than 10 milliseconds (on a single CPU core) and with an accuracy of 10^-4 m and 10^-3 rad based on a high-resolution world model generated from the robot's integrated 3D sensor. Our method massively outperforms a random multi-start baseline in a benchmark with the 19 DoF humanoid and challenging 3D environments. It requires ten times less training time than a supervised training method while achieving comparable results.
Object detection is a fundamental task in computer vision and image processing. Current deep learning based object detectors have been highly successful with abundant labeled data. But in real life, it is not guaranteed that each object category has enough labeled samples for training. These large object detectors are easy to overfit when the training data is limited. Therefore, it is necessary to introduce few-shot learning and zero-shot learning into object detection, which can be named low-shot object detection together. Low-Shot Object Detection (LSOD) aims to detect objects from a few or even zero labeled data, which can be categorized into few-shot object detection (FSOD) and zero-shot object detection (ZSD), respectively. This paper conducts a comprehensive survey for deep learning based FSOD and ZSD. First, this survey classifies methods for FSOD and ZSD into different categories and discusses the pros and cons of them. Second, this survey reviews dataset settings and evaluation metrics for FSOD and ZSD, then analyzes the performance of different methods on these benchmarks. Finally, this survey discusses future challenges and promising directions for FSOD and ZSD.
Neural machine translation (NMT) is a deep learning based approach for machine translation, which yields the state-of-the-art translation performance in scenarios where large-scale parallel corpora are available. Although the high-quality and domain-specific translation is crucial in the real world, domain-specific corpora are usually scarce or nonexistent, and thus vanilla NMT performs poorly in such scenarios. Domain adaptation that leverages both out-of-domain parallel corpora as well as monolingual corpora for in-domain translation, is very important for domain-specific translation. In this paper, we give a comprehensive survey of the state-of-the-art domain adaptation techniques for NMT.
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